1,1,55,0,0.221238," ","integrate(1/(-9*b*x+9*x^3+2*b^(3/2)*3^(1/2)),x, algorithm=""giac"")","\frac{\log\left({\left| 9 \, \sqrt{3} x + 18 \, \sqrt{b} \right|}\right)}{27 \, b} - \frac{\log\left({\left| -\sqrt{3} x + \sqrt{b} \right|}\right)}{27 \, b} - \frac{1}{9 \, {\left(\sqrt{3} x - \sqrt{b}\right)} \sqrt{b}}"," ",0,"1/27*log(abs(9*sqrt(3)*x + 18*sqrt(b)))/b - 1/27*log(abs(-sqrt(3)*x + sqrt(b)))/b - 1/9/((sqrt(3)*x - sqrt(b))*sqrt(b))","A",0
2,1,73,0,0.195747," ","integrate((b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^p,x, algorithm=""giac"")","\frac{{\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)}^{p} b x + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)}^{p} a}{3 \, b p + b}"," ",0,"((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)^p*b*x + (b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)^p*a)/(3*b*p + b)","B",0
3,1,97,0,0.254052," ","integrate((b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{9} x^{10} + a b^{8} x^{9} + \frac{9}{2} \, a^{2} b^{7} x^{8} + 12 \, a^{3} b^{6} x^{7} + 21 \, a^{4} b^{5} x^{6} + \frac{126}{5} \, a^{5} b^{4} x^{5} + 21 \, a^{6} b^{3} x^{4} + 12 \, a^{7} b^{2} x^{3} + \frac{9}{2} \, a^{8} b x^{2} + a^{9} x"," ",0,"1/10*b^9*x^10 + a*b^8*x^9 + 9/2*a^2*b^7*x^8 + 12*a^3*b^6*x^7 + 21*a^4*b^5*x^6 + 126/5*a^5*b^4*x^5 + 21*a^6*b^3*x^4 + 12*a^7*b^2*x^3 + 9/2*a^8*b*x^2 + a^9*x","B",0
4,1,64,0,0.374660," ","integrate((b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x"," ",0,"1/7*b^6*x^7 + a*b^5*x^6 + 3*a^2*b^4*x^5 + 5*a^3*b^3*x^4 + 5*a^4*b^2*x^3 + 3*a^5*b*x^2 + a^6*x","B",0
5,1,31,0,0.282546," ","integrate(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x"," ",0,"1/4*b^3*x^4 + a*b^2*x^3 + 3/2*a^2*b*x^2 + a^3*x","A",0
6,1,12,0,0.264311," ","integrate(1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3),x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b x + a\right)}^{2} b}"," ",0,"-1/2/((b*x + a)^2*b)","A",0
7,1,12,0,0.294991," ","integrate(1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^2,x, algorithm=""giac"")","-\frac{1}{5 \, {\left(b x + a\right)}^{5} b}"," ",0,"-1/5/((b*x + a)^5*b)","A",0
8,1,12,0,0.391583," ","integrate(1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^3,x, algorithm=""giac"")","-\frac{1}{8 \, {\left(b x + a\right)}^{8} b}"," ",0,"-1/8/((b*x + a)^8*b)","A",0
9,1,166,0,0.273050," ","integrate((c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{6} x^{10} + b c^{5} x^{9} + \frac{9}{2} \, b^{2} c^{4} x^{8} + \frac{81}{7} \, b^{3} c^{3} x^{7} + \frac{9}{7} \, a b c^{4} x^{7} + 18 \, b^{4} c^{2} x^{6} + 9 \, a b^{2} c^{3} x^{6} + \frac{81}{5} \, b^{5} c x^{5} + 27 \, a b^{3} c^{2} x^{5} + \frac{27}{4} \, b^{6} x^{4} + \frac{81}{2} \, a b^{4} c x^{4} + \frac{27}{4} \, a^{2} b^{2} c^{2} x^{4} + 27 \, a b^{5} x^{3} + 27 \, a^{2} b^{3} c x^{3} + \frac{81}{2} \, a^{2} b^{4} x^{2} + 27 \, a^{3} b^{3} x"," ",0,"1/10*c^6*x^10 + b*c^5*x^9 + 9/2*b^2*c^4*x^8 + 81/7*b^3*c^3*x^7 + 9/7*a*b*c^4*x^7 + 18*b^4*c^2*x^6 + 9*a*b^2*c^3*x^6 + 81/5*b^5*c*x^5 + 27*a*b^3*c^2*x^5 + 27/4*b^6*x^4 + 81/2*a*b^4*c*x^4 + 27/4*a^2*b^2*c^2*x^4 + 27*a*b^5*x^3 + 27*a^2*b^3*c*x^3 + 81/2*a^2*b^4*x^2 + 27*a^3*b^3*x","B",0
10,1,83,0,0.343762," ","integrate((c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{4} x^{7} + b c^{3} x^{6} + 3 \, b^{2} c^{2} x^{5} + \frac{9}{2} \, b^{3} c x^{4} + \frac{3}{2} \, a b c^{2} x^{4} + 3 \, b^{4} x^{3} + 6 \, a b^{2} c x^{3} + 9 \, a b^{3} x^{2} + 9 \, a^{2} b^{2} x"," ",0,"1/7*c^4*x^7 + b*c^3*x^6 + 3*b^2*c^2*x^5 + 9/2*b^3*c*x^4 + 3/2*a*b*c^2*x^4 + 3*b^4*x^3 + 6*a*b^2*c*x^3 + 9*a*b^3*x^2 + 9*a^2*b^2*x","A",0
11,1,28,0,0.269665," ","integrate(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b,x, algorithm=""giac"")","\frac{1}{4} \, c^{2} x^{4} + b c x^{3} + \frac{3}{2} \, b^{2} x^{2} + 3 \, a b x"," ",0,"1/4*c^2*x^4 + b*c*x^3 + 3/2*b^2*x^2 + 3*a*b*x","A",0
12,1,212,0,0.357543," ","integrate(1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}{c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}\right)}{3 \, {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}\right)}^{\frac{1}{3}}} - \frac{\log\left(4 \, {\left(\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2}\right)}{6 \, {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}\right)}^{\frac{1}{3}}} + \frac{\log\left({\left| c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}} \right|}\right)}{3 \, {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}\right)}^{\frac{1}{3}}}"," ",0,"1/3*sqrt(3)*arctan((sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))/(c*x + b + (-b^3 + 3*a*b*c)^(1/3)))/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2)^(1/3) - 1/6*log(4*(sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))^2 + 4*(c*x + b + (-b^3 + 3*a*b*c)^(1/3))^2)/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2)^(1/3) + 1/3*log(abs(c*x + b + (-b^3 + 3*a*b*c)^(1/3)))/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2)^(1/3)","A",0
13,1,289,0,0.356991," ","integrate(1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(\frac{c^{3}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}{c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}\right) - \left(\frac{c^{3}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{c^{3}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \log\left({\left| c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}} \right|}\right)}{9 \, {\left(b^{3} - 3 \, a b c\right)}} - \frac{c x + b}{3 \, {\left(c^{2} x^{3} + 3 \, b c x^{2} + 3 \, b^{2} x + 3 \, a b\right)} {\left(b^{3} - 3 \, a b c\right)}}"," ",0,"-1/9*(2*sqrt(3)*(c^3/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*arctan((sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))/(c*x + b + (-b^3 + 3*a*b*c)^(1/3))) - (c^3/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*log(4*(sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))^2 + 4*(c*x + b + (-b^3 + 3*a*b*c)^(1/3))^2) + 2*(c^3/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*log(abs(c*x + b + (-b^3 + 3*a*b*c)^(1/3))))/(b^3 - 3*a*b*c) - 1/3*(c*x + b)/((c^2*x^3 + 3*b*c*x^2 + 3*b^2*x + 3*a*b)*(b^3 - 3*a*b*c))","A",0
14,1,366,0,0.397351," ","integrate(1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^3,x, algorithm=""giac"")","\frac{5 \, {\left(2 \, \sqrt{3} \left(\frac{c^{6}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}{c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}}\right) - \left(\frac{c^{6}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} c x + \sqrt{3} b - \sqrt{3} {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{c^{6}}{b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}}\right)^{\frac{1}{3}} \log\left({\left| c x + b + {\left(-b^{3} + 3 \, a b c\right)}^{\frac{1}{3}} \right|}\right)\right)}}{54 \, {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}\right)}} + \frac{5 \, c^{4} x^{4} + 20 \, b c^{3} x^{3} + 30 \, b^{2} c^{2} x^{2} + 12 \, b^{3} c x + 24 \, a b c^{2} x - 3 \, b^{4} + 24 \, a b^{2} c}{18 \, {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2}\right)} {\left(c^{2} x^{3} + 3 \, b c x^{2} + 3 \, b^{2} x + 3 \, a b\right)}^{2}}"," ",0,"5/54*(2*sqrt(3)*(c^6/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*arctan((sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))/(c*x + b + (-b^3 + 3*a*b*c)^(1/3))) - (c^6/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*log(4*(sqrt(3)*c*x + sqrt(3)*b - sqrt(3)*(-b^3 + 3*a*b*c)^(1/3))^2 + 4*(c*x + b + (-b^3 + 3*a*b*c)^(1/3))^2) + 2*(c^6/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2))^(1/3)*log(abs(c*x + b + (-b^3 + 3*a*b*c)^(1/3))))/(b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2) + 1/18*(5*c^4*x^4 + 20*b*c^3*x^3 + 30*b^2*c^2*x^2 + 12*b^3*c*x + 24*a*b*c^2*x - 3*b^4 + 24*a*b^2*c)/((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2)*(c^2*x^3 + 3*b*c*x^2 + 3*b^2*x + 3*a*b)^2)","A",0
15,1,971,0,0.268244," ","integrate((a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} d^{3} f^{3} x^{10} + \frac{1}{3} \, b^{3} c d^{2} f^{3} x^{9} + \frac{1}{3} \, a b^{2} d^{3} f^{3} x^{9} + \frac{1}{3} \, b^{3} d^{3} f^{2} x^{9} e + \frac{3}{8} \, b^{3} c^{2} d f^{3} x^{8} + \frac{9}{8} \, a b^{2} c d^{2} f^{3} x^{8} + \frac{3}{8} \, a^{2} b d^{3} f^{3} x^{8} + \frac{9}{8} \, b^{3} c d^{2} f^{2} x^{8} e + \frac{9}{8} \, a b^{2} d^{3} f^{2} x^{8} e + \frac{1}{7} \, b^{3} c^{3} f^{3} x^{7} + \frac{9}{7} \, a b^{2} c^{2} d f^{3} x^{7} + \frac{9}{7} \, a^{2} b c d^{2} f^{3} x^{7} + \frac{1}{7} \, a^{3} d^{3} f^{3} x^{7} + \frac{3}{8} \, b^{3} d^{3} f x^{8} e^{2} + \frac{9}{7} \, b^{3} c^{2} d f^{2} x^{7} e + \frac{27}{7} \, a b^{2} c d^{2} f^{2} x^{7} e + \frac{9}{7} \, a^{2} b d^{3} f^{2} x^{7} e + \frac{1}{2} \, a b^{2} c^{3} f^{3} x^{6} + \frac{3}{2} \, a^{2} b c^{2} d f^{3} x^{6} + \frac{1}{2} \, a^{3} c d^{2} f^{3} x^{6} + \frac{9}{7} \, b^{3} c d^{2} f x^{7} e^{2} + \frac{9}{7} \, a b^{2} d^{3} f x^{7} e^{2} + \frac{1}{2} \, b^{3} c^{3} f^{2} x^{6} e + \frac{9}{2} \, a b^{2} c^{2} d f^{2} x^{6} e + \frac{9}{2} \, a^{2} b c d^{2} f^{2} x^{6} e + \frac{1}{2} \, a^{3} d^{3} f^{2} x^{6} e + \frac{3}{5} \, a^{2} b c^{3} f^{3} x^{5} + \frac{3}{5} \, a^{3} c^{2} d f^{3} x^{5} + \frac{1}{7} \, b^{3} d^{3} x^{7} e^{3} + \frac{3}{2} \, b^{3} c^{2} d f x^{6} e^{2} + \frac{9}{2} \, a b^{2} c d^{2} f x^{6} e^{2} + \frac{3}{2} \, a^{2} b d^{3} f x^{6} e^{2} + \frac{9}{5} \, a b^{2} c^{3} f^{2} x^{5} e + \frac{27}{5} \, a^{2} b c^{2} d f^{2} x^{5} e + \frac{9}{5} \, a^{3} c d^{2} f^{2} x^{5} e + \frac{1}{4} \, a^{3} c^{3} f^{3} x^{4} + \frac{1}{2} \, b^{3} c d^{2} x^{6} e^{3} + \frac{1}{2} \, a b^{2} d^{3} x^{6} e^{3} + \frac{3}{5} \, b^{3} c^{3} f x^{5} e^{2} + \frac{27}{5} \, a b^{2} c^{2} d f x^{5} e^{2} + \frac{27}{5} \, a^{2} b c d^{2} f x^{5} e^{2} + \frac{3}{5} \, a^{3} d^{3} f x^{5} e^{2} + \frac{9}{4} \, a^{2} b c^{3} f^{2} x^{4} e + \frac{9}{4} \, a^{3} c^{2} d f^{2} x^{4} e + \frac{3}{5} \, b^{3} c^{2} d x^{5} e^{3} + \frac{9}{5} \, a b^{2} c d^{2} x^{5} e^{3} + \frac{3}{5} \, a^{2} b d^{3} x^{5} e^{3} + \frac{9}{4} \, a b^{2} c^{3} f x^{4} e^{2} + \frac{27}{4} \, a^{2} b c^{2} d f x^{4} e^{2} + \frac{9}{4} \, a^{3} c d^{2} f x^{4} e^{2} + a^{3} c^{3} f^{2} x^{3} e + \frac{1}{4} \, b^{3} c^{3} x^{4} e^{3} + \frac{9}{4} \, a b^{2} c^{2} d x^{4} e^{3} + \frac{9}{4} \, a^{2} b c d^{2} x^{4} e^{3} + \frac{1}{4} \, a^{3} d^{3} x^{4} e^{3} + 3 \, a^{2} b c^{3} f x^{3} e^{2} + 3 \, a^{3} c^{2} d f x^{3} e^{2} + a b^{2} c^{3} x^{3} e^{3} + 3 \, a^{2} b c^{2} d x^{3} e^{3} + a^{3} c d^{2} x^{3} e^{3} + \frac{3}{2} \, a^{3} c^{3} f x^{2} e^{2} + \frac{3}{2} \, a^{2} b c^{3} x^{2} e^{3} + \frac{3}{2} \, a^{3} c^{2} d x^{2} e^{3} + a^{3} c^{3} x e^{3}"," ",0,"1/10*b^3*d^3*f^3*x^10 + 1/3*b^3*c*d^2*f^3*x^9 + 1/3*a*b^2*d^3*f^3*x^9 + 1/3*b^3*d^3*f^2*x^9*e + 3/8*b^3*c^2*d*f^3*x^8 + 9/8*a*b^2*c*d^2*f^3*x^8 + 3/8*a^2*b*d^3*f^3*x^8 + 9/8*b^3*c*d^2*f^2*x^8*e + 9/8*a*b^2*d^3*f^2*x^8*e + 1/7*b^3*c^3*f^3*x^7 + 9/7*a*b^2*c^2*d*f^3*x^7 + 9/7*a^2*b*c*d^2*f^3*x^7 + 1/7*a^3*d^3*f^3*x^7 + 3/8*b^3*d^3*f*x^8*e^2 + 9/7*b^3*c^2*d*f^2*x^7*e + 27/7*a*b^2*c*d^2*f^2*x^7*e + 9/7*a^2*b*d^3*f^2*x^7*e + 1/2*a*b^2*c^3*f^3*x^6 + 3/2*a^2*b*c^2*d*f^3*x^6 + 1/2*a^3*c*d^2*f^3*x^6 + 9/7*b^3*c*d^2*f*x^7*e^2 + 9/7*a*b^2*d^3*f*x^7*e^2 + 1/2*b^3*c^3*f^2*x^6*e + 9/2*a*b^2*c^2*d*f^2*x^6*e + 9/2*a^2*b*c*d^2*f^2*x^6*e + 1/2*a^3*d^3*f^2*x^6*e + 3/5*a^2*b*c^3*f^3*x^5 + 3/5*a^3*c^2*d*f^3*x^5 + 1/7*b^3*d^3*x^7*e^3 + 3/2*b^3*c^2*d*f*x^6*e^2 + 9/2*a*b^2*c*d^2*f*x^6*e^2 + 3/2*a^2*b*d^3*f*x^6*e^2 + 9/5*a*b^2*c^3*f^2*x^5*e + 27/5*a^2*b*c^2*d*f^2*x^5*e + 9/5*a^3*c*d^2*f^2*x^5*e + 1/4*a^3*c^3*f^3*x^4 + 1/2*b^3*c*d^2*x^6*e^3 + 1/2*a*b^2*d^3*x^6*e^3 + 3/5*b^3*c^3*f*x^5*e^2 + 27/5*a*b^2*c^2*d*f*x^5*e^2 + 27/5*a^2*b*c*d^2*f*x^5*e^2 + 3/5*a^3*d^3*f*x^5*e^2 + 9/4*a^2*b*c^3*f^2*x^4*e + 9/4*a^3*c^2*d*f^2*x^4*e + 3/5*b^3*c^2*d*x^5*e^3 + 9/5*a*b^2*c*d^2*x^5*e^3 + 3/5*a^2*b*d^3*x^5*e^3 + 9/4*a*b^2*c^3*f*x^4*e^2 + 27/4*a^2*b*c^2*d*f*x^4*e^2 + 9/4*a^3*c*d^2*f*x^4*e^2 + a^3*c^3*f^2*x^3*e + 1/4*b^3*c^3*x^4*e^3 + 9/4*a*b^2*c^2*d*x^4*e^3 + 9/4*a^2*b*c*d^2*x^4*e^3 + 1/4*a^3*d^3*x^4*e^3 + 3*a^2*b*c^3*f*x^3*e^2 + 3*a^3*c^2*d*f*x^3*e^2 + a*b^2*c^3*x^3*e^3 + 3*a^2*b*c^2*d*x^3*e^3 + a^3*c*d^2*x^3*e^3 + 3/2*a^3*c^3*f*x^2*e^2 + 3/2*a^2*b*c^3*x^2*e^3 + 3/2*a^3*c^2*d*x^2*e^3 + a^3*c^3*x*e^3","B",0
16,1,346,0,0.415246," ","integrate((a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} d^{2} f^{2} x^{7} + \frac{1}{3} \, b^{2} c d f^{2} x^{6} + \frac{1}{3} \, a b d^{2} f^{2} x^{6} + \frac{1}{3} \, b^{2} d^{2} f x^{6} e + \frac{1}{5} \, b^{2} c^{2} f^{2} x^{5} + \frac{4}{5} \, a b c d f^{2} x^{5} + \frac{1}{5} \, a^{2} d^{2} f^{2} x^{5} + \frac{4}{5} \, b^{2} c d f x^{5} e + \frac{4}{5} \, a b d^{2} f x^{5} e + \frac{1}{2} \, a b c^{2} f^{2} x^{4} + \frac{1}{2} \, a^{2} c d f^{2} x^{4} + \frac{1}{5} \, b^{2} d^{2} x^{5} e^{2} + \frac{1}{2} \, b^{2} c^{2} f x^{4} e + 2 \, a b c d f x^{4} e + \frac{1}{2} \, a^{2} d^{2} f x^{4} e + \frac{1}{3} \, a^{2} c^{2} f^{2} x^{3} + \frac{1}{2} \, b^{2} c d x^{4} e^{2} + \frac{1}{2} \, a b d^{2} x^{4} e^{2} + \frac{4}{3} \, a b c^{2} f x^{3} e + \frac{4}{3} \, a^{2} c d f x^{3} e + \frac{1}{3} \, b^{2} c^{2} x^{3} e^{2} + \frac{4}{3} \, a b c d x^{3} e^{2} + \frac{1}{3} \, a^{2} d^{2} x^{3} e^{2} + a^{2} c^{2} f x^{2} e + a b c^{2} x^{2} e^{2} + a^{2} c d x^{2} e^{2} + a^{2} c^{2} x e^{2}"," ",0,"1/7*b^2*d^2*f^2*x^7 + 1/3*b^2*c*d*f^2*x^6 + 1/3*a*b*d^2*f^2*x^6 + 1/3*b^2*d^2*f*x^6*e + 1/5*b^2*c^2*f^2*x^5 + 4/5*a*b*c*d*f^2*x^5 + 1/5*a^2*d^2*f^2*x^5 + 4/5*b^2*c*d*f*x^5*e + 4/5*a*b*d^2*f*x^5*e + 1/2*a*b*c^2*f^2*x^4 + 1/2*a^2*c*d*f^2*x^4 + 1/5*b^2*d^2*x^5*e^2 + 1/2*b^2*c^2*f*x^4*e + 2*a*b*c*d*f*x^4*e + 1/2*a^2*d^2*f*x^4*e + 1/3*a^2*c^2*f^2*x^3 + 1/2*b^2*c*d*x^4*e^2 + 1/2*a*b*d^2*x^4*e^2 + 4/3*a*b*c^2*f*x^3*e + 4/3*a^2*c*d*f*x^3*e + 1/3*b^2*c^2*x^3*e^2 + 4/3*a*b*c*d*x^3*e^2 + 1/3*a^2*d^2*x^3*e^2 + a^2*c^2*f*x^2*e + a*b*c^2*x^2*e^2 + a^2*c*d*x^2*e^2 + a^2*c^2*x*e^2","A",0
17,1,54,0,0.231967," ","integrate(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3,x, algorithm=""giac"")","\frac{1}{4} \, b d f x^{4} + \frac{1}{3} \, {\left(b c f + a d f + b d e\right)} x^{3} + a c x e + \frac{1}{2} \, {\left(a c f + b c e + a d e\right)} x^{2}"," ",0,"1/4*b*d*f*x^4 + 1/3*(b*c*f + a*d*f + b*d*e)*x^3 + a*c*x*e + 1/2*(a*c*f + b*c*e + a*d*e)*x^2","A",0
18,1,137,0,0.307346," ","integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left| b x + a \right|}\right)}{a b^{2} c f - a^{2} b d f - b^{3} c e + a b^{2} d e} + \frac{d^{2} \log\left({\left| d x + c \right|}\right)}{b c^{2} d f - a c d^{2} f - b c d^{2} e + a d^{3} e} + \frac{f^{2} \log\left({\left| f x + e \right|}\right)}{a c f^{3} - b c f^{2} e - a d f^{2} e + b d f e^{2}}"," ",0,"-b^2*log(abs(b*x + a))/(a*b^2*c*f - a^2*b*d*f - b^3*c*e + a*b^2*d*e) + d^2*log(abs(d*x + c))/(b*c^2*d*f - a*c*d^2*f - b*c*d^2*e + a*d^3*e) + f^2*log(abs(f*x + e))/(a*c*f^3 - b*c*f^2*e - a*d*f^2*e + b*d*f*e^2)","A",0
19,1,1414,0,0.391994," ","integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^2,x, algorithm=""giac"")","\frac{2 \, {\left(b^{5} c f - 2 \, a b^{4} d f + b^{5} d e\right)} \log\left({\left| b x + a \right|}\right)}{a^{3} b^{4} c^{3} f^{3} - 3 \, a^{4} b^{3} c^{2} d f^{3} + 3 \, a^{5} b^{2} c d^{2} f^{3} - a^{6} b d^{3} f^{3} - 3 \, a^{2} b^{5} c^{3} f^{2} e + 9 \, a^{3} b^{4} c^{2} d f^{2} e - 9 \, a^{4} b^{3} c d^{2} f^{2} e + 3 \, a^{5} b^{2} d^{3} f^{2} e + 3 \, a b^{6} c^{3} f e^{2} - 9 \, a^{2} b^{5} c^{2} d f e^{2} + 9 \, a^{3} b^{4} c d^{2} f e^{2} - 3 \, a^{4} b^{3} d^{3} f e^{2} - b^{7} c^{3} e^{3} + 3 \, a b^{6} c^{2} d e^{3} - 3 \, a^{2} b^{5} c d^{2} e^{3} + a^{3} b^{4} d^{3} e^{3}} + \frac{2 \, {\left(2 \, b c d^{4} f - a d^{5} f - b d^{5} e\right)} \log\left({\left| d x + c \right|}\right)}{b^{3} c^{6} d f^{3} - 3 \, a b^{2} c^{5} d^{2} f^{3} + 3 \, a^{2} b c^{4} d^{3} f^{3} - a^{3} c^{3} d^{4} f^{3} - 3 \, b^{3} c^{5} d^{2} f^{2} e + 9 \, a b^{2} c^{4} d^{3} f^{2} e - 9 \, a^{2} b c^{3} d^{4} f^{2} e + 3 \, a^{3} c^{2} d^{5} f^{2} e + 3 \, b^{3} c^{4} d^{3} f e^{2} - 9 \, a b^{2} c^{3} d^{4} f e^{2} + 9 \, a^{2} b c^{2} d^{5} f e^{2} - 3 \, a^{3} c d^{6} f e^{2} - b^{3} c^{3} d^{4} e^{3} + 3 \, a b^{2} c^{2} d^{5} e^{3} - 3 \, a^{2} b c d^{6} e^{3} + a^{3} d^{7} e^{3}} - \frac{2 \, {\left(b c f^{5} + a d f^{5} - 2 \, b d f^{4} e\right)} \log\left({\left| f x + e \right|}\right)}{a^{3} c^{3} f^{7} - 3 \, a^{2} b c^{3} f^{6} e - 3 \, a^{3} c^{2} d f^{6} e + 3 \, a b^{2} c^{3} f^{5} e^{2} + 9 \, a^{2} b c^{2} d f^{5} e^{2} + 3 \, a^{3} c d^{2} f^{5} e^{2} - b^{3} c^{3} f^{4} e^{3} - 9 \, a b^{2} c^{2} d f^{4} e^{3} - 9 \, a^{2} b c d^{2} f^{4} e^{3} - a^{3} d^{3} f^{4} e^{3} + 3 \, b^{3} c^{2} d f^{3} e^{4} + 9 \, a b^{2} c d^{2} f^{3} e^{4} + 3 \, a^{2} b d^{3} f^{3} e^{4} - 3 \, b^{3} c d^{2} f^{2} e^{5} - 3 \, a b^{2} d^{3} f^{2} e^{5} + b^{3} d^{3} f e^{6}} - \frac{2 \, b^{3} c^{2} d f^{3} x^{2} - 2 \, a b^{2} c d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{3} f^{3} x^{2} - 2 \, b^{3} c d^{2} f^{2} x^{2} e - 2 \, a b^{2} d^{3} f^{2} x^{2} e + 2 \, b^{3} c^{3} f^{3} x - a b^{2} c^{2} d f^{3} x - a^{2} b c d^{2} f^{3} x + 2 \, a^{3} d^{3} f^{3} x + 2 \, b^{3} d^{3} f x^{2} e^{2} - b^{3} c^{2} d f^{2} x e - a^{2} b d^{3} f^{2} x e + a b^{2} c^{3} f^{3} - 2 \, a^{2} b c^{2} d f^{3} + a^{3} c d^{2} f^{3} - b^{3} c d^{2} f x e^{2} - a b^{2} d^{3} f x e^{2} + b^{3} c^{3} f^{2} e + a^{3} d^{3} f^{2} e + 2 \, b^{3} d^{3} x e^{3} - 2 \, b^{3} c^{2} d f e^{2} - 2 \, a^{2} b d^{3} f e^{2} + b^{3} c d^{2} e^{3} + a b^{2} d^{3} e^{3}}{{\left(a^{2} b^{2} c^{4} f^{4} - 2 \, a^{3} b c^{3} d f^{4} + a^{4} c^{2} d^{2} f^{4} - 2 \, a b^{3} c^{4} f^{3} e + 2 \, a^{2} b^{2} c^{3} d f^{3} e + 2 \, a^{3} b c^{2} d^{2} f^{3} e - 2 \, a^{4} c d^{3} f^{3} e + b^{4} c^{4} f^{2} e^{2} + 2 \, a b^{3} c^{3} d f^{2} e^{2} - 6 \, a^{2} b^{2} c^{2} d^{2} f^{2} e^{2} + 2 \, a^{3} b c d^{3} f^{2} e^{2} + a^{4} d^{4} f^{2} e^{2} - 2 \, b^{4} c^{3} d f e^{3} + 2 \, a b^{3} c^{2} d^{2} f e^{3} + 2 \, a^{2} b^{2} c d^{3} f e^{3} - 2 \, a^{3} b d^{4} f e^{3} + b^{4} c^{2} d^{2} e^{4} - 2 \, a b^{3} c d^{3} e^{4} + a^{2} b^{2} d^{4} e^{4}\right)} {\left(b d f x^{3} + b c f x^{2} + a d f x^{2} + b d x^{2} e + a c f x + b c x e + a d x e + a c e\right)}}"," ",0,"2*(b^5*c*f - 2*a*b^4*d*f + b^5*d*e)*log(abs(b*x + a))/(a^3*b^4*c^3*f^3 - 3*a^4*b^3*c^2*d*f^3 + 3*a^5*b^2*c*d^2*f^3 - a^6*b*d^3*f^3 - 3*a^2*b^5*c^3*f^2*e + 9*a^3*b^4*c^2*d*f^2*e - 9*a^4*b^3*c*d^2*f^2*e + 3*a^5*b^2*d^3*f^2*e + 3*a*b^6*c^3*f*e^2 - 9*a^2*b^5*c^2*d*f*e^2 + 9*a^3*b^4*c*d^2*f*e^2 - 3*a^4*b^3*d^3*f*e^2 - b^7*c^3*e^3 + 3*a*b^6*c^2*d*e^3 - 3*a^2*b^5*c*d^2*e^3 + a^3*b^4*d^3*e^3) + 2*(2*b*c*d^4*f - a*d^5*f - b*d^5*e)*log(abs(d*x + c))/(b^3*c^6*d*f^3 - 3*a*b^2*c^5*d^2*f^3 + 3*a^2*b*c^4*d^3*f^3 - a^3*c^3*d^4*f^3 - 3*b^3*c^5*d^2*f^2*e + 9*a*b^2*c^4*d^3*f^2*e - 9*a^2*b*c^3*d^4*f^2*e + 3*a^3*c^2*d^5*f^2*e + 3*b^3*c^4*d^3*f*e^2 - 9*a*b^2*c^3*d^4*f*e^2 + 9*a^2*b*c^2*d^5*f*e^2 - 3*a^3*c*d^6*f*e^2 - b^3*c^3*d^4*e^3 + 3*a*b^2*c^2*d^5*e^3 - 3*a^2*b*c*d^6*e^3 + a^3*d^7*e^3) - 2*(b*c*f^5 + a*d*f^5 - 2*b*d*f^4*e)*log(abs(f*x + e))/(a^3*c^3*f^7 - 3*a^2*b*c^3*f^6*e - 3*a^3*c^2*d*f^6*e + 3*a*b^2*c^3*f^5*e^2 + 9*a^2*b*c^2*d*f^5*e^2 + 3*a^3*c*d^2*f^5*e^2 - b^3*c^3*f^4*e^3 - 9*a*b^2*c^2*d*f^4*e^3 - 9*a^2*b*c*d^2*f^4*e^3 - a^3*d^3*f^4*e^3 + 3*b^3*c^2*d*f^3*e^4 + 9*a*b^2*c*d^2*f^3*e^4 + 3*a^2*b*d^3*f^3*e^4 - 3*b^3*c*d^2*f^2*e^5 - 3*a*b^2*d^3*f^2*e^5 + b^3*d^3*f*e^6) - (2*b^3*c^2*d*f^3*x^2 - 2*a*b^2*c*d^2*f^3*x^2 + 2*a^2*b*d^3*f^3*x^2 - 2*b^3*c*d^2*f^2*x^2*e - 2*a*b^2*d^3*f^2*x^2*e + 2*b^3*c^3*f^3*x - a*b^2*c^2*d*f^3*x - a^2*b*c*d^2*f^3*x + 2*a^3*d^3*f^3*x + 2*b^3*d^3*f*x^2*e^2 - b^3*c^2*d*f^2*x*e - a^2*b*d^3*f^2*x*e + a*b^2*c^3*f^3 - 2*a^2*b*c^2*d*f^3 + a^3*c*d^2*f^3 - b^3*c*d^2*f*x*e^2 - a*b^2*d^3*f*x*e^2 + b^3*c^3*f^2*e + a^3*d^3*f^2*e + 2*b^3*d^3*x*e^3 - 2*b^3*c^2*d*f*e^2 - 2*a^2*b*d^3*f*e^2 + b^3*c*d^2*e^3 + a*b^2*d^3*e^3)/((a^2*b^2*c^4*f^4 - 2*a^3*b*c^3*d*f^4 + a^4*c^2*d^2*f^4 - 2*a*b^3*c^4*f^3*e + 2*a^2*b^2*c^3*d*f^3*e + 2*a^3*b*c^2*d^2*f^3*e - 2*a^4*c*d^3*f^3*e + b^4*c^4*f^2*e^2 + 2*a*b^3*c^3*d*f^2*e^2 - 6*a^2*b^2*c^2*d^2*f^2*e^2 + 2*a^3*b*c*d^3*f^2*e^2 + a^4*d^4*f^2*e^2 - 2*b^4*c^3*d*f*e^3 + 2*a*b^3*c^2*d^2*f*e^3 + 2*a^2*b^2*c*d^3*f*e^3 - 2*a^3*b*d^4*f*e^3 + b^4*c^2*d^2*e^4 - 2*a*b^3*c*d^3*e^4 + a^2*b^2*d^4*e^4)*(b*d*f*x^3 + b*c*f*x^2 + a*d*f*x^2 + b*d*x^2*e + a*c*f*x + b*c*x*e + a*d*x*e + a*c*e))","B",0
20,1,6908,0,1.103284," ","integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, b^{8} c^{2} f^{2} - 7 \, a b^{7} c d f^{2} + 7 \, a^{2} b^{6} d^{2} f^{2} + 3 \, b^{8} c d f e - 7 \, a b^{7} d^{2} f e + 2 \, b^{8} d^{2} e^{2}\right)} \log\left({\left| b x + a \right|}\right)}{a^{5} b^{6} c^{5} f^{5} - 5 \, a^{6} b^{5} c^{4} d f^{5} + 10 \, a^{7} b^{4} c^{3} d^{2} f^{5} - 10 \, a^{8} b^{3} c^{2} d^{3} f^{5} + 5 \, a^{9} b^{2} c d^{4} f^{5} - a^{10} b d^{5} f^{5} - 5 \, a^{4} b^{7} c^{5} f^{4} e + 25 \, a^{5} b^{6} c^{4} d f^{4} e - 50 \, a^{6} b^{5} c^{3} d^{2} f^{4} e + 50 \, a^{7} b^{4} c^{2} d^{3} f^{4} e - 25 \, a^{8} b^{3} c d^{4} f^{4} e + 5 \, a^{9} b^{2} d^{5} f^{4} e + 10 \, a^{3} b^{8} c^{5} f^{3} e^{2} - 50 \, a^{4} b^{7} c^{4} d f^{3} e^{2} + 100 \, a^{5} b^{6} c^{3} d^{2} f^{3} e^{2} - 100 \, a^{6} b^{5} c^{2} d^{3} f^{3} e^{2} + 50 \, a^{7} b^{4} c d^{4} f^{3} e^{2} - 10 \, a^{8} b^{3} d^{5} f^{3} e^{2} - 10 \, a^{2} b^{9} c^{5} f^{2} e^{3} + 50 \, a^{3} b^{8} c^{4} d f^{2} e^{3} - 100 \, a^{4} b^{7} c^{3} d^{2} f^{2} e^{3} + 100 \, a^{5} b^{6} c^{2} d^{3} f^{2} e^{3} - 50 \, a^{6} b^{5} c d^{4} f^{2} e^{3} + 10 \, a^{7} b^{4} d^{5} f^{2} e^{3} + 5 \, a b^{10} c^{5} f e^{4} - 25 \, a^{2} b^{9} c^{4} d f e^{4} + 50 \, a^{3} b^{8} c^{3} d^{2} f e^{4} - 50 \, a^{4} b^{7} c^{2} d^{3} f e^{4} + 25 \, a^{5} b^{6} c d^{4} f e^{4} - 5 \, a^{6} b^{5} d^{5} f e^{4} - b^{11} c^{5} e^{5} + 5 \, a b^{10} c^{4} d e^{5} - 10 \, a^{2} b^{9} c^{3} d^{2} e^{5} + 10 \, a^{3} b^{8} c^{2} d^{3} e^{5} - 5 \, a^{4} b^{7} c d^{4} e^{5} + a^{5} b^{6} d^{5} e^{5}} + \frac{3 \, {\left(7 \, b^{2} c^{2} d^{6} f^{2} - 7 \, a b c d^{7} f^{2} + 2 \, a^{2} d^{8} f^{2} - 7 \, b^{2} c d^{7} f e + 3 \, a b d^{8} f e + 2 \, b^{2} d^{8} e^{2}\right)} \log\left({\left| d x + c \right|}\right)}{b^{5} c^{10} d f^{5} - 5 \, a b^{4} c^{9} d^{2} f^{5} + 10 \, a^{2} b^{3} c^{8} d^{3} f^{5} - 10 \, a^{3} b^{2} c^{7} d^{4} f^{5} + 5 \, a^{4} b c^{6} d^{5} f^{5} - a^{5} c^{5} d^{6} f^{5} - 5 \, b^{5} c^{9} d^{2} f^{4} e + 25 \, a b^{4} c^{8} d^{3} f^{4} e - 50 \, a^{2} b^{3} c^{7} d^{4} f^{4} e + 50 \, a^{3} b^{2} c^{6} d^{5} f^{4} e - 25 \, a^{4} b c^{5} d^{6} f^{4} e + 5 \, a^{5} c^{4} d^{7} f^{4} e + 10 \, b^{5} c^{8} d^{3} f^{3} e^{2} - 50 \, a b^{4} c^{7} d^{4} f^{3} e^{2} + 100 \, a^{2} b^{3} c^{6} d^{5} f^{3} e^{2} - 100 \, a^{3} b^{2} c^{5} d^{6} f^{3} e^{2} + 50 \, a^{4} b c^{4} d^{7} f^{3} e^{2} - 10 \, a^{5} c^{3} d^{8} f^{3} e^{2} - 10 \, b^{5} c^{7} d^{4} f^{2} e^{3} + 50 \, a b^{4} c^{6} d^{5} f^{2} e^{3} - 100 \, a^{2} b^{3} c^{5} d^{6} f^{2} e^{3} + 100 \, a^{3} b^{2} c^{4} d^{7} f^{2} e^{3} - 50 \, a^{4} b c^{3} d^{8} f^{2} e^{3} + 10 \, a^{5} c^{2} d^{9} f^{2} e^{3} + 5 \, b^{5} c^{6} d^{5} f e^{4} - 25 \, a b^{4} c^{5} d^{6} f e^{4} + 50 \, a^{2} b^{3} c^{4} d^{7} f e^{4} - 50 \, a^{3} b^{2} c^{3} d^{8} f e^{4} + 25 \, a^{4} b c^{2} d^{9} f e^{4} - 5 \, a^{5} c d^{10} f e^{4} - b^{5} c^{5} d^{6} e^{5} + 5 \, a b^{4} c^{4} d^{7} e^{5} - 10 \, a^{2} b^{3} c^{3} d^{8} e^{5} + 10 \, a^{3} b^{2} c^{2} d^{9} e^{5} - 5 \, a^{4} b c d^{10} e^{5} + a^{5} d^{11} e^{5}} + \frac{3 \, {\left(2 \, b^{2} c^{2} f^{8} + 3 \, a b c d f^{8} + 2 \, a^{2} d^{2} f^{8} - 7 \, b^{2} c d f^{7} e - 7 \, a b d^{2} f^{7} e + 7 \, b^{2} d^{2} f^{6} e^{2}\right)} \log\left({\left| f x + e \right|}\right)}{a^{5} c^{5} f^{11} - 5 \, a^{4} b c^{5} f^{10} e - 5 \, a^{5} c^{4} d f^{10} e + 10 \, a^{3} b^{2} c^{5} f^{9} e^{2} + 25 \, a^{4} b c^{4} d f^{9} e^{2} + 10 \, a^{5} c^{3} d^{2} f^{9} e^{2} - 10 \, a^{2} b^{3} c^{5} f^{8} e^{3} - 50 \, a^{3} b^{2} c^{4} d f^{8} e^{3} - 50 \, a^{4} b c^{3} d^{2} f^{8} e^{3} - 10 \, a^{5} c^{2} d^{3} f^{8} e^{3} + 5 \, a b^{4} c^{5} f^{7} e^{4} + 50 \, a^{2} b^{3} c^{4} d f^{7} e^{4} + 100 \, a^{3} b^{2} c^{3} d^{2} f^{7} e^{4} + 50 \, a^{4} b c^{2} d^{3} f^{7} e^{4} + 5 \, a^{5} c d^{4} f^{7} e^{4} - b^{5} c^{5} f^{6} e^{5} - 25 \, a b^{4} c^{4} d f^{6} e^{5} - 100 \, a^{2} b^{3} c^{3} d^{2} f^{6} e^{5} - 100 \, a^{3} b^{2} c^{2} d^{3} f^{6} e^{5} - 25 \, a^{4} b c d^{4} f^{6} e^{5} - a^{5} d^{5} f^{6} e^{5} + 5 \, b^{5} c^{4} d f^{5} e^{6} + 50 \, a b^{4} c^{3} d^{2} f^{5} e^{6} + 100 \, a^{2} b^{3} c^{2} d^{3} f^{5} e^{6} + 50 \, a^{3} b^{2} c d^{4} f^{5} e^{6} + 5 \, a^{4} b d^{5} f^{5} e^{6} - 10 \, b^{5} c^{3} d^{2} f^{4} e^{7} - 50 \, a b^{4} c^{2} d^{3} f^{4} e^{7} - 50 \, a^{2} b^{3} c d^{4} f^{4} e^{7} - 10 \, a^{3} b^{2} d^{5} f^{4} e^{7} + 10 \, b^{5} c^{2} d^{3} f^{3} e^{8} + 25 \, a b^{4} c d^{4} f^{3} e^{8} + 10 \, a^{2} b^{3} d^{5} f^{3} e^{8} - 5 \, b^{5} c d^{4} f^{2} e^{9} - 5 \, a b^{4} d^{5} f^{2} e^{9} + b^{5} d^{5} f e^{10}} + \frac{12 \, b^{7} c^{5} d^{2} f^{7} x^{5} - 30 \, a b^{6} c^{4} d^{3} f^{7} x^{5} + 12 \, a^{2} b^{5} c^{3} d^{4} f^{7} x^{5} + 12 \, a^{3} b^{4} c^{2} d^{5} f^{7} x^{5} - 30 \, a^{4} b^{3} c d^{6} f^{7} x^{5} + 12 \, a^{5} b^{2} d^{7} f^{7} x^{5} - 30 \, b^{7} c^{4} d^{3} f^{6} x^{5} e + 96 \, a b^{6} c^{3} d^{4} f^{6} x^{5} e - 72 \, a^{2} b^{5} c^{2} d^{5} f^{6} x^{5} e + 96 \, a^{3} b^{4} c d^{6} f^{6} x^{5} e - 30 \, a^{4} b^{3} d^{7} f^{6} x^{5} e + 24 \, b^{7} c^{6} d f^{7} x^{4} - 42 \, a b^{6} c^{5} d^{2} f^{7} x^{4} - 21 \, a^{2} b^{5} c^{4} d^{3} f^{7} x^{4} + 42 \, a^{3} b^{4} c^{3} d^{4} f^{7} x^{4} - 21 \, a^{4} b^{3} c^{2} d^{5} f^{7} x^{4} - 42 \, a^{5} b^{2} c d^{6} f^{7} x^{4} + 24 \, a^{6} b d^{7} f^{7} x^{4} + 12 \, b^{7} c^{3} d^{4} f^{5} x^{5} e^{2} - 72 \, a b^{6} c^{2} d^{5} f^{5} x^{5} e^{2} - 72 \, a^{2} b^{5} c d^{6} f^{5} x^{5} e^{2} + 12 \, a^{3} b^{4} d^{7} f^{5} x^{5} e^{2} - 42 \, b^{7} c^{5} d^{2} f^{6} x^{4} e + 102 \, a b^{6} c^{4} d^{3} f^{6} x^{4} e + 18 \, a^{2} b^{5} c^{3} d^{4} f^{6} x^{4} e + 18 \, a^{3} b^{4} c^{2} d^{5} f^{6} x^{4} e + 102 \, a^{4} b^{3} c d^{6} f^{6} x^{4} e - 42 \, a^{5} b^{2} d^{7} f^{6} x^{4} e + 12 \, b^{7} c^{7} f^{7} x^{3} + 6 \, a b^{6} c^{6} d f^{7} x^{3} - 74 \, a^{2} b^{5} c^{5} d^{2} f^{7} x^{3} + 38 \, a^{3} b^{4} c^{4} d^{3} f^{7} x^{3} + 38 \, a^{4} b^{3} c^{3} d^{4} f^{7} x^{3} - 74 \, a^{5} b^{2} c^{2} d^{5} f^{7} x^{3} + 6 \, a^{6} b c d^{6} f^{7} x^{3} + 12 \, a^{7} d^{7} f^{7} x^{3} + 12 \, b^{7} c^{2} d^{5} f^{4} x^{5} e^{3} + 96 \, a b^{6} c d^{6} f^{4} x^{5} e^{3} + 12 \, a^{2} b^{5} d^{7} f^{4} x^{5} e^{3} - 21 \, b^{7} c^{4} d^{3} f^{5} x^{4} e^{2} + 18 \, a b^{6} c^{3} d^{4} f^{5} x^{4} e^{2} - 234 \, a^{2} b^{5} c^{2} d^{5} f^{5} x^{4} e^{2} + 18 \, a^{3} b^{4} c d^{6} f^{5} x^{4} e^{2} - 21 \, a^{4} b^{3} d^{7} f^{5} x^{4} e^{2} + 6 \, b^{7} c^{6} d f^{6} x^{3} e - 56 \, a b^{6} c^{5} d^{2} f^{6} x^{3} e + 172 \, a^{2} b^{5} c^{4} d^{3} f^{6} x^{3} e - 136 \, a^{3} b^{4} c^{3} d^{4} f^{6} x^{3} e + 172 \, a^{4} b^{3} c^{2} d^{5} f^{6} x^{3} e - 56 \, a^{5} b^{2} c d^{6} f^{6} x^{3} e + 6 \, a^{6} b d^{7} f^{6} x^{3} e + 18 \, a b^{6} c^{7} f^{7} x^{2} - 37 \, a^{2} b^{5} c^{6} d f^{7} x^{2} - 3 \, a^{3} b^{4} c^{5} d^{2} f^{7} x^{2} + 32 \, a^{4} b^{3} c^{4} d^{3} f^{7} x^{2} - 3 \, a^{5} b^{2} c^{3} d^{4} f^{7} x^{2} - 37 \, a^{6} b c^{2} d^{5} f^{7} x^{2} + 18 \, a^{7} c d^{6} f^{7} x^{2} - 30 \, b^{7} c d^{6} f^{3} x^{5} e^{4} - 30 \, a b^{6} d^{7} f^{3} x^{5} e^{4} + 42 \, b^{7} c^{3} d^{4} f^{4} x^{4} e^{3} + 18 \, a b^{6} c^{2} d^{5} f^{4} x^{4} e^{3} + 18 \, a^{2} b^{5} c d^{6} f^{4} x^{4} e^{3} + 42 \, a^{3} b^{4} d^{7} f^{4} x^{4} e^{3} - 74 \, b^{7} c^{5} d^{2} f^{5} x^{3} e^{2} + 172 \, a b^{6} c^{4} d^{3} f^{5} x^{3} e^{2} - 104 \, a^{2} b^{5} c^{3} d^{4} f^{5} x^{3} e^{2} - 104 \, a^{3} b^{4} c^{2} d^{5} f^{5} x^{3} e^{2} + 172 \, a^{4} b^{3} c d^{6} f^{5} x^{3} e^{2} - 74 \, a^{5} b^{2} d^{7} f^{5} x^{3} e^{2} + 18 \, b^{7} c^{7} f^{6} x^{2} e - 34 \, a b^{6} c^{6} d f^{6} x^{2} e + 9 \, a^{2} b^{5} c^{5} d^{2} f^{6} x^{2} e + a^{3} b^{4} c^{4} d^{3} f^{6} x^{2} e + a^{4} b^{3} c^{3} d^{4} f^{6} x^{2} e + 9 \, a^{5} b^{2} c^{2} d^{5} f^{6} x^{2} e - 34 \, a^{6} b c d^{6} f^{6} x^{2} e + 18 \, a^{7} d^{7} f^{6} x^{2} e + 4 \, a^{2} b^{5} c^{7} f^{7} x - 12 \, a^{3} b^{4} c^{6} d f^{7} x + 8 \, a^{4} b^{3} c^{5} d^{2} f^{7} x + 8 \, a^{5} b^{2} c^{4} d^{3} f^{7} x - 12 \, a^{6} b c^{3} d^{4} f^{7} x + 4 \, a^{7} c^{2} d^{5} f^{7} x + 12 \, b^{7} d^{7} f^{2} x^{5} e^{5} - 21 \, b^{7} c^{2} d^{5} f^{3} x^{4} e^{4} + 102 \, a b^{6} c d^{6} f^{3} x^{4} e^{4} - 21 \, a^{2} b^{5} d^{7} f^{3} x^{4} e^{4} + 38 \, b^{7} c^{4} d^{3} f^{4} x^{3} e^{3} - 136 \, a b^{6} c^{3} d^{4} f^{4} x^{3} e^{3} - 104 \, a^{2} b^{5} c^{2} d^{5} f^{4} x^{3} e^{3} - 136 \, a^{3} b^{4} c d^{6} f^{4} x^{3} e^{3} + 38 \, a^{4} b^{3} d^{7} f^{4} x^{3} e^{3} - 37 \, b^{7} c^{6} d f^{5} x^{2} e^{2} + 9 \, a b^{6} c^{5} d^{2} f^{5} x^{2} e^{2} + 234 \, a^{2} b^{5} c^{4} d^{3} f^{5} x^{2} e^{2} - 208 \, a^{3} b^{4} c^{3} d^{4} f^{5} x^{2} e^{2} + 234 \, a^{4} b^{3} c^{2} d^{5} f^{5} x^{2} e^{2} + 9 \, a^{5} b^{2} c d^{6} f^{5} x^{2} e^{2} - 37 \, a^{6} b d^{7} f^{5} x^{2} e^{2} + 28 \, a b^{6} c^{7} f^{6} x e - 66 \, a^{2} b^{5} c^{6} d f^{6} x e + 34 \, a^{3} b^{4} c^{5} d^{2} f^{6} x e - 16 \, a^{4} b^{3} c^{4} d^{3} f^{6} x e + 34 \, a^{5} b^{2} c^{3} d^{4} f^{6} x e - 66 \, a^{6} b c^{2} d^{5} f^{6} x e + 28 \, a^{7} c d^{6} f^{6} x e - a^{3} b^{4} c^{7} f^{7} + 4 \, a^{4} b^{3} c^{6} d f^{7} - 6 \, a^{5} b^{2} c^{5} d^{2} f^{7} + 4 \, a^{6} b c^{4} d^{3} f^{7} - a^{7} c^{3} d^{4} f^{7} - 42 \, b^{7} c d^{6} f^{2} x^{4} e^{5} - 42 \, a b^{6} d^{7} f^{2} x^{4} e^{5} + 38 \, b^{7} c^{3} d^{4} f^{3} x^{3} e^{4} + 172 \, a b^{6} c^{2} d^{5} f^{3} x^{3} e^{4} + 172 \, a^{2} b^{5} c d^{6} f^{3} x^{3} e^{4} + 38 \, a^{3} b^{4} d^{7} f^{3} x^{3} e^{4} - 3 \, b^{7} c^{5} d^{2} f^{4} x^{2} e^{3} + a b^{6} c^{4} d^{3} f^{4} x^{2} e^{3} - 208 \, a^{2} b^{5} c^{3} d^{4} f^{4} x^{2} e^{3} - 208 \, a^{3} b^{4} c^{2} d^{5} f^{4} x^{2} e^{3} + a^{4} b^{3} c d^{6} f^{4} x^{2} e^{3} - 3 \, a^{5} b^{2} d^{7} f^{4} x^{2} e^{3} + 4 \, b^{7} c^{7} f^{5} x e^{2} - 66 \, a b^{6} c^{6} d f^{5} x e^{2} + 156 \, a^{2} b^{5} c^{5} d^{2} f^{5} x e^{2} - 52 \, a^{3} b^{4} c^{4} d^{3} f^{5} x e^{2} - 52 \, a^{4} b^{3} c^{3} d^{4} f^{5} x e^{2} + 156 \, a^{5} b^{2} c^{2} d^{5} f^{5} x e^{2} - 66 \, a^{6} b c d^{6} f^{5} x e^{2} + 4 \, a^{7} d^{7} f^{5} x e^{2} + 7 \, a^{2} b^{5} c^{7} f^{6} e - 21 \, a^{3} b^{4} c^{6} d f^{6} e + 14 \, a^{4} b^{3} c^{5} d^{2} f^{6} e + 14 \, a^{5} b^{2} c^{4} d^{3} f^{6} e - 21 \, a^{6} b c^{3} d^{4} f^{6} e + 7 \, a^{7} c^{2} d^{5} f^{6} e + 24 \, b^{7} d^{7} f x^{4} e^{6} - 74 \, b^{7} c^{2} d^{5} f^{2} x^{3} e^{5} - 56 \, a b^{6} c d^{6} f^{2} x^{3} e^{5} - 74 \, a^{2} b^{5} d^{7} f^{2} x^{3} e^{5} + 32 \, b^{7} c^{4} d^{3} f^{3} x^{2} e^{4} + a b^{6} c^{3} d^{4} f^{3} x^{2} e^{4} + 234 \, a^{2} b^{5} c^{2} d^{5} f^{3} x^{2} e^{4} + a^{3} b^{4} c d^{6} f^{3} x^{2} e^{4} + 32 \, a^{4} b^{3} d^{7} f^{3} x^{2} e^{4} - 12 \, b^{7} c^{6} d f^{4} x e^{3} + 34 \, a b^{6} c^{5} d^{2} f^{4} x e^{3} - 52 \, a^{2} b^{5} c^{4} d^{3} f^{4} x e^{3} - 52 \, a^{4} b^{3} c^{2} d^{5} f^{4} x e^{3} + 34 \, a^{5} b^{2} c d^{6} f^{4} x e^{3} - 12 \, a^{6} b d^{7} f^{4} x e^{3} + 7 \, a b^{6} c^{7} f^{5} e^{2} - 26 \, a^{2} b^{5} c^{6} d f^{5} e^{2} + 52 \, a^{3} b^{4} c^{5} d^{2} f^{5} e^{2} - 78 \, a^{4} b^{3} c^{4} d^{3} f^{5} e^{2} + 52 \, a^{5} b^{2} c^{3} d^{4} f^{5} e^{2} - 26 \, a^{6} b c^{2} d^{5} f^{5} e^{2} + 7 \, a^{7} c d^{6} f^{5} e^{2} + 6 \, b^{7} c d^{6} f x^{3} e^{6} + 6 \, a b^{6} d^{7} f x^{3} e^{6} - 3 \, b^{7} c^{3} d^{4} f^{2} x^{2} e^{5} + 9 \, a b^{6} c^{2} d^{5} f^{2} x^{2} e^{5} + 9 \, a^{2} b^{5} c d^{6} f^{2} x^{2} e^{5} - 3 \, a^{3} b^{4} d^{7} f^{2} x^{2} e^{5} + 8 \, b^{7} c^{5} d^{2} f^{3} x e^{4} - 16 \, a b^{6} c^{4} d^{3} f^{3} x e^{4} - 52 \, a^{2} b^{5} c^{3} d^{4} f^{3} x e^{4} - 52 \, a^{3} b^{4} c^{2} d^{5} f^{3} x e^{4} - 16 \, a^{4} b^{3} c d^{6} f^{3} x e^{4} + 8 \, a^{5} b^{2} d^{7} f^{3} x e^{4} - b^{7} c^{7} f^{4} e^{3} - 21 \, a b^{6} c^{6} d f^{4} e^{3} + 52 \, a^{2} b^{5} c^{5} d^{2} f^{4} e^{3} + 52 \, a^{5} b^{2} c^{2} d^{5} f^{4} e^{3} - 21 \, a^{6} b c d^{6} f^{4} e^{3} - a^{7} d^{7} f^{4} e^{3} + 12 \, b^{7} d^{7} x^{3} e^{7} - 37 \, b^{7} c^{2} d^{5} f x^{2} e^{6} - 34 \, a b^{6} c d^{6} f x^{2} e^{6} - 37 \, a^{2} b^{5} d^{7} f x^{2} e^{6} + 8 \, b^{7} c^{4} d^{3} f^{2} x e^{5} + 34 \, a b^{6} c^{3} d^{4} f^{2} x e^{5} + 156 \, a^{2} b^{5} c^{2} d^{5} f^{2} x e^{5} + 34 \, a^{3} b^{4} c d^{6} f^{2} x e^{5} + 8 \, a^{4} b^{3} d^{7} f^{2} x e^{5} + 4 \, b^{7} c^{6} d f^{3} e^{4} + 14 \, a b^{6} c^{5} d^{2} f^{3} e^{4} - 78 \, a^{2} b^{5} c^{4} d^{3} f^{3} e^{4} - 78 \, a^{4} b^{3} c^{2} d^{5} f^{3} e^{4} + 14 \, a^{5} b^{2} c d^{6} f^{3} e^{4} + 4 \, a^{6} b d^{7} f^{3} e^{4} + 18 \, b^{7} c d^{6} x^{2} e^{7} + 18 \, a b^{6} d^{7} x^{2} e^{7} - 12 \, b^{7} c^{3} d^{4} f x e^{6} - 66 \, a b^{6} c^{2} d^{5} f x e^{6} - 66 \, a^{2} b^{5} c d^{6} f x e^{6} - 12 \, a^{3} b^{4} d^{7} f x e^{6} - 6 \, b^{7} c^{5} d^{2} f^{2} e^{5} + 14 \, a b^{6} c^{4} d^{3} f^{2} e^{5} + 52 \, a^{2} b^{5} c^{3} d^{4} f^{2} e^{5} + 52 \, a^{3} b^{4} c^{2} d^{5} f^{2} e^{5} + 14 \, a^{4} b^{3} c d^{6} f^{2} e^{5} - 6 \, a^{5} b^{2} d^{7} f^{2} e^{5} + 4 \, b^{7} c^{2} d^{5} x e^{7} + 28 \, a b^{6} c d^{6} x e^{7} + 4 \, a^{2} b^{5} d^{7} x e^{7} + 4 \, b^{7} c^{4} d^{3} f e^{6} - 21 \, a b^{6} c^{3} d^{4} f e^{6} - 26 \, a^{2} b^{5} c^{2} d^{5} f e^{6} - 21 \, a^{3} b^{4} c d^{6} f e^{6} + 4 \, a^{4} b^{3} d^{7} f e^{6} - b^{7} c^{3} d^{4} e^{7} + 7 \, a b^{6} c^{2} d^{5} e^{7} + 7 \, a^{2} b^{5} c d^{6} e^{7} - a^{3} b^{4} d^{7} e^{7}}{2 \, {\left(a^{4} b^{4} c^{8} f^{8} - 4 \, a^{5} b^{3} c^{7} d f^{8} + 6 \, a^{6} b^{2} c^{6} d^{2} f^{8} - 4 \, a^{7} b c^{5} d^{3} f^{8} + a^{8} c^{4} d^{4} f^{8} - 4 \, a^{3} b^{5} c^{8} f^{7} e + 12 \, a^{4} b^{4} c^{7} d f^{7} e - 8 \, a^{5} b^{3} c^{6} d^{2} f^{7} e - 8 \, a^{6} b^{2} c^{5} d^{3} f^{7} e + 12 \, a^{7} b c^{4} d^{4} f^{7} e - 4 \, a^{8} c^{3} d^{5} f^{7} e + 6 \, a^{2} b^{6} c^{8} f^{6} e^{2} - 8 \, a^{3} b^{5} c^{7} d f^{6} e^{2} - 22 \, a^{4} b^{4} c^{6} d^{2} f^{6} e^{2} + 48 \, a^{5} b^{3} c^{5} d^{3} f^{6} e^{2} - 22 \, a^{6} b^{2} c^{4} d^{4} f^{6} e^{2} - 8 \, a^{7} b c^{3} d^{5} f^{6} e^{2} + 6 \, a^{8} c^{2} d^{6} f^{6} e^{2} - 4 \, a b^{7} c^{8} f^{5} e^{3} - 8 \, a^{2} b^{6} c^{7} d f^{5} e^{3} + 48 \, a^{3} b^{5} c^{6} d^{2} f^{5} e^{3} - 36 \, a^{4} b^{4} c^{5} d^{3} f^{5} e^{3} - 36 \, a^{5} b^{3} c^{4} d^{4} f^{5} e^{3} + 48 \, a^{6} b^{2} c^{3} d^{5} f^{5} e^{3} - 8 \, a^{7} b c^{2} d^{6} f^{5} e^{3} - 4 \, a^{8} c d^{7} f^{5} e^{3} + b^{8} c^{8} f^{4} e^{4} + 12 \, a b^{7} c^{7} d f^{4} e^{4} - 22 \, a^{2} b^{6} c^{6} d^{2} f^{4} e^{4} - 36 \, a^{3} b^{5} c^{5} d^{3} f^{4} e^{4} + 90 \, a^{4} b^{4} c^{4} d^{4} f^{4} e^{4} - 36 \, a^{5} b^{3} c^{3} d^{5} f^{4} e^{4} - 22 \, a^{6} b^{2} c^{2} d^{6} f^{4} e^{4} + 12 \, a^{7} b c d^{7} f^{4} e^{4} + a^{8} d^{8} f^{4} e^{4} - 4 \, b^{8} c^{7} d f^{3} e^{5} - 8 \, a b^{7} c^{6} d^{2} f^{3} e^{5} + 48 \, a^{2} b^{6} c^{5} d^{3} f^{3} e^{5} - 36 \, a^{3} b^{5} c^{4} d^{4} f^{3} e^{5} - 36 \, a^{4} b^{4} c^{3} d^{5} f^{3} e^{5} + 48 \, a^{5} b^{3} c^{2} d^{6} f^{3} e^{5} - 8 \, a^{6} b^{2} c d^{7} f^{3} e^{5} - 4 \, a^{7} b d^{8} f^{3} e^{5} + 6 \, b^{8} c^{6} d^{2} f^{2} e^{6} - 8 \, a b^{7} c^{5} d^{3} f^{2} e^{6} - 22 \, a^{2} b^{6} c^{4} d^{4} f^{2} e^{6} + 48 \, a^{3} b^{5} c^{3} d^{5} f^{2} e^{6} - 22 \, a^{4} b^{4} c^{2} d^{6} f^{2} e^{6} - 8 \, a^{5} b^{3} c d^{7} f^{2} e^{6} + 6 \, a^{6} b^{2} d^{8} f^{2} e^{6} - 4 \, b^{8} c^{5} d^{3} f e^{7} + 12 \, a b^{7} c^{4} d^{4} f e^{7} - 8 \, a^{2} b^{6} c^{3} d^{5} f e^{7} - 8 \, a^{3} b^{5} c^{2} d^{6} f e^{7} + 12 \, a^{4} b^{4} c d^{7} f e^{7} - 4 \, a^{5} b^{3} d^{8} f e^{7} + b^{8} c^{4} d^{4} e^{8} - 4 \, a b^{7} c^{3} d^{5} e^{8} + 6 \, a^{2} b^{6} c^{2} d^{6} e^{8} - 4 \, a^{3} b^{5} c d^{7} e^{8} + a^{4} b^{4} d^{8} e^{8}\right)} {\left(b d f x^{3} + b c f x^{2} + a d f x^{2} + b d x^{2} e + a c f x + b c x e + a d x e + a c e\right)}^{2}}"," ",0,"-3*(2*b^8*c^2*f^2 - 7*a*b^7*c*d*f^2 + 7*a^2*b^6*d^2*f^2 + 3*b^8*c*d*f*e - 7*a*b^7*d^2*f*e + 2*b^8*d^2*e^2)*log(abs(b*x + a))/(a^5*b^6*c^5*f^5 - 5*a^6*b^5*c^4*d*f^5 + 10*a^7*b^4*c^3*d^2*f^5 - 10*a^8*b^3*c^2*d^3*f^5 + 5*a^9*b^2*c*d^4*f^5 - a^10*b*d^5*f^5 - 5*a^4*b^7*c^5*f^4*e + 25*a^5*b^6*c^4*d*f^4*e - 50*a^6*b^5*c^3*d^2*f^4*e + 50*a^7*b^4*c^2*d^3*f^4*e - 25*a^8*b^3*c*d^4*f^4*e + 5*a^9*b^2*d^5*f^4*e + 10*a^3*b^8*c^5*f^3*e^2 - 50*a^4*b^7*c^4*d*f^3*e^2 + 100*a^5*b^6*c^3*d^2*f^3*e^2 - 100*a^6*b^5*c^2*d^3*f^3*e^2 + 50*a^7*b^4*c*d^4*f^3*e^2 - 10*a^8*b^3*d^5*f^3*e^2 - 10*a^2*b^9*c^5*f^2*e^3 + 50*a^3*b^8*c^4*d*f^2*e^3 - 100*a^4*b^7*c^3*d^2*f^2*e^3 + 100*a^5*b^6*c^2*d^3*f^2*e^3 - 50*a^6*b^5*c*d^4*f^2*e^3 + 10*a^7*b^4*d^5*f^2*e^3 + 5*a*b^10*c^5*f*e^4 - 25*a^2*b^9*c^4*d*f*e^4 + 50*a^3*b^8*c^3*d^2*f*e^4 - 50*a^4*b^7*c^2*d^3*f*e^4 + 25*a^5*b^6*c*d^4*f*e^4 - 5*a^6*b^5*d^5*f*e^4 - b^11*c^5*e^5 + 5*a*b^10*c^4*d*e^5 - 10*a^2*b^9*c^3*d^2*e^5 + 10*a^3*b^8*c^2*d^3*e^5 - 5*a^4*b^7*c*d^4*e^5 + a^5*b^6*d^5*e^5) + 3*(7*b^2*c^2*d^6*f^2 - 7*a*b*c*d^7*f^2 + 2*a^2*d^8*f^2 - 7*b^2*c*d^7*f*e + 3*a*b*d^8*f*e + 2*b^2*d^8*e^2)*log(abs(d*x + c))/(b^5*c^10*d*f^5 - 5*a*b^4*c^9*d^2*f^5 + 10*a^2*b^3*c^8*d^3*f^5 - 10*a^3*b^2*c^7*d^4*f^5 + 5*a^4*b*c^6*d^5*f^5 - a^5*c^5*d^6*f^5 - 5*b^5*c^9*d^2*f^4*e + 25*a*b^4*c^8*d^3*f^4*e - 50*a^2*b^3*c^7*d^4*f^4*e + 50*a^3*b^2*c^6*d^5*f^4*e - 25*a^4*b*c^5*d^6*f^4*e + 5*a^5*c^4*d^7*f^4*e + 10*b^5*c^8*d^3*f^3*e^2 - 50*a*b^4*c^7*d^4*f^3*e^2 + 100*a^2*b^3*c^6*d^5*f^3*e^2 - 100*a^3*b^2*c^5*d^6*f^3*e^2 + 50*a^4*b*c^4*d^7*f^3*e^2 - 10*a^5*c^3*d^8*f^3*e^2 - 10*b^5*c^7*d^4*f^2*e^3 + 50*a*b^4*c^6*d^5*f^2*e^3 - 100*a^2*b^3*c^5*d^6*f^2*e^3 + 100*a^3*b^2*c^4*d^7*f^2*e^3 - 50*a^4*b*c^3*d^8*f^2*e^3 + 10*a^5*c^2*d^9*f^2*e^3 + 5*b^5*c^6*d^5*f*e^4 - 25*a*b^4*c^5*d^6*f*e^4 + 50*a^2*b^3*c^4*d^7*f*e^4 - 50*a^3*b^2*c^3*d^8*f*e^4 + 25*a^4*b*c^2*d^9*f*e^4 - 5*a^5*c*d^10*f*e^4 - b^5*c^5*d^6*e^5 + 5*a*b^4*c^4*d^7*e^5 - 10*a^2*b^3*c^3*d^8*e^5 + 10*a^3*b^2*c^2*d^9*e^5 - 5*a^4*b*c*d^10*e^5 + a^5*d^11*e^5) + 3*(2*b^2*c^2*f^8 + 3*a*b*c*d*f^8 + 2*a^2*d^2*f^8 - 7*b^2*c*d*f^7*e - 7*a*b*d^2*f^7*e + 7*b^2*d^2*f^6*e^2)*log(abs(f*x + e))/(a^5*c^5*f^11 - 5*a^4*b*c^5*f^10*e - 5*a^5*c^4*d*f^10*e + 10*a^3*b^2*c^5*f^9*e^2 + 25*a^4*b*c^4*d*f^9*e^2 + 10*a^5*c^3*d^2*f^9*e^2 - 10*a^2*b^3*c^5*f^8*e^3 - 50*a^3*b^2*c^4*d*f^8*e^3 - 50*a^4*b*c^3*d^2*f^8*e^3 - 10*a^5*c^2*d^3*f^8*e^3 + 5*a*b^4*c^5*f^7*e^4 + 50*a^2*b^3*c^4*d*f^7*e^4 + 100*a^3*b^2*c^3*d^2*f^7*e^4 + 50*a^4*b*c^2*d^3*f^7*e^4 + 5*a^5*c*d^4*f^7*e^4 - b^5*c^5*f^6*e^5 - 25*a*b^4*c^4*d*f^6*e^5 - 100*a^2*b^3*c^3*d^2*f^6*e^5 - 100*a^3*b^2*c^2*d^3*f^6*e^5 - 25*a^4*b*c*d^4*f^6*e^5 - a^5*d^5*f^6*e^5 + 5*b^5*c^4*d*f^5*e^6 + 50*a*b^4*c^3*d^2*f^5*e^6 + 100*a^2*b^3*c^2*d^3*f^5*e^6 + 50*a^3*b^2*c*d^4*f^5*e^6 + 5*a^4*b*d^5*f^5*e^6 - 10*b^5*c^3*d^2*f^4*e^7 - 50*a*b^4*c^2*d^3*f^4*e^7 - 50*a^2*b^3*c*d^4*f^4*e^7 - 10*a^3*b^2*d^5*f^4*e^7 + 10*b^5*c^2*d^3*f^3*e^8 + 25*a*b^4*c*d^4*f^3*e^8 + 10*a^2*b^3*d^5*f^3*e^8 - 5*b^5*c*d^4*f^2*e^9 - 5*a*b^4*d^5*f^2*e^9 + b^5*d^5*f*e^10) + 1/2*(12*b^7*c^5*d^2*f^7*x^5 - 30*a*b^6*c^4*d^3*f^7*x^5 + 12*a^2*b^5*c^3*d^4*f^7*x^5 + 12*a^3*b^4*c^2*d^5*f^7*x^5 - 30*a^4*b^3*c*d^6*f^7*x^5 + 12*a^5*b^2*d^7*f^7*x^5 - 30*b^7*c^4*d^3*f^6*x^5*e + 96*a*b^6*c^3*d^4*f^6*x^5*e - 72*a^2*b^5*c^2*d^5*f^6*x^5*e + 96*a^3*b^4*c*d^6*f^6*x^5*e - 30*a^4*b^3*d^7*f^6*x^5*e + 24*b^7*c^6*d*f^7*x^4 - 42*a*b^6*c^5*d^2*f^7*x^4 - 21*a^2*b^5*c^4*d^3*f^7*x^4 + 42*a^3*b^4*c^3*d^4*f^7*x^4 - 21*a^4*b^3*c^2*d^5*f^7*x^4 - 42*a^5*b^2*c*d^6*f^7*x^4 + 24*a^6*b*d^7*f^7*x^4 + 12*b^7*c^3*d^4*f^5*x^5*e^2 - 72*a*b^6*c^2*d^5*f^5*x^5*e^2 - 72*a^2*b^5*c*d^6*f^5*x^5*e^2 + 12*a^3*b^4*d^7*f^5*x^5*e^2 - 42*b^7*c^5*d^2*f^6*x^4*e + 102*a*b^6*c^4*d^3*f^6*x^4*e + 18*a^2*b^5*c^3*d^4*f^6*x^4*e + 18*a^3*b^4*c^2*d^5*f^6*x^4*e + 102*a^4*b^3*c*d^6*f^6*x^4*e - 42*a^5*b^2*d^7*f^6*x^4*e + 12*b^7*c^7*f^7*x^3 + 6*a*b^6*c^6*d*f^7*x^3 - 74*a^2*b^5*c^5*d^2*f^7*x^3 + 38*a^3*b^4*c^4*d^3*f^7*x^3 + 38*a^4*b^3*c^3*d^4*f^7*x^3 - 74*a^5*b^2*c^2*d^5*f^7*x^3 + 6*a^6*b*c*d^6*f^7*x^3 + 12*a^7*d^7*f^7*x^3 + 12*b^7*c^2*d^5*f^4*x^5*e^3 + 96*a*b^6*c*d^6*f^4*x^5*e^3 + 12*a^2*b^5*d^7*f^4*x^5*e^3 - 21*b^7*c^4*d^3*f^5*x^4*e^2 + 18*a*b^6*c^3*d^4*f^5*x^4*e^2 - 234*a^2*b^5*c^2*d^5*f^5*x^4*e^2 + 18*a^3*b^4*c*d^6*f^5*x^4*e^2 - 21*a^4*b^3*d^7*f^5*x^4*e^2 + 6*b^7*c^6*d*f^6*x^3*e - 56*a*b^6*c^5*d^2*f^6*x^3*e + 172*a^2*b^5*c^4*d^3*f^6*x^3*e - 136*a^3*b^4*c^3*d^4*f^6*x^3*e + 172*a^4*b^3*c^2*d^5*f^6*x^3*e - 56*a^5*b^2*c*d^6*f^6*x^3*e + 6*a^6*b*d^7*f^6*x^3*e + 18*a*b^6*c^7*f^7*x^2 - 37*a^2*b^5*c^6*d*f^7*x^2 - 3*a^3*b^4*c^5*d^2*f^7*x^2 + 32*a^4*b^3*c^4*d^3*f^7*x^2 - 3*a^5*b^2*c^3*d^4*f^7*x^2 - 37*a^6*b*c^2*d^5*f^7*x^2 + 18*a^7*c*d^6*f^7*x^2 - 30*b^7*c*d^6*f^3*x^5*e^4 - 30*a*b^6*d^7*f^3*x^5*e^4 + 42*b^7*c^3*d^4*f^4*x^4*e^3 + 18*a*b^6*c^2*d^5*f^4*x^4*e^3 + 18*a^2*b^5*c*d^6*f^4*x^4*e^3 + 42*a^3*b^4*d^7*f^4*x^4*e^3 - 74*b^7*c^5*d^2*f^5*x^3*e^2 + 172*a*b^6*c^4*d^3*f^5*x^3*e^2 - 104*a^2*b^5*c^3*d^4*f^5*x^3*e^2 - 104*a^3*b^4*c^2*d^5*f^5*x^3*e^2 + 172*a^4*b^3*c*d^6*f^5*x^3*e^2 - 74*a^5*b^2*d^7*f^5*x^3*e^2 + 18*b^7*c^7*f^6*x^2*e - 34*a*b^6*c^6*d*f^6*x^2*e + 9*a^2*b^5*c^5*d^2*f^6*x^2*e + a^3*b^4*c^4*d^3*f^6*x^2*e + a^4*b^3*c^3*d^4*f^6*x^2*e + 9*a^5*b^2*c^2*d^5*f^6*x^2*e - 34*a^6*b*c*d^6*f^6*x^2*e + 18*a^7*d^7*f^6*x^2*e + 4*a^2*b^5*c^7*f^7*x - 12*a^3*b^4*c^6*d*f^7*x + 8*a^4*b^3*c^5*d^2*f^7*x + 8*a^5*b^2*c^4*d^3*f^7*x - 12*a^6*b*c^3*d^4*f^7*x + 4*a^7*c^2*d^5*f^7*x + 12*b^7*d^7*f^2*x^5*e^5 - 21*b^7*c^2*d^5*f^3*x^4*e^4 + 102*a*b^6*c*d^6*f^3*x^4*e^4 - 21*a^2*b^5*d^7*f^3*x^4*e^4 + 38*b^7*c^4*d^3*f^4*x^3*e^3 - 136*a*b^6*c^3*d^4*f^4*x^3*e^3 - 104*a^2*b^5*c^2*d^5*f^4*x^3*e^3 - 136*a^3*b^4*c*d^6*f^4*x^3*e^3 + 38*a^4*b^3*d^7*f^4*x^3*e^3 - 37*b^7*c^6*d*f^5*x^2*e^2 + 9*a*b^6*c^5*d^2*f^5*x^2*e^2 + 234*a^2*b^5*c^4*d^3*f^5*x^2*e^2 - 208*a^3*b^4*c^3*d^4*f^5*x^2*e^2 + 234*a^4*b^3*c^2*d^5*f^5*x^2*e^2 + 9*a^5*b^2*c*d^6*f^5*x^2*e^2 - 37*a^6*b*d^7*f^5*x^2*e^2 + 28*a*b^6*c^7*f^6*x*e - 66*a^2*b^5*c^6*d*f^6*x*e + 34*a^3*b^4*c^5*d^2*f^6*x*e - 16*a^4*b^3*c^4*d^3*f^6*x*e + 34*a^5*b^2*c^3*d^4*f^6*x*e - 66*a^6*b*c^2*d^5*f^6*x*e + 28*a^7*c*d^6*f^6*x*e - a^3*b^4*c^7*f^7 + 4*a^4*b^3*c^6*d*f^7 - 6*a^5*b^2*c^5*d^2*f^7 + 4*a^6*b*c^4*d^3*f^7 - a^7*c^3*d^4*f^7 - 42*b^7*c*d^6*f^2*x^4*e^5 - 42*a*b^6*d^7*f^2*x^4*e^5 + 38*b^7*c^3*d^4*f^3*x^3*e^4 + 172*a*b^6*c^2*d^5*f^3*x^3*e^4 + 172*a^2*b^5*c*d^6*f^3*x^3*e^4 + 38*a^3*b^4*d^7*f^3*x^3*e^4 - 3*b^7*c^5*d^2*f^4*x^2*e^3 + a*b^6*c^4*d^3*f^4*x^2*e^3 - 208*a^2*b^5*c^3*d^4*f^4*x^2*e^3 - 208*a^3*b^4*c^2*d^5*f^4*x^2*e^3 + a^4*b^3*c*d^6*f^4*x^2*e^3 - 3*a^5*b^2*d^7*f^4*x^2*e^3 + 4*b^7*c^7*f^5*x*e^2 - 66*a*b^6*c^6*d*f^5*x*e^2 + 156*a^2*b^5*c^5*d^2*f^5*x*e^2 - 52*a^3*b^4*c^4*d^3*f^5*x*e^2 - 52*a^4*b^3*c^3*d^4*f^5*x*e^2 + 156*a^5*b^2*c^2*d^5*f^5*x*e^2 - 66*a^6*b*c*d^6*f^5*x*e^2 + 4*a^7*d^7*f^5*x*e^2 + 7*a^2*b^5*c^7*f^6*e - 21*a^3*b^4*c^6*d*f^6*e + 14*a^4*b^3*c^5*d^2*f^6*e + 14*a^5*b^2*c^4*d^3*f^6*e - 21*a^6*b*c^3*d^4*f^6*e + 7*a^7*c^2*d^5*f^6*e + 24*b^7*d^7*f*x^4*e^6 - 74*b^7*c^2*d^5*f^2*x^3*e^5 - 56*a*b^6*c*d^6*f^2*x^3*e^5 - 74*a^2*b^5*d^7*f^2*x^3*e^5 + 32*b^7*c^4*d^3*f^3*x^2*e^4 + a*b^6*c^3*d^4*f^3*x^2*e^4 + 234*a^2*b^5*c^2*d^5*f^3*x^2*e^4 + a^3*b^4*c*d^6*f^3*x^2*e^4 + 32*a^4*b^3*d^7*f^3*x^2*e^4 - 12*b^7*c^6*d*f^4*x*e^3 + 34*a*b^6*c^5*d^2*f^4*x*e^3 - 52*a^2*b^5*c^4*d^3*f^4*x*e^3 - 52*a^4*b^3*c^2*d^5*f^4*x*e^3 + 34*a^5*b^2*c*d^6*f^4*x*e^3 - 12*a^6*b*d^7*f^4*x*e^3 + 7*a*b^6*c^7*f^5*e^2 - 26*a^2*b^5*c^6*d*f^5*e^2 + 52*a^3*b^4*c^5*d^2*f^5*e^2 - 78*a^4*b^3*c^4*d^3*f^5*e^2 + 52*a^5*b^2*c^3*d^4*f^5*e^2 - 26*a^6*b*c^2*d^5*f^5*e^2 + 7*a^7*c*d^6*f^5*e^2 + 6*b^7*c*d^6*f*x^3*e^6 + 6*a*b^6*d^7*f*x^3*e^6 - 3*b^7*c^3*d^4*f^2*x^2*e^5 + 9*a*b^6*c^2*d^5*f^2*x^2*e^5 + 9*a^2*b^5*c*d^6*f^2*x^2*e^5 - 3*a^3*b^4*d^7*f^2*x^2*e^5 + 8*b^7*c^5*d^2*f^3*x*e^4 - 16*a*b^6*c^4*d^3*f^3*x*e^4 - 52*a^2*b^5*c^3*d^4*f^3*x*e^4 - 52*a^3*b^4*c^2*d^5*f^3*x*e^4 - 16*a^4*b^3*c*d^6*f^3*x*e^4 + 8*a^5*b^2*d^7*f^3*x*e^4 - b^7*c^7*f^4*e^3 - 21*a*b^6*c^6*d*f^4*e^3 + 52*a^2*b^5*c^5*d^2*f^4*e^3 + 52*a^5*b^2*c^2*d^5*f^4*e^3 - 21*a^6*b*c*d^6*f^4*e^3 - a^7*d^7*f^4*e^3 + 12*b^7*d^7*x^3*e^7 - 37*b^7*c^2*d^5*f*x^2*e^6 - 34*a*b^6*c*d^6*f*x^2*e^6 - 37*a^2*b^5*d^7*f*x^2*e^6 + 8*b^7*c^4*d^3*f^2*x*e^5 + 34*a*b^6*c^3*d^4*f^2*x*e^5 + 156*a^2*b^5*c^2*d^5*f^2*x*e^5 + 34*a^3*b^4*c*d^6*f^2*x*e^5 + 8*a^4*b^3*d^7*f^2*x*e^5 + 4*b^7*c^6*d*f^3*e^4 + 14*a*b^6*c^5*d^2*f^3*e^4 - 78*a^2*b^5*c^4*d^3*f^3*e^4 - 78*a^4*b^3*c^2*d^5*f^3*e^4 + 14*a^5*b^2*c*d^6*f^3*e^4 + 4*a^6*b*d^7*f^3*e^4 + 18*b^7*c*d^6*x^2*e^7 + 18*a*b^6*d^7*x^2*e^7 - 12*b^7*c^3*d^4*f*x*e^6 - 66*a*b^6*c^2*d^5*f*x*e^6 - 66*a^2*b^5*c*d^6*f*x*e^6 - 12*a^3*b^4*d^7*f*x*e^6 - 6*b^7*c^5*d^2*f^2*e^5 + 14*a*b^6*c^4*d^3*f^2*e^5 + 52*a^2*b^5*c^3*d^4*f^2*e^5 + 52*a^3*b^4*c^2*d^5*f^2*e^5 + 14*a^4*b^3*c*d^6*f^2*e^5 - 6*a^5*b^2*d^7*f^2*e^5 + 4*b^7*c^2*d^5*x*e^7 + 28*a*b^6*c*d^6*x*e^7 + 4*a^2*b^5*d^7*x*e^7 + 4*b^7*c^4*d^3*f*e^6 - 21*a*b^6*c^3*d^4*f*e^6 - 26*a^2*b^5*c^2*d^5*f*e^6 - 21*a^3*b^4*c*d^6*f*e^6 + 4*a^4*b^3*d^7*f*e^6 - b^7*c^3*d^4*e^7 + 7*a*b^6*c^2*d^5*e^7 + 7*a^2*b^5*c*d^6*e^7 - a^3*b^4*d^7*e^7)/((a^4*b^4*c^8*f^8 - 4*a^5*b^3*c^7*d*f^8 + 6*a^6*b^2*c^6*d^2*f^8 - 4*a^7*b*c^5*d^3*f^8 + a^8*c^4*d^4*f^8 - 4*a^3*b^5*c^8*f^7*e + 12*a^4*b^4*c^7*d*f^7*e - 8*a^5*b^3*c^6*d^2*f^7*e - 8*a^6*b^2*c^5*d^3*f^7*e + 12*a^7*b*c^4*d^4*f^7*e - 4*a^8*c^3*d^5*f^7*e + 6*a^2*b^6*c^8*f^6*e^2 - 8*a^3*b^5*c^7*d*f^6*e^2 - 22*a^4*b^4*c^6*d^2*f^6*e^2 + 48*a^5*b^3*c^5*d^3*f^6*e^2 - 22*a^6*b^2*c^4*d^4*f^6*e^2 - 8*a^7*b*c^3*d^5*f^6*e^2 + 6*a^8*c^2*d^6*f^6*e^2 - 4*a*b^7*c^8*f^5*e^3 - 8*a^2*b^6*c^7*d*f^5*e^3 + 48*a^3*b^5*c^6*d^2*f^5*e^3 - 36*a^4*b^4*c^5*d^3*f^5*e^3 - 36*a^5*b^3*c^4*d^4*f^5*e^3 + 48*a^6*b^2*c^3*d^5*f^5*e^3 - 8*a^7*b*c^2*d^6*f^5*e^3 - 4*a^8*c*d^7*f^5*e^3 + b^8*c^8*f^4*e^4 + 12*a*b^7*c^7*d*f^4*e^4 - 22*a^2*b^6*c^6*d^2*f^4*e^4 - 36*a^3*b^5*c^5*d^3*f^4*e^4 + 90*a^4*b^4*c^4*d^4*f^4*e^4 - 36*a^5*b^3*c^3*d^5*f^4*e^4 - 22*a^6*b^2*c^2*d^6*f^4*e^4 + 12*a^7*b*c*d^7*f^4*e^4 + a^8*d^8*f^4*e^4 - 4*b^8*c^7*d*f^3*e^5 - 8*a*b^7*c^6*d^2*f^3*e^5 + 48*a^2*b^6*c^5*d^3*f^3*e^5 - 36*a^3*b^5*c^4*d^4*f^3*e^5 - 36*a^4*b^4*c^3*d^5*f^3*e^5 + 48*a^5*b^3*c^2*d^6*f^3*e^5 - 8*a^6*b^2*c*d^7*f^3*e^5 - 4*a^7*b*d^8*f^3*e^5 + 6*b^8*c^6*d^2*f^2*e^6 - 8*a*b^7*c^5*d^3*f^2*e^6 - 22*a^2*b^6*c^4*d^4*f^2*e^6 + 48*a^3*b^5*c^3*d^5*f^2*e^6 - 22*a^4*b^4*c^2*d^6*f^2*e^6 - 8*a^5*b^3*c*d^7*f^2*e^6 + 6*a^6*b^2*d^8*f^2*e^6 - 4*b^8*c^5*d^3*f*e^7 + 12*a*b^7*c^4*d^4*f*e^7 - 8*a^2*b^6*c^3*d^5*f*e^7 - 8*a^3*b^5*c^2*d^6*f*e^7 + 12*a^4*b^4*c*d^7*f*e^7 - 4*a^5*b^3*d^8*f*e^7 + b^8*c^4*d^4*e^8 - 4*a*b^7*c^3*d^5*e^8 + 6*a^2*b^6*c^2*d^6*e^8 - 4*a^3*b^5*c*d^7*e^8 + a^4*b^4*d^8*e^8)*(b*d*f*x^3 + b*c*f*x^2 + a*d*f*x^2 + b*d*x^2*e + a*c*f*x + b*c*x*e + a*d*x*e + a*c*e)^2)","B",0
21,1,20,0,0.305227," ","integrate(1/(x^3+x^2+x+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(x\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right) + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*arctan(x) - 1/4*log(x^2 + 1) + 1/2*log(abs(x + 1))","A",0
22,1,26,0,0.352490," ","integrate(1/(16*x^3-4*x^2+4*x-1),x, algorithm=""giac"")","-\frac{1}{10} \, \arctan\left(2 \, x\right) - \frac{1}{10} \, \log\left(4 \, x^{2} + 1\right) + \frac{1}{5} \, \log\left({\left| 4 \, x - 1 \right|}\right)"," ",0,"-1/10*arctan(2*x) - 1/10*log(4*x^2 + 1) + 1/5*log(abs(4*x - 1))","A",0
23,1,8,0,0.273675," ","integrate(1/d/x^3,x, algorithm=""giac"")","-\frac{1}{2 \, d x^{2}}"," ",0,"-1/2/(d*x^2)","A",0
24,1,30,0,0.361670," ","integrate(1/(d*x^3+c*x^2),x, algorithm=""giac"")","\frac{d \log\left({\left| d x + c \right|}\right)}{c^{2}} - \frac{d \log\left({\left| x \right|}\right)}{c^{2}} - \frac{1}{c x}"," ",0,"d*log(abs(d*x + c))/c^2 - d*log(abs(x))/c^2 - 1/(c*x)","A",0
25,1,24,0,0.296159," ","integrate(1/(d*x^3+b*x),x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, b} - \frac{\log\left({\left| d x^{2} + b \right|}\right)}{2 \, b}"," ",0,"1/2*log(x^2)/b - 1/2*log(abs(d*x^2 + b))/b","A",0
26,1,62,0,0.294095," ","integrate(1/(d*x^3+c*x^2+b*x),x, algorithm=""giac"")","-\frac{c \arctan\left(\frac{2 \, d x + c}{\sqrt{-c^{2} + 4 \, b d}}\right)}{\sqrt{-c^{2} + 4 \, b d} b} - \frac{\log\left(d x^{2} + c x + b\right)}{2 \, b} + \frac{\log\left({\left| x \right|}\right)}{b}"," ",0,"-c*arctan((2*d*x + c)/sqrt(-c^2 + 4*b*d))/(sqrt(-c^2 + 4*b*d)*b) - 1/2*log(d*x^2 + c*x + b)/b + log(abs(x))/b","A",0
27,1,112,0,0.264152," ","integrate(1/(d*x^3+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{\sqrt{3} \left(-a d^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{d}\right)^{\frac{1}{3}}}\right)}{3 \, a d} + \frac{\left(-a d^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{d}\right)^{\frac{1}{3}} + \left(-\frac{a}{d}\right)^{\frac{2}{3}}\right)}{6 \, a d}"," ",0,"-1/3*(-a/d)^(1/3)*log(abs(x - (-a/d)^(1/3)))/a + 1/3*sqrt(3)*(-a*d^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/d)^(1/3))/(-a/d)^(1/3))/(a*d) + 1/6*(-a*d^2)^(1/3)*log(x^2 + x*(-a/d)^(1/3) + (-a/d)^(2/3))/(a*d)","A",0
28,1,16,0,0.308730," ","integrate((d*x^3)^n,x, algorithm=""giac"")","\frac{\left(d x^{3}\right)^{n} x}{3 \, n + 1}"," ",0,"(d*x^3)^n*x/(3*n + 1)","A",0
29,0,0,0,0.000000," ","integrate((d*x^3+c*x^2)^n,x, algorithm=""giac"")","\int {\left(d x^{3} + c x^{2}\right)}^{n}\,{d x}"," ",0,"integrate((d*x^3 + c*x^2)^n, x)","F",0
30,0,0,0,0.000000," ","integrate((d*x^3+b*x)^n,x, algorithm=""giac"")","\int {\left(d x^{3} + b x\right)}^{n}\,{d x}"," ",0,"integrate((d*x^3 + b*x)^n, x)","F",0
31,0,0,0,0.000000," ","integrate((d*x^3+c*x^2+b*x)^n,x, algorithm=""giac"")","\int {\left(d x^{3} + c x^{2} + b x\right)}^{n}\,{d x}"," ",0,"integrate((d*x^3 + c*x^2 + b*x)^n, x)","F",0
32,0,0,0,0.000000," ","integrate((d*x^3+a)^n,x, algorithm=""giac"")","\int {\left(d x^{3} + a\right)}^{n}\,{d x}"," ",0,"integrate((d*x^3 + a)^n, x)","F",0
33,1,277,0,0.235010," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^4,x, algorithm=""giac"")","\frac{1}{17} \, d^{8} x^{17} + c d^{7} x^{16} + \frac{112}{15} \, c^{2} d^{6} x^{15} + 32 \, c^{3} d^{5} x^{14} + \frac{1120}{13} \, c^{4} d^{4} x^{13} + \frac{16}{13} \, a c d^{6} x^{13} + \frac{448}{3} \, c^{5} d^{3} x^{12} + 16 \, a c^{2} d^{5} x^{12} + \frac{1792}{11} \, c^{6} d^{2} x^{11} + \frac{960}{11} \, a c^{3} d^{4} x^{11} + \frac{512}{5} \, c^{7} d x^{10} + 256 \, a c^{4} d^{3} x^{10} + \frac{256}{9} \, c^{8} x^{9} + \frac{1280}{3} \, a c^{5} d^{2} x^{9} + \frac{32}{3} \, a^{2} c^{2} d^{4} x^{9} + 384 \, a c^{6} d x^{8} + 96 \, a^{2} c^{3} d^{3} x^{8} + \frac{1024}{7} \, a c^{7} x^{7} + \frac{2304}{7} \, a^{2} c^{4} d^{2} x^{7} + 512 \, a^{2} c^{5} d x^{6} + \frac{1536}{5} \, a^{2} c^{6} x^{5} + \frac{256}{5} \, a^{3} c^{3} d^{2} x^{5} + 256 \, a^{3} c^{4} d x^{4} + \frac{1024}{3} \, a^{3} c^{5} x^{3} + 256 \, a^{4} c^{4} x"," ",0,"1/17*d^8*x^17 + c*d^7*x^16 + 112/15*c^2*d^6*x^15 + 32*c^3*d^5*x^14 + 1120/13*c^4*d^4*x^13 + 16/13*a*c*d^6*x^13 + 448/3*c^5*d^3*x^12 + 16*a*c^2*d^5*x^12 + 1792/11*c^6*d^2*x^11 + 960/11*a*c^3*d^4*x^11 + 512/5*c^7*d*x^10 + 256*a*c^4*d^3*x^10 + 256/9*c^8*x^9 + 1280/3*a*c^5*d^2*x^9 + 32/3*a^2*c^2*d^4*x^9 + 384*a*c^6*d*x^8 + 96*a^2*c^3*d^3*x^8 + 1024/7*a*c^7*x^7 + 2304/7*a^2*c^4*d^2*x^7 + 512*a^2*c^5*d*x^6 + 1536/5*a^2*c^6*x^5 + 256/5*a^3*c^3*d^2*x^5 + 256*a^3*c^4*d*x^4 + 1024/3*a^3*c^5*x^3 + 256*a^4*c^4*x","A",0
34,1,166,0,0.243242," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^3,x, algorithm=""giac"")","\frac{1}{13} \, d^{6} x^{13} + c d^{5} x^{12} + \frac{60}{11} \, c^{2} d^{4} x^{11} + 16 \, c^{3} d^{3} x^{10} + \frac{80}{3} \, c^{4} d^{2} x^{9} + \frac{4}{3} \, a c d^{4} x^{9} + 24 \, c^{5} d x^{8} + 12 \, a c^{2} d^{3} x^{8} + \frac{64}{7} \, c^{6} x^{7} + \frac{288}{7} \, a c^{3} d^{2} x^{7} + 64 \, a c^{4} d x^{6} + \frac{192}{5} \, a c^{5} x^{5} + \frac{48}{5} \, a^{2} c^{2} d^{2} x^{5} + 48 \, a^{2} c^{3} d x^{4} + 64 \, a^{2} c^{4} x^{3} + 64 \, a^{3} c^{3} x"," ",0,"1/13*d^6*x^13 + c*d^5*x^12 + 60/11*c^2*d^4*x^11 + 16*c^3*d^3*x^10 + 80/3*c^4*d^2*x^9 + 4/3*a*c*d^4*x^9 + 24*c^5*d*x^8 + 12*a*c^2*d^3*x^8 + 64/7*c^6*x^7 + 288/7*a*c^3*d^2*x^7 + 64*a*c^4*d*x^6 + 192/5*a*c^5*x^5 + 48/5*a^2*c^2*d^2*x^5 + 48*a^2*c^3*d*x^4 + 64*a^2*c^4*x^3 + 64*a^3*c^3*x","A",0
35,1,83,0,0.252348," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^2,x, algorithm=""giac"")","\frac{1}{9} \, d^{4} x^{9} + c d^{3} x^{8} + \frac{24}{7} \, c^{2} d^{2} x^{7} + \frac{16}{3} \, c^{3} d x^{6} + \frac{16}{5} \, c^{4} x^{5} + \frac{8}{5} \, a c d^{2} x^{5} + 8 \, a c^{2} d x^{4} + \frac{32}{3} \, a c^{3} x^{3} + 16 \, a^{2} c^{2} x"," ",0,"1/9*d^4*x^9 + c*d^3*x^8 + 24/7*c^2*d^2*x^7 + 16/3*c^3*d*x^6 + 16/5*c^4*x^5 + 8/5*a*c*d^2*x^5 + 8*a*c^2*d*x^4 + 32/3*a*c^3*x^3 + 16*a^2*c^2*x","A",0
36,1,28,0,0.267806," ","integrate(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c,x, algorithm=""giac"")","\frac{1}{5} \, d^{2} x^{5} + c d x^{4} + \frac{4}{3} \, c^{2} x^{3} + 4 \, a c x"," ",0,"1/5*d^2*x^5 + c*d*x^4 + 4/3*c^2*x^3 + 4*a*c*x","A",0
37,1,603,0,0.336279," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c),x, algorithm=""giac"")","-\frac{\log\left(x + \sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{4 \, {\left(d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{3} - 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}\right)}} + \frac{\log\left(x - \sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{4 \, {\left(d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{3} + 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}\right)}} - \frac{\log\left(x + \sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{4 \, {\left(d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{3} - 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}\right)}} + \frac{\log\left(x - \sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{4 \, {\left(d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{3} + 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}\right)}}"," ",0,"-1/4*log(x + sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)^3 - 3*c*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 + 2*c^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)) + 1/4*log(x - sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)^3 + 3*c*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)) - 1/4*log(x + sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)^3 - 3*c*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 + 2*c^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)) + 1/4*log(x - sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)^3 + 3*c*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d))","A",0
38,1,1057,0,0.367397," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(c d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} - 2 \, c^{2} d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)} + 2 \, c^{3} + 12 \, a d^{2}\right)} \log\left(x + \sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{3} - 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}} - \frac{{\left(c d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)} + 2 \, c^{3} + 12 \, a d^{2}\right)} \log\left(x - \sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{d^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{3} + 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} + 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}} + \frac{{\left(c d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} - 2 \, c^{2} d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)} + 2 \, c^{3} + 12 \, a d^{2}\right)} \log\left(x + \sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{3} - 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}} - \frac{{\left(c d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)} + 2 \, c^{3} + 12 \, a d^{2}\right)} \log\left(x - \sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} + \frac{c}{d}\right)}{d^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{3} + 3 \, c d {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}^{2} + 2 \, c^{2} {\left(\sqrt{\frac{c^{2} d^{2} - 2 \, \sqrt{-a c} d^{3}}{d^{4}}} - \frac{c}{d}\right)}}}{64 \, {\left(a c^{4} + 4 \, a^{2} c d^{2}\right)}} + \frac{c d^{2} x^{3} + 3 \, c^{2} d x^{2} + 2 \, c^{3} x + 4 \, a d^{2} x + 4 \, a c d}{16 \, {\left(d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c\right)} {\left(a c^{4} + 4 \, a^{2} c d^{2}\right)}}"," ",0,"-1/64*((c*d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 - 2*c^2*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d) + 2*c^3 + 12*a*d^2)*log(x + sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)^3 - 3*c*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 + 2*c^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)) - (c*d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d) + 2*c^3 + 12*a*d^2)*log(x - sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)^3 + 3*c*d*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*(sqrt((c^2*d^2 + 2*sqrt(-a*c)*d^3)/d^4) - c/d)) + (c*d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 - 2*c^2*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d) + 2*c^3 + 12*a*d^2)*log(x + sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)^3 - 3*c*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)^2 + 2*c^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)) - (c*d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d) + 2*c^3 + 12*a*d^2)*log(x - sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) + c/d)/(d^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)^3 + 3*c*d*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)^2 + 2*c^2*(sqrt((c^2*d^2 - 2*sqrt(-a*c)*d^3)/d^4) - c/d)))/(a*c^4 + 4*a^2*c*d^2) + 1/16*(c*d^2*x^3 + 3*c^2*d*x^2 + 2*c^3*x + 4*a*d^2*x + 4*a*c*d)/((d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c)*(a*c^4 + 4*a^2*c*d^2))","A",0
39,1,323,0,0.308114," ","integrate((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^4,x, algorithm=""giac"")","\frac{4096}{17} \, x^{17} e^{12} + 1024 \, d x^{16} e^{11} + \frac{8192}{5} \, d^{2} x^{15} e^{10} + 1024 \, d^{3} x^{14} e^{9} - \frac{2048}{13} \, d^{4} x^{13} e^{8} - 512 \, d^{5} x^{12} e^{7} - \frac{1664}{11} \, d^{6} x^{11} e^{6} + \frac{384}{5} \, d^{7} x^{10} e^{5} + \frac{128}{3} \, d^{8} x^{9} e^{4} - 4 \, d^{9} x^{8} e^{3} - \frac{32}{7} \, d^{10} x^{7} e^{2} + \frac{1}{5} \, d^{12} x^{5} + \frac{16384}{13} \, a x^{13} e^{11} + 4096 \, a d x^{12} e^{10} + \frac{49152}{11} \, a d^{2} x^{11} e^{9} + 1024 \, a d^{3} x^{10} e^{8} - \frac{4096}{3} \, a d^{4} x^{9} e^{7} - 768 \, a d^{5} x^{8} e^{6} + \frac{768}{7} \, a d^{6} x^{7} e^{5} + 128 \, a d^{7} x^{6} e^{4} - 8 \, a d^{9} x^{4} e^{2} + \frac{8192}{3} \, a^{2} x^{9} e^{10} + 6144 \, a^{2} d x^{8} e^{9} + \frac{24576}{7} \, a^{2} d^{2} x^{7} e^{8} - 1024 \, a^{2} d^{3} x^{6} e^{7} - \frac{6144}{5} \, a^{2} d^{4} x^{5} e^{6} + 128 \, a^{2} d^{6} x^{3} e^{4} + \frac{16384}{5} \, a^{3} x^{5} e^{9} + 4096 \, a^{3} d x^{4} e^{8} - 1024 \, a^{3} d^{3} x^{2} e^{6} + 4096 \, a^{4} x e^{8}"," ",0,"4096/17*x^17*e^12 + 1024*d*x^16*e^11 + 8192/5*d^2*x^15*e^10 + 1024*d^3*x^14*e^9 - 2048/13*d^4*x^13*e^8 - 512*d^5*x^12*e^7 - 1664/11*d^6*x^11*e^6 + 384/5*d^7*x^10*e^5 + 128/3*d^8*x^9*e^4 - 4*d^9*x^8*e^3 - 32/7*d^10*x^7*e^2 + 1/5*d^12*x^5 + 16384/13*a*x^13*e^11 + 4096*a*d*x^12*e^10 + 49152/11*a*d^2*x^11*e^9 + 1024*a*d^3*x^10*e^8 - 4096/3*a*d^4*x^9*e^7 - 768*a*d^5*x^8*e^6 + 768/7*a*d^6*x^7*e^5 + 128*a*d^7*x^6*e^4 - 8*a*d^9*x^4*e^2 + 8192/3*a^2*x^9*e^10 + 6144*a^2*d*x^8*e^9 + 24576/7*a^2*d^2*x^7*e^8 - 1024*a^2*d^3*x^6*e^7 - 6144/5*a^2*d^4*x^5*e^6 + 128*a^2*d^6*x^3*e^4 + 16384/5*a^3*x^5*e^9 + 4096*a^3*d*x^4*e^8 - 1024*a^3*d^3*x^2*e^6 + 4096*a^4*x*e^8","A",0
40,1,187,0,0.237865," ","integrate((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^3,x, algorithm=""giac"")","\frac{512}{13} \, x^{13} e^{9} + 128 \, d x^{12} e^{8} + \frac{1536}{11} \, d^{2} x^{11} e^{7} + 32 \, d^{3} x^{10} e^{6} - \frac{128}{3} \, d^{4} x^{9} e^{5} - 24 \, d^{5} x^{8} e^{4} + \frac{24}{7} \, d^{6} x^{7} e^{3} + 4 \, d^{7} x^{6} e^{2} - \frac{1}{4} \, d^{9} x^{4} + \frac{512}{3} \, a x^{9} e^{8} + 384 \, a d x^{8} e^{7} + \frac{1536}{7} \, a d^{2} x^{7} e^{6} - 64 \, a d^{3} x^{6} e^{5} - \frac{384}{5} \, a d^{4} x^{5} e^{4} + 8 \, a d^{6} x^{3} e^{2} + \frac{1536}{5} \, a^{2} x^{5} e^{7} + 384 \, a^{2} d x^{4} e^{6} - 96 \, a^{2} d^{3} x^{2} e^{4} + 512 \, a^{3} x e^{6}"," ",0,"512/13*x^13*e^9 + 128*d*x^12*e^8 + 1536/11*d^2*x^11*e^7 + 32*d^3*x^10*e^6 - 128/3*d^4*x^9*e^5 - 24*d^5*x^8*e^4 + 24/7*d^6*x^7*e^3 + 4*d^7*x^6*e^2 - 1/4*d^9*x^4 + 512/3*a*x^9*e^8 + 384*a*d*x^8*e^7 + 1536/7*a*d^2*x^7*e^6 - 64*a*d^3*x^6*e^5 - 384/5*a*d^4*x^5*e^4 + 8*a*d^6*x^3*e^2 + 1536/5*a^2*x^5*e^7 + 384*a^2*d*x^4*e^6 - 96*a^2*d^3*x^2*e^4 + 512*a^3*x*e^6","A",0
41,1,90,0,0.292717," ","integrate((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^2,x, algorithm=""giac"")","\frac{64}{9} \, x^{9} e^{6} + 16 \, d x^{8} e^{5} + \frac{64}{7} \, d^{2} x^{7} e^{4} - \frac{8}{3} \, d^{3} x^{6} e^{3} - \frac{16}{5} \, d^{4} x^{5} e^{2} + \frac{1}{3} \, d^{6} x^{3} + \frac{128}{5} \, a x^{5} e^{5} + 32 \, a d x^{4} e^{4} - 8 \, a d^{3} x^{2} e^{2} + 64 \, a^{2} x e^{4}"," ",0,"64/9*x^9*e^6 + 16*d*x^8*e^5 + 64/7*d^2*x^7*e^4 - 8/3*d^3*x^6*e^3 - 16/5*d^4*x^5*e^2 + 1/3*d^6*x^3 + 128/5*a*x^5*e^5 + 32*a*d*x^4*e^4 - 8*a*d^3*x^2*e^2 + 64*a^2*x*e^4","A",0
42,1,30,0,0.379732," ","integrate(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2,x, algorithm=""giac"")","\frac{8}{5} \, x^{5} e^{3} + 2 \, d x^{4} e^{2} - \frac{1}{2} \, d^{3} x^{2} + 8 \, a x e^{2}"," ",0,"8/5*x^5*e^3 + 2*d*x^4*e^2 - 1/2*d^3*x^2 + 8*a*x*e^2","A",0
43,0,0,0,0.000000," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2),x, algorithm=""giac"")","\int \frac{1}{8 \, e^{3} x^{4} + 8 \, d e^{2} x^{3} - d^{3} x + 8 \, a e^{2}}\,{d x}"," ",0,"integrate(1/(8*e^3*x^4 + 8*d*e^2*x^3 - d^3*x + 8*a*e^2), x)","F",0
44,-1,0,0,0.000000," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,1,84,0,0.306577," ","integrate((8*x^4-x^3+8*x+8)^4,x, algorithm=""giac"")","\frac{4096}{17} \, x^{17} - 128 \, x^{16} + \frac{128}{5} \, x^{15} + 1168 \, x^{14} + \frac{10241}{13} \, x^{13} - 448 \, x^{12} + \frac{25312}{11} \, x^{11} + \frac{21488}{5} \, x^{10} + 1408 \, x^{9} + 1376 \, x^{8} + 6784 \, x^{7} + 7168 \, x^{6} + \frac{14336}{5} \, x^{5} + 3584 \, x^{4} + 8192 \, x^{3} + 8192 \, x^{2} + 4096 \, x"," ",0,"4096/17*x^17 - 128*x^16 + 128/5*x^15 + 1168*x^14 + 10241/13*x^13 - 448*x^12 + 25312/11*x^11 + 21488/5*x^10 + 1408*x^9 + 1376*x^8 + 6784*x^7 + 7168*x^6 + 14336/5*x^5 + 3584*x^4 + 8192*x^3 + 8192*x^2 + 4096*x","A",0
46,1,64,0,0.334342," ","integrate((8*x^4-x^3+8*x+8)^3,x, algorithm=""giac"")","\frac{512}{13} \, x^{13} - 16 \, x^{12} + \frac{24}{11} \, x^{11} + \frac{307}{2} \, x^{10} + 128 \, x^{9} - 45 \, x^{8} + \frac{1560}{7} \, x^{7} + 480 \, x^{6} + \frac{1152}{5} \, x^{5} + 80 \, x^{4} + 512 \, x^{3} + 768 \, x^{2} + 512 \, x"," ",0,"512/13*x^13 - 16*x^12 + 24/11*x^11 + 307/2*x^10 + 128*x^9 - 45*x^8 + 1560/7*x^7 + 480*x^6 + 1152/5*x^5 + 80*x^4 + 512*x^3 + 768*x^2 + 512*x","A",0
47,1,44,0,0.331662," ","integrate((8*x^4-x^3+8*x+8)^2,x, algorithm=""giac"")","\frac{64}{9} \, x^{9} - 2 \, x^{8} + \frac{1}{7} \, x^{7} + \frac{64}{3} \, x^{6} + \frac{112}{5} \, x^{5} - 4 \, x^{4} + \frac{64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x"," ",0,"64/9*x^9 - 2*x^8 + 1/7*x^7 + 64/3*x^6 + 112/5*x^5 - 4*x^4 + 64/3*x^3 + 64*x^2 + 64*x","A",0
48,1,19,0,0.315341," ","integrate(8*x^4-x^3+8*x+8,x, algorithm=""giac"")","\frac{8}{5} \, x^{5} - \frac{1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x"," ",0,"8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x","A",0
49,0,0,0,0.000000," ","integrate(1/(8*x^4-x^3+8*x+8),x, algorithm=""giac"")","\int \frac{1}{8 \, x^{4} - x^{3} + 8 \, x + 8}\,{d x}"," ",0,"integrate(1/(8*x^4 - x^3 + 8*x + 8), x)","F",0
50,0,0,0,0.000000," ","integrate(1/(8*x^4-x^3+8*x+8)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(8 \, x^{4} - x^{3} + 8 \, x + 8\right)}^{2}}\,{d x}"," ",0,"integrate((8*x^4 - x^3 + 8*x + 8)^(-2), x)","F",0
51,1,77,0,0.363999," ","integrate((4*x^4+4*x^2+4*x+1)^4,x, algorithm=""giac"")","\frac{256}{17} \, x^{17} + \frac{1024}{15} \, x^{15} + \frac{512}{7} \, x^{14} + \frac{1792}{13} \, x^{13} + 256 \, x^{12} + \frac{3328}{11} \, x^{11} + 384 \, x^{10} + \frac{4192}{9} \, x^{9} + 448 \, x^{8} + \frac{2752}{7} \, x^{7} + \frac{992}{3} \, x^{6} + \frac{1136}{5} \, x^{5} + 112 \, x^{4} + \frac{112}{3} \, x^{3} + 8 \, x^{2} + x"," ",0,"256/17*x^17 + 1024/15*x^15 + 512/7*x^14 + 1792/13*x^13 + 256*x^12 + 3328/11*x^11 + 384*x^10 + 4192/9*x^9 + 448*x^8 + 2752/7*x^7 + 992/3*x^6 + 1136/5*x^5 + 112*x^4 + 112/3*x^3 + 8*x^2 + x","A",0
52,1,57,0,0.361830," ","integrate((4*x^4+4*x^2+4*x+1)^3,x, algorithm=""giac"")","\frac{64}{13} \, x^{13} + \frac{192}{11} \, x^{11} + \frac{96}{5} \, x^{10} + \frac{80}{3} \, x^{9} + 48 \, x^{8} + \frac{352}{7} \, x^{7} + 48 \, x^{6} + \frac{252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x"," ",0,"64/13*x^13 + 192/11*x^11 + 96/5*x^10 + 80/3*x^9 + 48*x^8 + 352/7*x^7 + 48*x^6 + 252/5*x^5 + 40*x^4 + 20*x^3 + 6*x^2 + x","A",0
53,1,37,0,0.254558," ","integrate((4*x^4+4*x^2+4*x+1)^2,x, algorithm=""giac"")","\frac{16}{9} \, x^{9} + \frac{32}{7} \, x^{7} + \frac{16}{3} \, x^{6} + \frac{24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x"," ",0,"16/9*x^9 + 32/7*x^7 + 16/3*x^6 + 24/5*x^5 + 8*x^4 + 8*x^3 + 4*x^2 + x","A",0
54,1,17,0,0.360901," ","integrate(4*x^4+4*x^2+4*x+1,x, algorithm=""giac"")","\frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x"," ",0,"4/5*x^5 + 4/3*x^3 + 2*x^2 + x","A",0
55,1,265,0,0.520437," ","integrate(1/(4*x^4+4*x^2+4*x+1),x, algorithm=""giac"")","-\frac{1}{20} \, {\left(\left(i + 2\right) \, \sqrt{\sqrt{5} - 2} {\left(\frac{i}{\sqrt{5} - 2} + 1\right)} + 5 i\right)} \log\left(\left(406 i + 174\right) \, \sqrt{5} x + \left(868 i + 372\right) \, x + 29 \, \sqrt{5} \sqrt{29 \, \sqrt{5} + 62} + \left(87 i - 203\right) \, \sqrt{5} + \left(19 i + 62\right) \, \sqrt{29 \, \sqrt{5} + 62} + 186 i - 434\right) - \frac{1}{20} \, {\left(\left(i + 2\right) \, \sqrt{\sqrt{5} - 2} {\left(-\frac{i}{\sqrt{5} - 2} - 1\right)} + 5 i\right)} \log\left(\left(406 i + 174\right) \, \sqrt{5} x + \left(868 i + 372\right) \, x - 29 \, \sqrt{5} \sqrt{29 \, \sqrt{5} + 62} + \left(87 i - 203\right) \, \sqrt{5} - \left(19 i + 62\right) \, \sqrt{29 \, \sqrt{5} + 62} + 186 i - 434\right) - \frac{1}{20} \, {\left(\left(2 i + 1\right) \, \sqrt{\sqrt{5} + 2} {\left(-\frac{i}{\sqrt{5} + 2} - 1\right)} - 5 i\right)} \log\left(\left(26 i + 130\right) \, \sqrt{5} x - \left(44 i + 220\right) \, x + 13 \, \sqrt{5} \sqrt{13 \, \sqrt{5} - 22} - \left(65 i - 13\right) \, \sqrt{5} + \left(19 i - 22\right) \, \sqrt{13 \, \sqrt{5} - 22} + 110 i - 22\right) - \frac{1}{20} \, {\left(\left(2 i + 1\right) \, \sqrt{\sqrt{5} + 2} {\left(\frac{i}{\sqrt{5} + 2} + 1\right)} - 5 i\right)} \log\left(\left(26 i + 130\right) \, \sqrt{5} x - \left(44 i + 220\right) \, x - 13 \, \sqrt{5} \sqrt{13 \, \sqrt{5} - 22} - \left(65 i - 13\right) \, \sqrt{5} - \left(19 i - 22\right) \, \sqrt{13 \, \sqrt{5} - 22} + 110 i - 22\right)"," ",0,"-1/20*((I + 2)*sqrt(sqrt(5) - 2)*(I/(sqrt(5) - 2) + 1) + 5*I)*log((406*I + 174)*sqrt(5)*x + (868*I + 372)*x + 29*sqrt(5)*sqrt(29*sqrt(5) + 62) + (87*I - 203)*sqrt(5) + (19*I + 62)*sqrt(29*sqrt(5) + 62) + 186*I - 434) - 1/20*((I + 2)*sqrt(sqrt(5) - 2)*(-I/(sqrt(5) - 2) - 1) + 5*I)*log((406*I + 174)*sqrt(5)*x + (868*I + 372)*x - 29*sqrt(5)*sqrt(29*sqrt(5) + 62) + (87*I - 203)*sqrt(5) - (19*I + 62)*sqrt(29*sqrt(5) + 62) + 186*I - 434) - 1/20*((2*I + 1)*sqrt(sqrt(5) + 2)*(-I/(sqrt(5) + 2) - 1) - 5*I)*log((26*I + 130)*sqrt(5)*x - (44*I + 220)*x + 13*sqrt(5)*sqrt(13*sqrt(5) - 22) - (65*I - 13)*sqrt(5) + (19*I - 22)*sqrt(13*sqrt(5) - 22) + 110*I - 22) - 1/20*((2*I + 1)*sqrt(sqrt(5) + 2)*(I/(sqrt(5) + 2) + 1) - 5*I)*log((26*I + 130)*sqrt(5)*x - (44*I + 220)*x - 13*sqrt(5)*sqrt(13*sqrt(5) - 22) - (65*I - 13)*sqrt(5) - (19*I - 22)*sqrt(13*sqrt(5) - 22) + 110*I - 22)","C",0
56,1,315,0,0.723507," ","integrate(1/(4*x^4+4*x^2+4*x+1)^2,x, algorithm=""giac"")","-\frac{1}{400} \, {\left(-\left(i + 3\right) \, \sqrt{2665 \, \sqrt{5} - 4790} {\left(\frac{709 i}{533 \, \sqrt{5} - 958} + 1\right)} - 350 i\right)} \log\left(\left(2534636224790 i + 16853816172010\right) \, \sqrt{5} x - \left(3913528401620 i + 26022625108780\right) \, x + 5049076145 \, \sqrt{5} \sqrt{1424281 \, \sqrt{5} - 2199118} - \left(8426908086005 i - 1267318112395\right) \, \sqrt{5} + \left(8166407345 i - 7795873310\right) \, \sqrt{1424281 \, \sqrt{5} - 2199118} + 13011312554390 i - 1956764200810\right) - \frac{1}{400} \, {\left(\left(i + 3\right) \, \sqrt{2665 \, \sqrt{5} - 4790} {\left(\frac{709 i}{533 \, \sqrt{5} - 958} + 1\right)} - 350 i\right)} \log\left(\left(2534636224790 i + 16853816172010\right) \, \sqrt{5} x - \left(3913528401620 i + 26022625108780\right) \, x - 5049076145 \, \sqrt{5} \sqrt{1424281 \, \sqrt{5} - 2199118} - \left(8426908086005 i - 1267318112395\right) \, \sqrt{5} - \left(8166407345 i - 7795873310\right) \, \sqrt{1424281 \, \sqrt{5} - 2199118} + 13011312554390 i - 1956764200810\right) - \frac{1}{400} \, {\left(\left(3 i + 1\right) \, \sqrt{2665 \, \sqrt{5} + 4790} {\left(\frac{709 i}{533 \, \sqrt{5} + 958} + 1\right)} + 350 i\right)} \log\left(\left(16722951192450 i + 2480822188910\right) \, \sqrt{5} x + \left(25712356272300 i + 3814385585140\right) \, x + 5021907265 \, \sqrt{5} \sqrt{1416617 \, \sqrt{5} + 2178118} + \left(1240411094455 i - 8361475596225\right) \, \sqrt{5} + \left(8153361745 i + 7721428310\right) \, \sqrt{1416617 \, \sqrt{5} + 2178118} + 1907192792570 i - 12856178136150\right) - \frac{1}{400} \, {\left(-\left(3 i + 1\right) \, \sqrt{2665 \, \sqrt{5} + 4790} {\left(\frac{709 i}{533 \, \sqrt{5} + 958} + 1\right)} + 350 i\right)} \log\left(\left(16722951192450 i + 2480822188910\right) \, \sqrt{5} x + \left(25712356272300 i + 3814385585140\right) \, x - 5021907265 \, \sqrt{5} \sqrt{1416617 \, \sqrt{5} + 2178118} + \left(1240411094455 i - 8361475596225\right) \, \sqrt{5} - \left(8153361745 i + 7721428310\right) \, \sqrt{1416617 \, \sqrt{5} + 2178118} + 1907192792570 i - 12856178136150\right) + \frac{36 \, x^{3} - 16 \, x^{2} + 42 \, x + 19}{20 \, {\left(4 \, x^{4} + 4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"-1/400*(-(I + 3)*sqrt(2665*sqrt(5) - 4790)*(709*I/(533*sqrt(5) - 958) + 1) - 350*I)*log((2534636224790*I + 16853816172010)*sqrt(5)*x - (3913528401620*I + 26022625108780)*x + 5049076145*sqrt(5)*sqrt(1424281*sqrt(5) - 2199118) - (8426908086005*I - 1267318112395)*sqrt(5) + (8166407345*I - 7795873310)*sqrt(1424281*sqrt(5) - 2199118) + 13011312554390*I - 1956764200810) - 1/400*((I + 3)*sqrt(2665*sqrt(5) - 4790)*(709*I/(533*sqrt(5) - 958) + 1) - 350*I)*log((2534636224790*I + 16853816172010)*sqrt(5)*x - (3913528401620*I + 26022625108780)*x - 5049076145*sqrt(5)*sqrt(1424281*sqrt(5) - 2199118) - (8426908086005*I - 1267318112395)*sqrt(5) - (8166407345*I - 7795873310)*sqrt(1424281*sqrt(5) - 2199118) + 13011312554390*I - 1956764200810) - 1/400*((3*I + 1)*sqrt(2665*sqrt(5) + 4790)*(709*I/(533*sqrt(5) + 958) + 1) + 350*I)*log((16722951192450*I + 2480822188910)*sqrt(5)*x + (25712356272300*I + 3814385585140)*x + 5021907265*sqrt(5)*sqrt(1416617*sqrt(5) + 2178118) + (1240411094455*I - 8361475596225)*sqrt(5) + (8153361745*I + 7721428310)*sqrt(1416617*sqrt(5) + 2178118) + 1907192792570*I - 12856178136150) - 1/400*(-(3*I + 1)*sqrt(2665*sqrt(5) + 4790)*(709*I/(533*sqrt(5) + 958) + 1) + 350*I)*log((16722951192450*I + 2480822188910)*sqrt(5)*x + (25712356272300*I + 3814385585140)*x - 5021907265*sqrt(5)*sqrt(1416617*sqrt(5) + 2178118) + (1240411094455*I - 8361475596225)*sqrt(5) - (8153361745*I + 7721428310)*sqrt(1416617*sqrt(5) + 2178118) + 1907192792570*I - 12856178136150) + 1/20*(36*x^3 - 16*x^2 + 42*x + 19)/(4*x^4 + 4*x^2 + 4*x + 1)","C",0
57,1,84,0,0.364208," ","integrate((8*x^4-15*x^3+8*x^2+24*x+8)^4,x, algorithm=""giac"")","\frac{4096}{17} \, x^{17} - 1920 \, x^{16} + \frac{102784}{15} \, x^{15} - \frac{75504}{7} \, x^{14} - \frac{12095}{13} \, x^{13} + 31128 \, x^{12} - \frac{331040}{11} \, x^{11} - \frac{169584}{5} \, x^{10} + \frac{641152}{9} \, x^{9} + 36384 \, x^{8} - \frac{566912}{7} \, x^{7} - 30720 \, x^{6} + \frac{538624}{5} \, x^{5} + 139776 \, x^{4} + \frac{237568}{3} \, x^{3} + 24576 \, x^{2} + 4096 \, x"," ",0,"4096/17*x^17 - 1920*x^16 + 102784/15*x^15 - 75504/7*x^14 - 12095/13*x^13 + 31128*x^12 - 331040/11*x^11 - 169584/5*x^10 + 641152/9*x^9 + 36384*x^8 - 566912/7*x^7 - 30720*x^6 + 538624/5*x^5 + 139776*x^4 + 237568/3*x^3 + 24576*x^2 + 4096*x","A",0
58,1,64,0,0.383976," ","integrate((8*x^4-15*x^3+8*x^2+24*x+8)^3,x, algorithm=""giac"")","\frac{512}{13} \, x^{13} - 240 \, x^{12} + \frac{6936}{11} \, x^{11} - \frac{4527}{10} \, x^{10} - \frac{2936}{3} \, x^{9} + 2097 \, x^{8} + \frac{5528}{7} \, x^{7} - 2976 \, x^{6} - \frac{384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x"," ",0,"512/13*x^13 - 240*x^12 + 6936/11*x^11 - 4527/10*x^10 - 2936/3*x^9 + 2097*x^8 + 5528/7*x^7 - 2976*x^6 - 384/5*x^5 + 5040*x^4 + 5120*x^3 + 2304*x^2 + 512*x","A",0
59,1,44,0,0.356585," ","integrate((8*x^4-15*x^3+8*x^2+24*x+8)^2,x, algorithm=""giac"")","\frac{64}{9} \, x^{9} - 30 \, x^{8} + \frac{353}{7} \, x^{7} + 24 \, x^{6} - \frac{528}{5} \, x^{5} + 36 \, x^{4} + \frac{704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x"," ",0,"64/9*x^9 - 30*x^8 + 353/7*x^7 + 24*x^6 - 528/5*x^5 + 36*x^4 + 704/3*x^3 + 192*x^2 + 64*x","A",0
60,1,24,0,0.299518," ","integrate(8*x^4-15*x^3+8*x^2+24*x+8,x, algorithm=""giac"")","\frac{8}{5} \, x^{5} - \frac{15}{4} \, x^{4} + \frac{8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x"," ",0,"8/5*x^5 - 15/4*x^4 + 8/3*x^3 + 12*x^2 + 8*x","A",0
61,0,0,0,0.000000," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8),x, algorithm=""giac"")","\int \frac{1}{8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8}\,{d x}"," ",0,"integrate(1/(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8\right)}^{2}}\,{d x}"," ",0,"integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^(-2), x)","F",0
63,1,163,0,0.282750," ","integrate((b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5)^3,x, algorithm=""giac"")","\frac{1}{16} \, b^{15} x^{16} + a b^{14} x^{15} + \frac{15}{2} \, a^{2} b^{13} x^{14} + 35 \, a^{3} b^{12} x^{13} + \frac{455}{4} \, a^{4} b^{11} x^{12} + 273 \, a^{5} b^{10} x^{11} + \frac{1001}{2} \, a^{6} b^{9} x^{10} + 715 \, a^{7} b^{8} x^{9} + \frac{6435}{8} \, a^{8} b^{7} x^{8} + 715 \, a^{9} b^{6} x^{7} + \frac{1001}{2} \, a^{10} b^{5} x^{6} + 273 \, a^{11} b^{4} x^{5} + \frac{455}{4} \, a^{12} b^{3} x^{4} + 35 \, a^{13} b^{2} x^{3} + \frac{15}{2} \, a^{14} b x^{2} + a^{15} x"," ",0,"1/16*b^15*x^16 + a*b^14*x^15 + 15/2*a^2*b^13*x^14 + 35*a^3*b^12*x^13 + 455/4*a^4*b^11*x^12 + 273*a^5*b^10*x^11 + 1001/2*a^6*b^9*x^10 + 715*a^7*b^8*x^9 + 6435/8*a^8*b^7*x^8 + 715*a^9*b^6*x^7 + 1001/2*a^10*b^5*x^6 + 273*a^11*b^4*x^5 + 455/4*a^12*b^3*x^4 + 35*a^13*b^2*x^3 + 15/2*a^14*b*x^2 + a^15*x","B",0
64,1,108,0,0.242157," ","integrate((b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{10} x^{11} + a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{9} + 15 \, a^{3} b^{7} x^{8} + 30 \, a^{4} b^{6} x^{7} + 42 \, a^{5} b^{5} x^{6} + 42 \, a^{6} b^{4} x^{5} + 30 \, a^{7} b^{3} x^{4} + 15 \, a^{8} b^{2} x^{3} + 5 \, a^{9} b x^{2} + a^{10} x"," ",0,"1/11*b^10*x^11 + a*b^9*x^10 + 5*a^2*b^8*x^9 + 15*a^3*b^7*x^8 + 30*a^4*b^6*x^7 + 42*a^5*b^5*x^6 + 42*a^6*b^4*x^5 + 30*a^7*b^3*x^4 + 15*a^8*b^2*x^3 + 5*a^9*b*x^2 + a^10*x","B",0
65,1,53,0,0.292142," ","integrate(b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5,x, algorithm=""giac"")","\frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x"," ",0,"1/6*b^5*x^6 + a*b^4*x^5 + 5/2*a^2*b^3*x^4 + 10/3*a^3*b^2*x^3 + 5/2*a^4*b*x^2 + a^5*x","B",0
66,1,12,0,0.354415," ","integrate(1/(b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5),x, algorithm=""giac"")","-\frac{1}{4 \, {\left(b x + a\right)}^{4} b}"," ",0,"-1/4/((b*x + a)^4*b)","A",0
67,1,12,0,0.275930," ","integrate(1/(b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5)^2,x, algorithm=""giac"")","-\frac{1}{9 \, {\left(b x + a\right)}^{9} b}"," ",0,"-1/9/((b*x + a)^9*b)","A",0
68,1,12,0,0.354991," ","integrate(1/(b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5)^3,x, algorithm=""giac"")","-\frac{1}{14 \, {\left(b x + a\right)}^{14} b}"," ",0,"-1/14/((b*x + a)^14*b)","A",0
69,1,31,0,0.294669," ","integrate(1/(x^5+x^3+x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(x\right) - \frac{1}{3} \, \log\left(x^{2} - x + 1\right) + \frac{1}{4} \, \log\left(x^{2} + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*arctan(x) - 1/3*log(x^2 - x + 1) + 1/4*log(x^2 + 1) + 1/6*log(abs(x + 1))","A",0
70,1,64,0,0.379517," ","integrate((-16*x^6+32*x^4-19*x^2+3)^4,x, algorithm=""giac"")","\frac{65536}{25} \, x^{25} - \frac{524288}{23} \, x^{23} + \frac{1884160}{21} \, x^{21} - \frac{4014080}{19} \, x^{19} + \frac{5633536}{17} \, x^{17} - \frac{1094656}{3} \, x^{15} + \frac{3764416}{13} \, x^{13} - \frac{1841600}{11} \, x^{11} + \frac{634321}{9} \, x^{9} - \frac{149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x"," ",0,"65536/25*x^25 - 524288/23*x^23 + 1884160/21*x^21 - 4014080/19*x^19 + 5633536/17*x^17 - 1094656/3*x^15 + 3764416/13*x^13 - 1841600/11*x^11 + 634321/9*x^9 - 149700/7*x^7 + 4590*x^5 - 684*x^3 + 81*x","A",0
71,1,49,0,0.364749," ","integrate((-16*x^6+32*x^4-19*x^2+3)^3,x, algorithm=""giac"")","-\frac{4096}{19} \, x^{19} + \frac{24576}{17} \, x^{17} - \frac{21248}{5} \, x^{15} + \frac{93440}{13} \, x^{13} - \frac{84912}{11} \, x^{11} + \frac{16448}{3} \, x^{9} - 2605 \, x^{7} + \frac{4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x"," ",0,"-4096/19*x^19 + 24576/17*x^17 - 21248/5*x^15 + 93440/13*x^13 - 84912/11*x^11 + 16448/3*x^9 - 2605*x^7 + 4113/5*x^5 - 171*x^3 + 27*x","A",0
72,1,34,0,0.362368," ","integrate((-16*x^6+32*x^4-19*x^2+3)^2,x, algorithm=""giac"")","\frac{256}{13} \, x^{13} - \frac{1024}{11} \, x^{11} + \frac{544}{3} \, x^{9} - \frac{1312}{7} \, x^{7} + \frac{553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x"," ",0,"256/13*x^13 - 1024/11*x^11 + 544/3*x^9 - 1312/7*x^7 + 553/5*x^5 - 38*x^3 + 9*x","A",0
73,1,19,0,0.279439," ","integrate(-16*x^6+32*x^4-19*x^2+3,x, algorithm=""giac"")","-\frac{16}{7} \, x^{7} + \frac{32}{5} \, x^{5} - \frac{19}{3} \, x^{3} + 3 \, x"," ",0,"-16/7*x^7 + 32/5*x^5 - 19/3*x^3 + 3*x","A",0
74,1,62,0,0.281915," ","integrate(1/(-16*x^6+32*x^4-19*x^2+3),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 8 \, x - 4 \, \sqrt{3} \right|}}{{\left| 8 \, x + 4 \, \sqrt{3} \right|}}\right) + \frac{1}{6} \, \log\left({\left| 2 \, x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| 2 \, x - 1 \right|}\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*log(abs(8*x - 4*sqrt(3))/abs(8*x + 4*sqrt(3))) + 1/6*log(abs(2*x + 1)) - 1/6*log(abs(2*x - 1)) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","B",0
75,1,97,0,0.278392," ","integrate(1/(-16*x^6+32*x^4-19*x^2+3)^2,x, algorithm=""giac"")","\frac{5}{18} \, \sqrt{3} \log\left(\frac{{\left| 8 \, x - 4 \, \sqrt{3} \right|}}{{\left| 8 \, x + 4 \, \sqrt{3} \right|}}\right) - \frac{80 \, x^{5} - 104 \, x^{3} + 27 \, x}{18 \, {\left(16 \, x^{6} - 32 \, x^{4} + 19 \, x^{2} - 3\right)}} - \frac{7}{54} \, \log\left({\left| 2 \, x + 1 \right|}\right) + \frac{7}{54} \, \log\left({\left| 2 \, x - 1 \right|}\right) + \frac{67}{108} \, \log\left({\left| x + 1 \right|}\right) - \frac{67}{108} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"5/18*sqrt(3)*log(abs(8*x - 4*sqrt(3))/abs(8*x + 4*sqrt(3))) - 1/18*(80*x^5 - 104*x^3 + 27*x)/(16*x^6 - 32*x^4 + 19*x^2 - 3) - 7/54*log(abs(2*x + 1)) + 7/54*log(abs(2*x - 1)) + 67/108*log(abs(x + 1)) - 67/108*log(abs(x - 1))","A",0
76,1,112,0,0.308470," ","integrate(1/(-16*x^6+32*x^4-19*x^2+3)^3,x, algorithm=""giac"")","\frac{67}{36} \, \sqrt{3} \log\left(\frac{{\left| 8 \, x - 4 \, \sqrt{3} \right|}}{{\left| 8 \, x + 4 \, \sqrt{3} \right|}}\right) - \frac{36608 \, x^{11} - 111360 \, x^{9} + 125280 \, x^{7} - 63680 \, x^{5} + 14331 \, x^{3} - 1197 \, x}{216 \, {\left(16 \, x^{6} - 32 \, x^{4} + 19 \, x^{2} - 3\right)}^{2}} + \frac{67}{324} \, \log\left({\left| 2 \, x + 1 \right|}\right) - \frac{67}{324} \, \log\left({\left| 2 \, x - 1 \right|}\right) + \frac{3913}{1296} \, \log\left({\left| x + 1 \right|}\right) - \frac{3913}{1296} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"67/36*sqrt(3)*log(abs(8*x - 4*sqrt(3))/abs(8*x + 4*sqrt(3))) - 1/216*(36608*x^11 - 111360*x^9 + 125280*x^7 - 63680*x^5 + 14331*x^3 - 1197*x)/(16*x^6 - 32*x^4 + 19*x^2 - 3)^2 + 67/324*log(abs(2*x + 1)) - 67/324*log(abs(2*x - 1)) + 3913/1296*log(abs(x + 1)) - 3913/1296*log(abs(x - 1))","A",0
77,1,134,0,0.435260," ","integrate(1/(x^6-7*x^4+7*x^2-1)^2,x, algorithm=""giac"")","-\frac{3}{1024} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} + 2 \right|}}\right) - \frac{3}{1024} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} - 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} - 2 \right|}}\right) - \frac{21 \, x^{5} - 140 \, x^{3} + 103 \, x}{128 \, {\left(x^{6} - 7 \, x^{4} + 7 \, x^{2} - 1\right)}} - \frac{1}{256} \, \log\left({\left| x^{2} + 2 \, x - 1 \right|}\right) + \frac{1}{256} \, \log\left({\left| x^{2} - 2 \, x - 1 \right|}\right) + \frac{5}{64} \, \log\left({\left| x + 1 \right|}\right) - \frac{5}{64} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-3/1024*sqrt(2)*log(abs(2*x - 2*sqrt(2) + 2)/abs(2*x + 2*sqrt(2) + 2)) - 3/1024*sqrt(2)*log(abs(2*x - 2*sqrt(2) - 2)/abs(2*x + 2*sqrt(2) - 2)) - 1/128*(21*x^5 - 140*x^3 + 103*x)/(x^6 - 7*x^4 + 7*x^2 - 1) - 1/256*log(abs(x^2 + 2*x - 1)) + 1/256*log(abs(x^2 - 2*x - 1)) + 5/64*log(abs(x + 1)) - 5/64*log(abs(x - 1))","A",0
78,1,77,0,0.341192," ","integrate(x^3/(c+(b*x+a)^2),x, algorithm=""giac"")","\frac{{\left(3 \, a^{2} - c\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{2 \, b^{4}} - \frac{{\left(a^{3} - 3 \, a c\right)} \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{b^{4} \sqrt{c}} + \frac{b^{2} x^{2} - 4 \, a b x}{2 \, b^{4}}"," ",0,"1/2*(3*a^2 - c)*log(b^2*x^2 + 2*a*b*x + a^2 + c)/b^4 - (a^3 - 3*a*c)*arctan((b*x + a)/sqrt(c))/(b^4*sqrt(c)) + 1/2*(b^2*x^2 - 4*a*b*x)/b^4","A",0
79,1,54,0,0.308225," ","integrate(x^2/(c+(b*x+a)^2),x, algorithm=""giac"")","\frac{x}{b^{2}} - \frac{a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{b^{3}} + \frac{{\left(a^{2} - c\right)} \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{b^{3} \sqrt{c}}"," ",0,"x/b^2 - a*log(b^2*x^2 + 2*a*b*x + a^2 + c)/b^3 + (a^2 - c)*arctan((b*x + a)/sqrt(c))/(b^3*sqrt(c))","A",0
80,1,43,0,0.356058," ","integrate(x/(c+(b*x+a)^2),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{b^{2} \sqrt{c}} + \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{2 \, b^{2}}"," ",0,"-a*arctan((b*x + a)/sqrt(c))/(b^2*sqrt(c)) + 1/2*log(b^2*x^2 + 2*a*b*x + a^2 + c)/b^2","A",0
81,1,17,0,0.376979," ","integrate(1/(c+(b*x+a)^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{b \sqrt{c}}"," ",0,"arctan((b*x + a)/sqrt(c))/(b*sqrt(c))","A",0
82,1,62,0,0.377133," ","integrate(1/x/(c+(b*x+a)^2),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{{\left(a^{2} + c\right)} \sqrt{c}} - \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{2 \, {\left(a^{2} + c\right)}} + \frac{\log\left({\left| x \right|}\right)}{a^{2} + c}"," ",0,"-a*arctan((b*x + a)/sqrt(c))/((a^2 + c)*sqrt(c)) - 1/2*log(b^2*x^2 + 2*a*b*x + a^2 + c)/(a^2 + c) + log(abs(x))/(a^2 + c)","A",0
83,1,117,0,0.367183," ","integrate(1/x^2/(c+(b*x+a)^2),x, algorithm=""giac"")","\frac{a b \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{a^{4} + 2 \, a^{2} c + c^{2}} - \frac{2 \, a b \log\left({\left| x \right|}\right)}{a^{4} + 2 \, a^{2} c + c^{2}} + \frac{{\left(a^{2} b^{2} - b^{2} c\right)} \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{{\left(a^{4} + 2 \, a^{2} c + c^{2}\right)} b \sqrt{c}} - \frac{1}{{\left(a^{2} + c\right)} x}"," ",0,"a*b*log(b^2*x^2 + 2*a*b*x + a^2 + c)/(a^4 + 2*a^2*c + c^2) - 2*a*b*log(abs(x))/(a^4 + 2*a^2*c + c^2) + (a^2*b^2 - b^2*c)*arctan((b*x + a)/sqrt(c))/((a^4 + 2*a^2*c + c^2)*b*sqrt(c)) - 1/((a^2 + c)*x)","A",0
84,1,195,0,0.415407," ","integrate(1/x^3/(c+(b*x+a)^2),x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b^{2} - b^{2} c\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c\right)}{2 \, {\left(a^{6} + 3 \, a^{4} c + 3 \, a^{2} c^{2} + c^{3}\right)}} + \frac{{\left(3 \, a^{2} b^{2} - b^{2} c\right)} \log\left({\left| x \right|}\right)}{a^{6} + 3 \, a^{4} c + 3 \, a^{2} c^{2} + c^{3}} - \frac{{\left(a^{3} b^{3} - 3 \, a b^{3} c\right)} \arctan\left(\frac{b x + a}{\sqrt{c}}\right)}{{\left(a^{6} + 3 \, a^{4} c + 3 \, a^{2} c^{2} + c^{3}\right)} b \sqrt{c}} - \frac{a^{4} + 2 \, a^{2} c + c^{2} - 4 \, {\left(a^{3} b + a b c\right)} x}{2 \, {\left(a^{2} + c\right)}^{3} x^{2}}"," ",0,"-1/2*(3*a^2*b^2 - b^2*c)*log(b^2*x^2 + 2*a*b*x + a^2 + c)/(a^6 + 3*a^4*c + 3*a^2*c^2 + c^3) + (3*a^2*b^2 - b^2*c)*log(abs(x))/(a^6 + 3*a^4*c + 3*a^2*c^2 + c^3) - (a^3*b^3 - 3*a*b^3*c)*arctan((b*x + a)/sqrt(c))/((a^6 + 3*a^4*c + 3*a^2*c^2 + c^3)*b*sqrt(c)) - 1/2*(a^4 + 2*a^2*c + c^2 - 4*(a^3*b + a*b*c)*x)/((a^2 + c)^3*x^2)","A",0
85,1,24,0,0.453482," ","integrate(1/(a+b*(d*x+c)^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b d x + b c}{\sqrt{a b}}\right)}{\sqrt{a b} d}"," ",0,"arctan((b*d*x + b*c)/sqrt(a*b))/(sqrt(a*b)*d)","A",0
86,1,65,0,0.358907," ","integrate(1/(a+b*(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{b d x + b c}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a d} + \frac{d x + c}{2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)} a d}"," ",0,"1/2*arctan((b*d*x + b*c)/sqrt(a*b))/(sqrt(a*b)*a*d) + 1/2*(d*x + c)/((b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)*a*d)","A",0
87,1,103,0,0.408595," ","integrate(1/(a+b*(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{b d x + b c}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} d} + \frac{3 \, b d^{3} x^{3} + 9 \, b c d^{2} x^{2} + 9 \, b c^{2} d x + 3 \, b c^{3} + 5 \, a d x + 5 \, a c}{8 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{2} a^{2} d}"," ",0,"3/8*arctan((b*d*x + b*c)/sqrt(a*b))/(sqrt(a*b)*a^2*d) + 1/8*(3*b*d^3*x^3 + 9*b*c*d^2*x^2 + 9*b*c^2*d*x + 3*b*c^3 + 5*a*d*x + 5*a*c)/((b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^2*a^2*d)","A",0
88,1,30,0,0.446003," ","integrate(1/(b*(d*x+c)^2+(-a)^(1/2)),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b d x + b c}{\left(-a\right)^{\frac{1}{4}} \sqrt{b}}\right)}{\left(-a\right)^{\frac{1}{4}} \sqrt{b} d}"," ",0,"arctan((b*d*x + b*c)/((-a)^(1/4)*sqrt(b)))/((-a)^(1/4)*sqrt(b)*d)","A",0
89,1,10,0,0.318422," ","integrate(1/(1+(d*x+c)^2),x, algorithm=""giac"")","\frac{\arctan\left(d x + c\right)}{d}"," ",0,"arctan(d*x + c)/d","A",0
90,1,41,0,0.377144," ","integrate(1/(1+(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(d x + c\right)}{2 \, d} + \frac{d x + c}{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} d}"," ",0,"1/2*arctan(d*x + c)/d + 1/2*(d*x + c)/((d^2*x^2 + 2*c*d*x + c^2 + 1)*d)","A",0
91,1,73,0,0.303626," ","integrate(1/(1+(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(d x + c\right)}{8 \, d} + \frac{3 \, d^{3} x^{3} + 9 \, c d^{2} x^{2} + 9 \, c^{2} d x + 3 \, c^{3} + 5 \, d x + 5 \, c}{8 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} d}"," ",0,"3/8*arctan(d*x + c)/d + 1/8*(3*d^3*x^3 + 9*c*d^2*x^2 + 9*c^2*d*x + 3*c^3 + 5*d*x + 5*c)/((d^2*x^2 + 2*c*d*x + c^2 + 1)^2*d)","A",0
92,1,27,0,0.384253," ","integrate(1/(1-(d*x+c)^2),x, algorithm=""giac"")","\frac{\log\left({\left| d x + c + 1 \right|}\right)}{2 \, d} - \frac{\log\left({\left| d x + c - 1 \right|}\right)}{2 \, d}"," ",0,"1/2*log(abs(d*x + c + 1))/d - 1/2*log(abs(d*x + c - 1))/d","B",0
93,1,56,0,0.351290," ","integrate(1/(1-(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\log\left({\left| d x + c + 1 \right|}\right)}{4 \, d} - \frac{\log\left({\left| d x + c - 1 \right|}\right)}{4 \, d} - \frac{d x + c}{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} d}"," ",0,"1/4*log(abs(d*x + c + 1))/d - 1/4*log(abs(d*x + c - 1))/d - 1/2*(d*x + c)/((d^2*x^2 + 2*c*d*x + c^2 - 1)*d)","A",0
94,1,88,0,0.356523," ","integrate(1/(1-(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| d x + c + 1 \right|}\right)}{16 \, d} - \frac{3 \, \log\left({\left| d x + c - 1 \right|}\right)}{16 \, d} - \frac{3 \, d^{3} x^{3} + 9 \, c d^{2} x^{2} + 9 \, c^{2} d x + 3 \, c^{3} - 5 \, d x - 5 \, c}{8 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)}^{2} d}"," ",0,"3/16*log(abs(d*x + c + 1))/d - 3/16*log(abs(d*x + c - 1))/d - 1/8*(3*d^3*x^3 + 9*c*d^2*x^2 + 9*c^2*d*x + 3*c^3 - 5*d*x - 5*c)/((d^2*x^2 + 2*c*d*x + c^2 - 1)^2*d)","A",0
95,1,13,0,0.354753," ","integrate(1/(1-(1+x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x + 2 \right|}\right) - \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"1/2*log(abs(x + 2)) - 1/2*log(abs(x))","B",0
96,1,27,0,0.325397," ","integrate(1/(1-(1+x)^2)^2,x, algorithm=""giac"")","-\frac{x + 1}{2 \, {\left(x^{2} + 2 \, x\right)}} + \frac{1}{4} \, \log\left({\left| x + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2*(x + 1)/(x^2 + 2*x) + 1/4*log(abs(x + 2)) - 1/4*log(abs(x))","A",0
97,1,39,0,0.339454," ","integrate(1/(1-(1+x)^2)^3,x, algorithm=""giac"")","-\frac{3 \, x^{3} + 9 \, x^{2} + 4 \, x - 2}{8 \, {\left(x^{2} + 2 \, x\right)}^{2}} + \frac{3}{16} \, \log\left({\left| x + 2 \right|}\right) - \frac{3}{16} \, \log\left({\left| x \right|}\right)"," ",0,"-1/8*(3*x^3 + 9*x^2 + 4*x - 2)/(x^2 + 2*x)^2 + 3/16*log(abs(x + 2)) - 3/16*log(abs(x))","A",0
98,1,62,0,0.309702," ","integrate((1+(b*x+a)^2)^2/x,x, algorithm=""giac"")","\frac{1}{4} \, b^{4} x^{4} + \frac{4}{3} \, a b^{3} x^{3} + 3 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + b^{2} x^{2} + 4 \, a b x + {\left(a^{4} + 2 \, a^{2} + 1\right)} \log\left({\left| x \right|}\right)"," ",0,"1/4*b^4*x^4 + 4/3*a*b^3*x^3 + 3*a^2*b^2*x^2 + 4*a^3*b*x + b^2*x^2 + 4*a*b*x + (a^4 + 2*a^2 + 1)*log(abs(x))","A",0
99,1,11,0,0.352899," ","integrate(x^2/(1+(-1+x)^2),x, algorithm=""giac"")","x + \log\left(x^{2} - 2 \, x + 2\right)"," ",0,"x + log(x^2 - 2*x + 2)","A",0
100,1,23,0,0.385644," ","integrate(x^2/(1-(1+x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-{\left(x + 1\right)}^{2} + 1} {\left(x - 3\right)} + \frac{3}{2} \, \arcsin\left(x + 1\right)"," ",0,"-1/2*sqrt(-(x + 1)^2 + 1)*(x - 3) + 3/2*arcsin(x + 1)","A",0
101,1,55,0,0.486045," ","integrate(x^2/(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(\frac{x}{b^{2}} - \frac{3 \, a}{b^{3}}\right)} - \frac{{\left(2 \, a^{2} + 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{2} {\left| b \right|}}"," ",0,"-1/2*sqrt(-(b*x + a)^2 + 1)*(x/b^2 - 3*a/b^3) - 1/2*(2*a^2 + 1)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b))","A",0
102,1,70,0,0.416832," ","integrate(x^2/(1+(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{{\left(b x + a\right)}^{2} + 1} {\left(\frac{x}{b^{2}} - \frac{3 \, a}{b^{3}}\right)} - \frac{{\left(2 \, a^{2} - 1\right)} \log\left(-a b - {\left(x {\left| b \right|} - \sqrt{{\left(b x + a\right)}^{2} + 1}\right)} {\left| b \right|}\right)}{2 \, b^{2} {\left| b \right|}}"," ",0,"1/2*sqrt((b*x + a)^2 + 1)*(x/b^2 - 3*a/b^3) - 1/2*(2*a^2 - 1)*log(-a*b - (x*abs(b) - sqrt((b*x + a)^2 + 1))*abs(b))/(b^2*abs(b))","A",0
103,0,0,0,0.000000," ","integrate(x^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(d x + c\right)}^{3} b + a}\,{d x}"," ",0,"integrate(x^3/((d*x + c)^3*b + a), x)","F",0
104,0,0,0,0.000000," ","integrate(x^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(d x + c\right)}^{3} b + a}\,{d x}"," ",0,"integrate(x^2/((d*x + c)^3*b + a), x)","F",0
105,0,0,0,0.000000," ","integrate(x/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{x}{{\left(d x + c\right)}^{3} b + a}\,{d x}"," ",0,"integrate(x/((d*x + c)^3*b + a), x)","F",0
106,1,160,0,0.451567," ","integrate(1/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \frac{1}{6} \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + \frac{1}{3} \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)"," ",0,"1/3*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - 1/6*(1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 1/3*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3)))","A",0
107,0,0,0,0.000000," ","integrate(1/x/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{1}{{\left({\left(d x + c\right)}^{3} b + a\right)} x}\,{d x}"," ",0,"integrate(1/(((d*x + c)^3*b + a)*x), x)","F",0
108,0,0,0,0.000000," ","integrate(1/x^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{1}{{\left({\left(d x + c\right)}^{3} b + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(((d*x + c)^3*b + a)*x^2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/x^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\int \frac{1}{{\left({\left(d x + c\right)}^{3} b + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/(((d*x + c)^3*b + a)*x^3), x)","F",0
110,0,0,0,0.000000," ","integrate(x^3/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(d x + c\right)}^{4} b + a}\,{d x}"," ",0,"integrate(x^3/((d*x + c)^4*b + a), x)","F",0
111,0,0,0,0.000000," ","integrate(x^2/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(d x + c\right)}^{4} b + a}\,{d x}"," ",0,"integrate(x^2/((d*x + c)^4*b + a), x)","F",0
112,0,0,0,0.000000," ","integrate(x/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\int \frac{x}{{\left(d x + c\right)}^{4} b + a}\,{d x}"," ",0,"integrate(x/((d*x + c)^4*b + a), x)","F",0
113,1,103,0,0.501295," ","integrate(1/(a+b*(d*x+c)^4),x, algorithm=""giac"")","-\frac{1}{2} \, \left(-\frac{1}{a^{3} b d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b d x + b c}{\left(-a b^{3}\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{3} b d^{4}}\right)^{\frac{1}{4}} \log\left({\left| b d x + b c + \left(-a b^{3}\right)^{\frac{1}{4}} \right|}\right) - \frac{1}{4} \, \left(-\frac{1}{a^{3} b d^{4}}\right)^{\frac{1}{4}} \log\left({\left| -b d x - b c + \left(-a b^{3}\right)^{\frac{1}{4}} \right|}\right)"," ",0,"-1/2*(-1/(a^3*b*d^4))^(1/4)*arctan(-(b*d*x + b*c)/(-a*b^3)^(1/4)) + 1/4*(-1/(a^3*b*d^4))^(1/4)*log(abs(b*d*x + b*c + (-a*b^3)^(1/4))) - 1/4*(-1/(a^3*b*d^4))^(1/4)*log(abs(-b*d*x - b*c + (-a*b^3)^(1/4)))","A",0
114,0,0,0,0.000000," ","integrate(1/x/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\int \frac{1}{{\left({\left(d x + c\right)}^{4} b + a\right)} x}\,{d x}"," ",0,"integrate(1/(((d*x + c)^4*b + a)*x), x)","F",0
115,0,0,0,0.000000," ","integrate(1/x^2/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\int \frac{1}{{\left({\left(d x + c\right)}^{4} b + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(((d*x + c)^4*b + a)*x^2), x)","F",0
116,1,219,0,0.327565," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^4,x, algorithm=""giac"")","\frac{1}{17} \, x^{17} - x^{16} + \frac{128}{15} \, x^{15} - \frac{4}{13} \, a x^{13} - 48 \, x^{14} + 4 \, a x^{12} + \frac{2560}{13} \, x^{13} - \frac{288}{11} \, a x^{11} - \frac{1856}{3} \, x^{12} + \frac{2}{3} \, a^{2} x^{9} + 112 \, a x^{10} + \frac{16768}{11} \, x^{11} - 6 \, a^{2} x^{8} - \frac{1024}{3} \, a x^{9} - \frac{14848}{5} \, x^{10} + \frac{192}{7} \, a^{2} x^{7} + 768 \, a x^{8} + \frac{40960}{9} \, x^{9} - \frac{4}{5} \, a^{3} x^{5} - 80 \, a^{2} x^{6} - 1280 \, a x^{7} - 5376 \, x^{8} + 4 \, a^{3} x^{4} + \frac{768}{5} \, a^{2} x^{5} + 1536 \, a x^{6} + \frac{32768}{7} \, x^{7} - \frac{32}{3} \, a^{3} x^{3} - 192 \, a^{2} x^{4} - \frac{6144}{5} \, a x^{5} - \frac{8192}{3} \, x^{6} + a^{4} x + 16 \, a^{3} x^{2} + 128 \, a^{2} x^{3} + 512 \, a x^{4} + \frac{4096}{5} \, x^{5}"," ",0,"1/17*x^17 - x^16 + 128/15*x^15 - 4/13*a*x^13 - 48*x^14 + 4*a*x^12 + 2560/13*x^13 - 288/11*a*x^11 - 1856/3*x^12 + 2/3*a^2*x^9 + 112*a*x^10 + 16768/11*x^11 - 6*a^2*x^8 - 1024/3*a*x^9 - 14848/5*x^10 + 192/7*a^2*x^7 + 768*a*x^8 + 40960/9*x^9 - 4/5*a^3*x^5 - 80*a^2*x^6 - 1280*a*x^7 - 5376*x^8 + 4*a^3*x^4 + 768/5*a^2*x^5 + 1536*a*x^6 + 32768/7*x^7 - 32/3*a^3*x^3 - 192*a^2*x^4 - 6144/5*a*x^5 - 8192/3*x^6 + a^4*x + 16*a^3*x^2 + 128*a^2*x^3 + 512*a*x^4 + 4096/5*x^5","B",0
117,1,128,0,0.296030," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^3,x, algorithm=""giac"")","-\frac{1}{13} \, x^{13} + x^{12} - \frac{72}{11} \, x^{11} + \frac{1}{3} \, a x^{9} + 28 \, x^{10} - 3 \, a x^{8} - \frac{256}{3} \, x^{9} + \frac{96}{7} \, a x^{7} + 192 \, x^{8} - \frac{3}{5} \, a^{2} x^{5} - 40 \, a x^{6} - 320 \, x^{7} + 3 \, a^{2} x^{4} + \frac{384}{5} \, a x^{5} + 384 \, x^{6} - 8 \, a^{2} x^{3} - 96 \, a x^{4} - \frac{1536}{5} \, x^{5} + a^{3} x + 12 \, a^{2} x^{2} + 64 \, a x^{3} + 128 \, x^{4}"," ",0,"-1/13*x^13 + x^12 - 72/11*x^11 + 1/3*a*x^9 + 28*x^10 - 3*a*x^8 - 256/3*x^9 + 96/7*a*x^7 + 192*x^8 - 3/5*a^2*x^5 - 40*a*x^6 - 320*x^7 + 3*a^2*x^4 + 384/5*a*x^5 + 384*x^6 - 8*a^2*x^3 - 96*a*x^4 - 1536/5*x^5 + a^3*x + 12*a^2*x^2 + 64*a*x^3 + 128*x^4","A",0
118,1,65,0,0.313355," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\frac{1}{9} \, x^{9} - x^{8} + \frac{32}{7} \, x^{7} - \frac{2}{5} \, a x^{5} - \frac{40}{3} \, x^{6} + 2 \, a x^{4} + \frac{128}{5} \, x^{5} - \frac{16}{3} \, a x^{3} - 32 \, x^{4} + a^{2} x + 8 \, a x^{2} + \frac{64}{3} \, x^{3}"," ",0,"1/9*x^9 - x^8 + 32/7*x^7 - 2/5*a*x^5 - 40/3*x^6 + 2*a*x^4 + 128/5*x^5 - 16/3*a*x^3 - 32*x^4 + a^2*x + 8*a*x^2 + 64/3*x^3","A",0
119,1,22,0,0.302678," ","integrate(-x^4+4*x^3-8*x^2+a+8*x,x, algorithm=""giac"")","-\frac{1}{5} \, x^{5} + x^{4} - \frac{8}{3} \, x^{3} + a x + 4 \, x^{2}"," ",0,"-1/5*x^5 + x^4 - 8/3*x^3 + a*x + 4*x^2","A",0
120,-2,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[12]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[34]-sqrt(1/16)*sqrt(1/256*(256*sqrt(a+4)*(a+4)-256*a-1024)/(-a^3-11*a^2-40*a-48))*ln(abs(-a^5*sqrt(a+4)+a^5+a^4*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x-a^4*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-17*a^4*sqrt(a+4)+17*a^4-a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x+a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)+14*a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x-14*a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-111*a^3*sqrt(a+4)+111*a^3-10*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x+10*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)+69*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x-69*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-351*a^2*sqrt(a+4)+351*a^2-29*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x+29*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)+144*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x-144*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-544*a*sqrt(a+4)+544*a-28*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x+28*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)+112*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x-112*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-336*sqrt(a+4)+336))+sqrt(1/16)*sqrt(1/256*(256*sqrt(a+4)*(a+4)-256*a-1024)/(-a^3-11*a^2-40*a-48))*ln(abs(-a^5*sqrt(a+4)+a^5-a^4*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x+a^4*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-17*a^4*sqrt(a+4)+17*a^4+a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x-a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)-14*a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x+14*a^3*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-111*a^3*sqrt(a+4)+111*a^3+10*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x-10*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)-69*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x+69*a^2*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-351*a^2*sqrt(a+4)+351*a^2+29*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x-29*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)-144*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x+144*a*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-544*a*sqrt(a+4)+544*a+28*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)*x-28*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*sqrt(a+4)-112*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)*x+112*sqrt(sqrt(a+4)*(-a^2-7*a-12)+a^2+7*a+12)-336*sqrt(a+4)+336))-sqrt(1/16)*sqrt(1/256*(-256*sqrt(a+4)*(a+4)-256*a-1024)/(-a^3-11*a^2-40*a-48))*ln(abs(a^5*sqrt(a+4)+a^5+a^4*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x-a^4*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+17*a^4*sqrt(a+4)+17*a^4+a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x-a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)+14*a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x-14*a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+111*a^3*sqrt(a+4)+111*a^3+10*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x-10*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)+69*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x-69*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+351*a^2*sqrt(a+4)+351*a^2+29*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x-29*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)+144*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x-144*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+544*a*sqrt(a+4)+544*a+28*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x-28*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)+112*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x-112*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+336*sqrt(a+4)+336))+sqrt(1/16)*sqrt(1/256*(-256*sqrt(a+4)*(a+4)-256*a-1024)/(-a^3-11*a^2-40*a-48))*ln(abs(a^5*sqrt(a+4)+a^5-a^4*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x+a^4*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+17*a^4*sqrt(a+4)+17*a^4-a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x+a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)-14*a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x+14*a^3*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+111*a^3*sqrt(a+4)+111*a^3-10*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x+10*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)-69*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x+69*a^2*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+351*a^2*sqrt(a+4)+351*a^2-29*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x+29*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)-144*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x+144*a*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+544*a*sqrt(a+4)+544*a-28*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)*x+28*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*sqrt(a+4)-112*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)*x+112*sqrt(sqrt(a+4)*(a^2+7*a+12)+a^2+7*a+12)+336*sqrt(a+4)+336))","F(-2)",0
121,-2,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[12]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[34](x^3-3*x^2+x*a+8*x-a-6)/(-4*a^2-28*a-48)/(x^4-4*x^3+8*x^2-8*x-a)+(sqrt(1/16)*sqrt(1/256*(256*sqrt(a+4)*(9*a^3+103*a^2+392*a+496)+3840*a^3+42240*a^2+154624*a+188416)/(a^3+11*a^2+40*a+48))*ln(abs(243*a^10*sqrt(a+4)+324*a^10+8640*a^9*sqrt(a+4)+11466*a^9+81*a^8*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-81*a^8*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+138027*a^8*sqrt(a+4)+182314*a^8+81*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-81*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+2340*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-2340*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+1304648*a^7*sqrt(a+4)+1715172*a^7+2016*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-2016*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+29518*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-29518*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+8079749*a^6*sqrt(a+4)+10572392*a^6+21454*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-21454*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+212356*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-212356*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+34255200*a^5*sqrt(a+4)+44613658*a^5+126540*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-126540*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+952845*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-952845*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+100679657*a^4*sqrt(a+4)+130513730*a^4+446685*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-446685*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+2730184*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-2730184*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+202540404*a^3*sqrt(a+4)+261341928*a^3+943444*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-943444*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+4877364*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-4877364*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+266882676*a^2*sqrt(a+4)+342778384*a^2+1103588*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-1103588*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+4965684*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-4965684*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+207974132*a*sqrt(a+4)+265897256*a+551332*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x-551332*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+2205328*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-2205328*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+72775824*sqrt(a+4)+92623776))-sqrt(1/16)*sqrt(1/256*(256*sqrt(a+4)*(9*a^3+103*a^2+392*a+496)+3840*a^3+42240*a^2+154624*a+188416)/(a^3+11*a^2+40*a+48))*ln(abs(243*a^10*sqrt(a+4)+324*a^10+8640*a^9*sqrt(a+4)+11466*a^9-81*a^8*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+81*a^8*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+138027*a^8*sqrt(a+4)+182314*a^8-81*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+81*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-2340*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+2340*a^7*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+1304648*a^7*sqrt(a+4)+1715172*a^7-2016*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+2016*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-29518*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+29518*a^6*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+8079749*a^6*sqrt(a+4)+10572392*a^6-21454*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+21454*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-212356*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+212356*a^5*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+34255200*a^5*sqrt(a+4)+44613658*a^5-126540*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+126540*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-952845*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+952845*a^4*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+100679657*a^4*sqrt(a+4)+130513730*a^4-446685*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+446685*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-2730184*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+2730184*a^3*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+202540404*a^3*sqrt(a+4)+261341928*a^3-943444*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+943444*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-4877364*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+4877364*a^2*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+266882676*a^2*sqrt(a+4)+342778384*a^2-1103588*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+1103588*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-4965684*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+4965684*a*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+207974132*a*sqrt(a+4)+265897256*a-551332*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+551332*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)-2205328*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x+2205328*sqrt(sqrt(a+4)*(9*a^4+130*a^3+701*a^2+1672*a+1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)+72775824*sqrt(a+4)+92623776))+sqrt(1/16)*sqrt(1/256*(-256*sqrt(a+4)*(9*a^3+103*a^2+392*a+496)+3840*a^3+42240*a^2+154624*a+188416)/(a^3+11*a^2+40*a+48))*ln(abs(-243*a^10*sqrt(a+4)+324*a^10-8640*a^9*sqrt(a+4)+11466*a^9+81*a^8*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-81*a^8*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)-138027*a^8*sqrt(a+4)+182314*a^8-81*a^7*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+81*a^7*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+2340*a^7*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-2340*a^7*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)-1304648*a^7*sqrt(a+4)+1715172*a^7-2016*a^6*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+2016*a^6*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+29518*a^6*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-29518*a^6*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)-8079749*a^6*sqrt(a+4)+10572392*a^6-21454*a^5*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+21454*a^5*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)+212356*a^5*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*x-212356*a^5*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)-34255200*a^5*sqrt(a+4)+44613658*a^5-126540*a^4*sqrt(sqrt(a+4)*(-9*a^4-130*a^3-701*a^2-1672*a-1488)+15*a^4+210*a^3+1099*a^2+2548*a+2208)*sqrt(a+4)*x+126540*a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122,-2,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[12]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 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123,1,222,0,0.389851," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^4,x, algorithm=""giac"")","\frac{1}{18} \, x^{18} - \frac{16}{17} \, x^{17} + 8 \, x^{16} - \frac{2}{7} \, a x^{14} - \frac{224}{5} \, x^{15} + \frac{48}{13} \, a x^{13} + \frac{1280}{7} \, x^{14} - 24 \, a x^{12} - \frac{7424}{13} \, x^{13} + \frac{3}{5} \, a^{2} x^{10} + \frac{1120}{11} \, a x^{11} + \frac{4192}{3} \, x^{12} - \frac{16}{3} \, a^{2} x^{9} - \frac{1536}{5} \, a x^{10} - \frac{29696}{11} \, x^{11} + 24 \, a^{2} x^{8} + \frac{2048}{3} \, a x^{9} + 4096 \, x^{10} - \frac{2}{3} \, a^{3} x^{6} - \frac{480}{7} \, a^{2} x^{7} - 1120 \, a x^{8} - \frac{14336}{3} \, x^{9} + \frac{16}{5} \, a^{3} x^{5} + 128 \, a^{2} x^{6} + \frac{9216}{7} \, a x^{7} + 4096 \, x^{8} - 8 \, a^{3} x^{4} - \frac{768}{5} \, a^{2} x^{5} - 1024 \, a x^{6} - \frac{16384}{7} \, x^{7} + \frac{1}{2} \, a^{4} x^{2} + \frac{32}{3} \, a^{3} x^{3} + 96 \, a^{2} x^{4} + \frac{2048}{5} \, a x^{5} + \frac{2048}{3} \, x^{6}"," ",0,"1/18*x^18 - 16/17*x^17 + 8*x^16 - 2/7*a*x^14 - 224/5*x^15 + 48/13*a*x^13 + 1280/7*x^14 - 24*a*x^12 - 7424/13*x^13 + 3/5*a^2*x^10 + 1120/11*a*x^11 + 4192/3*x^12 - 16/3*a^2*x^9 - 1536/5*a*x^10 - 29696/11*x^11 + 24*a^2*x^8 + 2048/3*a*x^9 + 4096*x^10 - 2/3*a^3*x^6 - 480/7*a^2*x^7 - 1120*a*x^8 - 14336/3*x^9 + 16/5*a^3*x^5 + 128*a^2*x^6 + 9216/7*a*x^7 + 4096*x^8 - 8*a^3*x^4 - 768/5*a^2*x^5 - 1024*a*x^6 - 16384/7*x^7 + 1/2*a^4*x^2 + 32/3*a^3*x^3 + 96*a^2*x^4 + 2048/5*a*x^5 + 2048/3*x^6","A",0
124,1,133,0,0.351104," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^3,x, algorithm=""giac"")","-\frac{1}{14} \, x^{14} + \frac{12}{13} \, x^{13} - 6 \, x^{12} + \frac{3}{10} \, a x^{10} + \frac{280}{11} \, x^{11} - \frac{8}{3} \, a x^{9} - \frac{384}{5} \, x^{10} + 12 \, a x^{8} + \frac{512}{3} \, x^{9} - \frac{1}{2} \, a^{2} x^{6} - \frac{240}{7} \, a x^{7} - 280 \, x^{8} + \frac{12}{5} \, a^{2} x^{5} + 64 \, a x^{6} + \frac{2304}{7} \, x^{7} - 6 \, a^{2} x^{4} - \frac{384}{5} \, a x^{5} - 256 \, x^{6} + \frac{1}{2} \, a^{3} x^{2} + 8 \, a^{2} x^{3} + 48 \, a x^{4} + \frac{512}{5} \, x^{5}"," ",0,"-1/14*x^14 + 12/13*x^13 - 6*x^12 + 3/10*a*x^10 + 280/11*x^11 - 8/3*a*x^9 - 384/5*x^10 + 12*a*x^8 + 512/3*x^9 - 1/2*a^2*x^6 - 240/7*a*x^7 - 280*x^8 + 12/5*a^2*x^5 + 64*a*x^6 + 2304/7*x^7 - 6*a^2*x^4 - 384/5*a*x^5 - 256*x^6 + 1/2*a^3*x^2 + 8*a^2*x^3 + 48*a*x^4 + 512/5*x^5","A",0
125,1,68,0,0.347669," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\frac{1}{10} \, x^{10} - \frac{8}{9} \, x^{9} + 4 \, x^{8} - \frac{1}{3} \, a x^{6} - \frac{80}{7} \, x^{7} + \frac{8}{5} \, a x^{5} + \frac{64}{3} \, x^{6} - 4 \, a x^{4} - \frac{128}{5} \, x^{5} + \frac{1}{2} \, a^{2} x^{2} + \frac{16}{3} \, a x^{3} + 16 \, x^{4}"," ",0,"1/10*x^10 - 8/9*x^9 + 4*x^8 - 1/3*a*x^6 - 80/7*x^7 + 8/5*a*x^5 + 64/3*x^6 - 4*a*x^4 - 128/5*x^5 + 1/2*a^2*x^2 + 16/3*a*x^3 + 16*x^4","A",0
126,1,27,0,0.360283," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x),x, algorithm=""giac"")","-\frac{1}{6} \, x^{6} + \frac{4}{5} \, x^{5} - 2 \, x^{4} + \frac{1}{2} \, a x^{2} + \frac{8}{3} \, x^{3}"," ",0,"-1/6*x^6 + 4/5*x^5 - 2*x^4 + 1/2*a*x^2 + 8/3*x^3","A",0
127,0,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x),x, algorithm=""giac"")","\int -\frac{x}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x}\,{d x}"," ",0,"integrate(-x/(x^4 - 4*x^3 + 8*x^2 - a - 8*x), x)","F",0
128,0,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\int \frac{x}{{\left(x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x\right)}^{2}}\,{d x}"," ",0,"integrate(x/(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^2, x)","F",0
129,0,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^3,x, algorithm=""giac"")","\int -\frac{x}{{\left(x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x\right)}^{3}}\,{d x}"," ",0,"integrate(-x/(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^3, x)","F",0
130,1,222,0,0.242891," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^4,x, algorithm=""giac"")","\frac{1}{19} \, x^{19} - \frac{8}{9} \, x^{18} + \frac{128}{17} \, x^{17} - \frac{4}{15} \, a x^{15} - 42 \, x^{16} + \frac{24}{7} \, a x^{14} + \frac{512}{3} \, x^{15} - \frac{288}{13} \, a x^{13} - \frac{3712}{7} \, x^{14} + \frac{6}{11} \, a^{2} x^{11} + \frac{280}{3} \, a x^{12} + \frac{16768}{13} \, x^{13} - \frac{24}{5} \, a^{2} x^{10} - \frac{3072}{11} \, a x^{11} - \frac{7424}{3} \, x^{12} + \frac{64}{3} \, a^{2} x^{9} + \frac{3072}{5} \, a x^{10} + \frac{40960}{11} \, x^{11} - \frac{4}{7} \, a^{3} x^{7} - 60 \, a^{2} x^{8} - \frac{8960}{9} \, a x^{9} - \frac{21504}{5} \, x^{10} + \frac{8}{3} \, a^{3} x^{6} + \frac{768}{7} \, a^{2} x^{7} + 1152 \, a x^{8} + \frac{32768}{9} \, x^{9} - \frac{32}{5} \, a^{3} x^{5} - 128 \, a^{2} x^{6} - \frac{6144}{7} \, a x^{7} - 2048 \, x^{8} + \frac{1}{3} \, a^{4} x^{3} + 8 \, a^{3} x^{4} + \frac{384}{5} \, a^{2} x^{5} + \frac{1024}{3} \, a x^{6} + \frac{4096}{7} \, x^{7}"," ",0,"1/19*x^19 - 8/9*x^18 + 128/17*x^17 - 4/15*a*x^15 - 42*x^16 + 24/7*a*x^14 + 512/3*x^15 - 288/13*a*x^13 - 3712/7*x^14 + 6/11*a^2*x^11 + 280/3*a*x^12 + 16768/13*x^13 - 24/5*a^2*x^10 - 3072/11*a*x^11 - 7424/3*x^12 + 64/3*a^2*x^9 + 3072/5*a*x^10 + 40960/11*x^11 - 4/7*a^3*x^7 - 60*a^2*x^8 - 8960/9*a*x^9 - 21504/5*x^10 + 8/3*a^3*x^6 + 768/7*a^2*x^7 + 1152*a*x^8 + 32768/9*x^9 - 32/5*a^3*x^5 - 128*a^2*x^6 - 6144/7*a*x^7 - 2048*x^8 + 1/3*a^4*x^3 + 8*a^3*x^4 + 384/5*a^2*x^5 + 1024/3*a*x^6 + 4096/7*x^7","A",0
131,1,133,0,0.285093," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^3,x, algorithm=""giac"")","-\frac{1}{15} \, x^{15} + \frac{6}{7} \, x^{14} - \frac{72}{13} \, x^{13} + \frac{3}{11} \, a x^{11} + \frac{70}{3} \, x^{12} - \frac{12}{5} \, a x^{10} - \frac{768}{11} \, x^{11} + \frac{32}{3} \, a x^{9} + \frac{768}{5} \, x^{10} - \frac{3}{7} \, a^{2} x^{7} - 30 \, a x^{8} - \frac{2240}{9} \, x^{9} + 2 \, a^{2} x^{6} + \frac{384}{7} \, a x^{7} + 288 \, x^{8} - \frac{24}{5} \, a^{2} x^{5} - 64 \, a x^{6} - \frac{1536}{7} \, x^{7} + \frac{1}{3} \, a^{3} x^{3} + 6 \, a^{2} x^{4} + \frac{192}{5} \, a x^{5} + \frac{256}{3} \, x^{6}"," ",0,"-1/15*x^15 + 6/7*x^14 - 72/13*x^13 + 3/11*a*x^11 + 70/3*x^12 - 12/5*a*x^10 - 768/11*x^11 + 32/3*a*x^9 + 768/5*x^10 - 3/7*a^2*x^7 - 30*a*x^8 - 2240/9*x^9 + 2*a^2*x^6 + 384/7*a*x^7 + 288*x^8 - 24/5*a^2*x^5 - 64*a*x^6 - 1536/7*x^7 + 1/3*a^3*x^3 + 6*a^2*x^4 + 192/5*a*x^5 + 256/3*x^6","A",0
132,1,68,0,0.287360," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\frac{1}{11} \, x^{11} - \frac{4}{5} \, x^{10} + \frac{32}{9} \, x^{9} - \frac{2}{7} \, a x^{7} - 10 \, x^{8} + \frac{4}{3} \, a x^{6} + \frac{128}{7} \, x^{7} - \frac{16}{5} \, a x^{5} - \frac{64}{3} \, x^{6} + \frac{1}{3} \, a^{2} x^{3} + 4 \, a x^{4} + \frac{64}{5} \, x^{5}"," ",0,"1/11*x^11 - 4/5*x^10 + 32/9*x^9 - 2/7*a*x^7 - 10*x^8 + 4/3*a*x^6 + 128/7*x^7 - 16/5*a*x^5 - 64/3*x^6 + 1/3*a^2*x^3 + 4*a*x^4 + 64/5*x^5","A",0
133,1,27,0,0.312978," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x),x, algorithm=""giac"")","-\frac{1}{7} \, x^{7} + \frac{2}{3} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{1}{3} \, a x^{3} + 2 \, x^{4}"," ",0,"-1/7*x^7 + 2/3*x^6 - 8/5*x^5 + 1/3*a*x^3 + 2*x^4","A",0
134,0,0,0,0.000000," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x),x, algorithm=""giac"")","\int -\frac{x^{2}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x}\,{d x}"," ",0,"integrate(-x^2/(x^4 - 4*x^3 + 8*x^2 - a - 8*x), x)","F",0
135,0,0,0,0.000000," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^2,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x\right)}^{2}}\,{d x}"," ",0,"integrate(x^2/(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^2, x)","F",0
136,0,0,0,0.000000," ","integrate(x^4/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{x^{4}}{b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}}\,{d x}"," ",0,"integrate(x^4/(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3), x)","F",0
137,0,0,0,0.000000," ","integrate(x^3/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{x^{3}}{b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}}\,{d x}"," ",0,"integrate(x^3/(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3), x)","F",0
138,0,0,0,0.000000," ","integrate(x^2/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{x^{2}}{b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}}\,{d x}"," ",0,"integrate(x^2/(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3), x)","F",0
139,0,0,0,0.000000," ","integrate(x/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{x}{b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}}\,{d x}"," ",0,"integrate(x/(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{1}{b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}}\,{d x}"," ",0,"integrate(1/(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3), x)","F",0
141,0,0,0,0.000000," ","integrate(1/x/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} x}\,{d x}"," ",0,"integrate(1/((b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3)*x), x)","F",0
142,0,0,0,0.000000," ","integrate(1/x^2/(b^3*x^6+9*a*b^2*x^4+27*a^2*c*x^3+27*a^2*b*x^2+27*a^3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} c x^{3} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*c*x^3 + 27*a^2*b*x^2 + 27*a^3)*x^2), x)","F",0
143,0,0,0,0.000000," ","integrate(x^5/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{x^{5}}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(x^5/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
144,0,0,0,0.000000," ","integrate(x^4/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{x^{4}}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(x^4/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
145,0,0,0,0.000000," ","integrate(x^3/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{x^{3}}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(x^3/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
146,0,0,0,0.000000," ","integrate(x^2/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{x^{2}}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(x^2/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
147,0,0,0,0.000000," ","integrate(x/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{x}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(x/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
148,0,0,0,0.000000," ","integrate(1/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{1}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x}"," ",0,"integrate(1/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216), x)","F",0
149,0,0,0,0.000000," ","integrate(1/x/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)} x}\,{d x}"," ",0,"integrate(1/((x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)*x), x)","F",0
150,0,0,0,0.000000," ","integrate(1/x^2/(x^6+18*x^4+324*x^3+108*x^2+216),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)*x^2), x)","F",0
151,0,0,0,0.000000," ","integrate(x^8/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^8/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
152,0,0,0,0.000000," ","integrate(x^7/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^7/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
153,0,0,0,0.000000," ","integrate(x^6/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^6/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
154,0,0,0,0.000000," ","integrate(x^5/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^5/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
155,0,0,0,0.000000," ","integrate(x^4/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
156,0,0,0,0.000000," ","integrate(x^3/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^3/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
157,0,0,0,0.000000," ","integrate(x^2/(x^6+18*x^4+324*x^3+108*x^2+216)^2,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right)}^{2}}\,{d x}"," ",0,"integrate(x^2/(x^6 + 18*x^4 + 324*x^3 + 108*x^2 + 216)^2, x)","F",0
158,1,21,0,0.369818," ","integrate((b^2*d*x^5+b^2*c*x^4+2*a*b*d*x^3+2*a*b*c*x^2+a^2*d*x+a^2*c)/(d*x+c),x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x"," ",0,"1/5*b^2*x^5 + 2/3*a*b*x^3 + a^2*x","A",0
159,1,365,0,0.263066," ","integrate((b^2*d*x^5+b^2*c*x^4+2*a*b*d*x^3+2*a*b*c*x^2+a^2*d*x+a^2*c)/(d*x+c)^2,x, algorithm=""giac"")","-\frac{1}{12} \, b^{2} d {\left(\frac{{\left(d x + c\right)}^{4} {\left(\frac{20 \, c}{d x + c} - \frac{60 \, c^{2}}{{\left(d x + c\right)}^{2}} + \frac{120 \, c^{3}}{{\left(d x + c\right)}^{3}} - 3\right)}}{d^{6}} + \frac{60 \, c^{4} \log\left(\frac{{\left| d x + c \right|}}{{\left(d x + c\right)}^{2} {\left| d \right|}}\right)}{d^{6}} - \frac{12 \, c^{5}}{{\left(d x + c\right)} d^{6}}\right)} - \frac{1}{3} \, b^{2} c {\left(\frac{{\left(d x + c\right)}^{3} {\left(\frac{6 \, c}{d x + c} - \frac{18 \, c^{2}}{{\left(d x + c\right)}^{2}} - 1\right)}}{d^{5}} - \frac{12 \, c^{3} \log\left(\frac{{\left| d x + c \right|}}{{\left(d x + c\right)}^{2} {\left| d \right|}}\right)}{d^{5}} + \frac{3 \, c^{4}}{{\left(d x + c\right)} d^{5}}\right)} - a b d {\left(\frac{{\left(d x + c\right)}^{2} {\left(\frac{6 \, c}{d x + c} - 1\right)}}{d^{4}} + \frac{6 \, c^{2} \log\left(\frac{{\left| d x + c \right|}}{{\left(d x + c\right)}^{2} {\left| d \right|}}\right)}{d^{4}} - \frac{2 \, c^{3}}{{\left(d x + c\right)} d^{4}}\right)} + 2 \, a b c {\left(\frac{2 \, c \log\left(\frac{{\left| d x + c \right|}}{{\left(d x + c\right)}^{2} {\left| d \right|}}\right)}{d^{3}} + \frac{d x + c}{d^{3}} - \frac{c^{2}}{{\left(d x + c\right)} d^{3}}\right)} - a^{2} {\left(\frac{\log\left(\frac{{\left| d x + c \right|}}{{\left(d x + c\right)}^{2} {\left| d \right|}}\right)}{d} - \frac{c}{{\left(d x + c\right)} d}\right)} - \frac{a^{2} c}{{\left(d x + c\right)} d}"," ",0,"-1/12*b^2*d*((d*x + c)^4*(20*c/(d*x + c) - 60*c^2/(d*x + c)^2 + 120*c^3/(d*x + c)^3 - 3)/d^6 + 60*c^4*log(abs(d*x + c)/((d*x + c)^2*abs(d)))/d^6 - 12*c^5/((d*x + c)*d^6)) - 1/3*b^2*c*((d*x + c)^3*(6*c/(d*x + c) - 18*c^2/(d*x + c)^2 - 1)/d^5 - 12*c^3*log(abs(d*x + c)/((d*x + c)^2*abs(d)))/d^5 + 3*c^4/((d*x + c)*d^5)) - a*b*d*((d*x + c)^2*(6*c/(d*x + c) - 1)/d^4 + 6*c^2*log(abs(d*x + c)/((d*x + c)^2*abs(d)))/d^4 - 2*c^3/((d*x + c)*d^4)) + 2*a*b*c*(2*c*log(abs(d*x + c)/((d*x + c)^2*abs(d)))/d^3 + (d*x + c)/d^3 - c^2/((d*x + c)*d^3)) - a^2*(log(abs(d*x + c)/((d*x + c)^2*abs(d)))/d - c/((d*x + c)*d)) - a^2*c/((d*x + c)*d)","B",0
160,1,13,0,0.299901," ","integrate((2*c*x+b)*(c*x^2+b*x)^13,x, algorithm=""giac"")","\frac{1}{14} \, {\left(c x^{2} + b x\right)}^{14}"," ",0,"1/14*(c*x^2 + b*x)^14","A",0
161,1,156,0,0.313071," ","integrate(x^14*(2*c*x^2+b)*(c*x^3+b*x)^13,x, algorithm=""giac"")","\frac{1}{28} \, c^{14} x^{56} + \frac{1}{2} \, b c^{13} x^{54} + \frac{13}{4} \, b^{2} c^{12} x^{52} + 13 \, b^{3} c^{11} x^{50} + \frac{143}{4} \, b^{4} c^{10} x^{48} + \frac{143}{2} \, b^{5} c^{9} x^{46} + \frac{429}{4} \, b^{6} c^{8} x^{44} + \frac{858}{7} \, b^{7} c^{7} x^{42} + \frac{429}{4} \, b^{8} c^{6} x^{40} + \frac{143}{2} \, b^{9} c^{5} x^{38} + \frac{143}{4} \, b^{10} c^{4} x^{36} + 13 \, b^{11} c^{3} x^{34} + \frac{13}{4} \, b^{12} c^{2} x^{32} + \frac{1}{2} \, b^{13} c x^{30} + \frac{1}{28} \, b^{14} x^{28}"," ",0,"1/28*c^14*x^56 + 1/2*b*c^13*x^54 + 13/4*b^2*c^12*x^52 + 13*b^3*c^11*x^50 + 143/4*b^4*c^10*x^48 + 143/2*b^5*c^9*x^46 + 429/4*b^6*c^8*x^44 + 858/7*b^7*c^7*x^42 + 429/4*b^8*c^6*x^40 + 143/2*b^9*c^5*x^38 + 143/4*b^10*c^4*x^36 + 13*b^11*c^3*x^34 + 13/4*b^12*c^2*x^32 + 1/2*b^13*c*x^30 + 1/28*b^14*x^28","B",0
162,1,156,0,0.332291," ","integrate(x^28*(2*c*x^3+b)*(c*x^4+b*x)^13,x, algorithm=""giac"")","\frac{1}{42} \, c^{14} x^{84} + \frac{1}{3} \, b c^{13} x^{81} + \frac{13}{6} \, b^{2} c^{12} x^{78} + \frac{26}{3} \, b^{3} c^{11} x^{75} + \frac{143}{6} \, b^{4} c^{10} x^{72} + \frac{143}{3} \, b^{5} c^{9} x^{69} + \frac{143}{2} \, b^{6} c^{8} x^{66} + \frac{572}{7} \, b^{7} c^{7} x^{63} + \frac{143}{2} \, b^{8} c^{6} x^{60} + \frac{143}{3} \, b^{9} c^{5} x^{57} + \frac{143}{6} \, b^{10} c^{4} x^{54} + \frac{26}{3} \, b^{11} c^{3} x^{51} + \frac{13}{6} \, b^{12} c^{2} x^{48} + \frac{1}{3} \, b^{13} c x^{45} + \frac{1}{42} \, b^{14} x^{42}"," ",0,"1/42*c^14*x^84 + 1/3*b*c^13*x^81 + 13/6*b^2*c^12*x^78 + 26/3*b^3*c^11*x^75 + 143/6*b^4*c^10*x^72 + 143/3*b^5*c^9*x^69 + 143/2*b^6*c^8*x^66 + 572/7*b^7*c^7*x^63 + 143/2*b^8*c^6*x^60 + 143/3*b^9*c^5*x^57 + 143/6*b^10*c^4*x^54 + 26/3*b^11*c^3*x^51 + 13/6*b^12*c^2*x^48 + 1/3*b^13*c*x^45 + 1/42*b^14*x^42","B",0
163,1,189,0,1.857256," ","integrate(x^(-14+14*n)*(b+2*c*x^n)*(b*x+c*x^(1+n))^13,x, algorithm=""giac"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) + 364*b^3*c^11*x^(25*n) + 1001*b^4*c^10*x^(24*n) + 2002*b^5*c^9*x^(23*n) + 3003*b^6*c^8*x^(22*n) + 3432*b^7*c^7*x^(21*n) + 3003*b^8*c^6*x^(20*n) + 2002*b^9*c^5*x^(19*n) + 1001*b^10*c^4*x^(18*n) + 364*b^11*c^3*x^(17*n) + 91*b^12*c^2*x^(16*n) + 14*b^13*c*x^(15*n) + b^14*x^(14*n))/n","B",0
164,1,11,0,0.230433," ","integrate((2*c*x+b)/(c*x^2+b*x),x, algorithm=""giac"")","\log\left({\left| c x^{2} + b x \right|}\right)"," ",0,"log(abs(c*x^2 + b*x))","A",0
165,1,18,0,0.333581," ","integrate((2*c*x^2+b)/(c*x^3+b*x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(x^{2}\right) + \frac{1}{2} \, \log\left({\left| c x^{2} + b \right|}\right)"," ",0,"1/2*log(x^2) + 1/2*log(abs(c*x^2 + b))","A",0
166,1,15,0,0.314119," ","integrate((2*c*x^3+b)/(c*x^4+b*x),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| c x^{3} + b \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"1/3*log(abs(c*x^3 + b)) + log(abs(x))","A",0
167,0,0,0,0.000000," ","integrate((b+2*c*x^n)/(b*x+c*x^(1+n)),x, algorithm=""giac"")","\int \frac{2 \, c x^{n} + b}{b x + c x^{n + 1}}\,{d x}"," ",0,"integrate((2*c*x^n + b)/(b*x + c*x^(n + 1)), x)","F",0
168,1,13,0,0.270343," ","integrate((2*c*x+b)/(c*x^2+b*x)^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2} + b x\right)}^{7}}"," ",0,"-1/7/(c*x^2 + b*x)^7","A",0
169,1,15,0,0.405558," ","integrate((2*c*x^2+b)/x^7/(c*x^3+b*x)^8,x, algorithm=""giac"")","-\frac{1}{14 \, {\left(c x^{4} + b x^{2}\right)}^{7}}"," ",0,"-1/14/(c*x^4 + b*x^2)^7","A",0
170,1,15,0,0.304460," ","integrate((2*c*x^3+b)/x^14/(c*x^4+b*x)^8,x, algorithm=""giac"")","-\frac{1}{21 \, {\left(c x^{6} + b x^{3}\right)}^{7}}"," ",0,"-1/21/(c*x^6 + b*x^3)^7","A",0
171,0,0,0,0.000000," ","integrate((b+2*c*x^n)/(x^(-7+7*n))/(b*x+c*x^(1+n))^8,x, algorithm=""giac"")","\int \frac{2 \, c x^{n} + b}{{\left(b x + c x^{n + 1}\right)}^{8} x^{7 \, n - 7}}\,{d x}"," ",0,"integrate((2*c*x^n + b)/((b*x + c*x^(n + 1))^8*x^(7*n - 7)), x)","F",0
172,1,19,0,0.373699," ","integrate((2*c*x+b)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b x\right)}^{p + 1}}{p + 1}"," ",0,"(c*x^2 + b*x)^(p + 1)/(p + 1)","A",0
173,1,54,0,0.334442," ","integrate(x^(1+p)*(2*c*x^2+b)*(c*x^3+b*x)^p,x, algorithm=""giac"")","\frac{c x^{3} e^{\left(p \log\left(c x^{2} + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)} + b x e^{\left(p \log\left(c x^{2} + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^3*e^(p*log(c*x^2 + b) + 2*p*log(x) + log(x)) + b*x*e^(p*log(c*x^2 + b) + 2*p*log(x) + log(x)))/(p + 1)","B",0
174,1,54,0,0.494204," ","integrate(b*x^(1+p)*(c*x^3+b*x)^p+2*c*x^(3+p)*(c*x^3+b*x)^p,x, algorithm=""giac"")","\frac{c x^{3} e^{\left(p \log\left(c x^{2} + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)} + b x e^{\left(p \log\left(c x^{2} + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^3*e^(p*log(c*x^2 + b) + 2*p*log(x) + log(x)) + b*x*e^(p*log(c*x^2 + b) + 2*p*log(x) + log(x)))/(p + 1)","B",0
175,1,58,0,0.345761," ","integrate(x^(2+2*p)*(2*c*x^3+b)*(c*x^4+b*x)^p,x, algorithm=""giac"")","\frac{c x^{4} e^{\left(p \log\left(c x^{3} + b\right) + 3 \, p \log\left(x\right) + 2 \, \log\left(x\right)\right)} + b x e^{\left(p \log\left(c x^{3} + b\right) + 3 \, p \log\left(x\right) + 2 \, \log\left(x\right)\right)}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^4*e^(p*log(c*x^3 + b) + 3*p*log(x) + 2*log(x)) + b*x*e^(p*log(c*x^3 + b) + 3*p*log(x) + 2*log(x)))/(p + 1)","B",0
176,0,0,0,0.000000," ","integrate(x^((-1+n)*(1+p))*(b+2*c*x^n)*(b*x+c*x^(1+n))^p,x, algorithm=""giac"")","\int {\left(2 \, c x^{n} + b\right)} {\left(b x + c x^{n + 1}\right)}^{p} x^{{\left(n - 1\right)} {\left(p + 1\right)}}\,{d x}"," ",0,"integrate((2*c*x^n + b)*(b*x + c*x^(n + 1))^p*x^((n - 1)*(p + 1)), x)","F",0
177,1,26,0,0.312936," ","integrate((b^2*d*x^5+b^2*c*x^4+2*a*b*d*x^3+2*a*b*c*x^2+a^2*d*x+a^2*c)/(b*x^2+a),x, algorithm=""giac"")","\frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/4*b*d*x^4 + 1/3*b*c*x^3 + 1/2*a*d*x^2 + a*c*x","A",0
178,1,10,0,0.396144," ","integrate((b^2*d*x^5+b^2*c*x^4+2*a*b*d*x^3+2*a*b*c*x^2+a^2*d*x+a^2*c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{2} \, d x^{2} + c x"," ",0,"1/2*d*x^2 + c*x","A",0
179,1,31,0,0.404396," ","integrate((b^2*d*x^5+b^2*c*x^4+2*a*b*d*x^3+2*a*b*c*x^2+a^2*d*x+a^2*c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}} + \frac{d \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"c*arctan(b*x/sqrt(a*b))/sqrt(a*b) + 1/2*d*log(b*x^2 + a)/b","A",0
180,1,25,0,0.293984," ","integrate((3*d*x^2+2*c*x+b)*(d*x^3+c*x^2+b*x+a)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2} + b x + a\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2 + b*x + a)^(n + 1)/(n + 1)","A",0
181,1,24,0,0.307203," ","integrate((3*d*x^2+2*c*x+b)*(d*x^3+c*x^2+b*x)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2} + b x\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2 + b*x)^(n + 1)/(n + 1)","A",0
182,1,65,0,0.395406," ","integrate(x^n*(d*x^2+c*x+b)^n*(3*d*x^2+2*c*x+b),x, algorithm=""giac"")","\frac{{\left(d x^{2} + c x + b\right)}^{n} d x^{3} x^{n} + {\left(d x^{2} + c x + b\right)}^{n} c x^{2} x^{n} + {\left(d x^{2} + c x + b\right)}^{n} b x x^{n}}{n + 1}"," ",0,"((d*x^2 + c*x + b)^n*d*x^3*x^n + (d*x^2 + c*x + b)^n*c*x^2*x^n + (d*x^2 + c*x + b)^n*b*x*x^n)/(n + 1)","B",0
183,1,20,0,0.281928," ","integrate((3*d*x^2+b)*(d*x^3+b*x+a)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + b x + a\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + b*x + a)^(n + 1)/(n + 1)","A",0
184,1,19,0,0.341372," ","integrate((3*d*x^2+b)*(d*x^3+b*x)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + b x\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + b*x)^(n + 1)/(n + 1)","A",0
185,1,39,0,0.338046," ","integrate(x^n*(d*x^2+b)^n*(3*d*x^2+b),x, algorithm=""giac"")","\frac{{\left(d x^{2} + b\right)}^{n} d x^{3} x^{n} + {\left(d x^{2} + b\right)}^{n} b x x^{n}}{n + 1}"," ",0,"((d*x^2 + b)^n*d*x^3*x^n + (d*x^2 + b)^n*b*x*x^n)/(n + 1)","A",0
186,1,22,0,0.344843," ","integrate((3*d*x^2+2*c*x)*(d*x^3+c*x^2+a)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2} + a\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2 + a)^(n + 1)/(n + 1)","A",0
187,1,21,0,0.310005," ","integrate((3*d*x^2+2*c*x)*(d*x^3+c*x^2)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2}\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2)^(n + 1)/(n + 1)","A",0
188,1,51,0,0.460179," ","integrate(x^n*(d*x^2+c*x)^n*(3*d*x^2+2*c*x),x, algorithm=""giac"")","\frac{d x^{3} x^{n} e^{\left(n \log\left(d x + c\right) + n \log\left(x\right)\right)} + c x^{2} x^{n} e^{\left(n \log\left(d x + c\right) + n \log\left(x\right)\right)}}{n + 1}"," ",0,"(d*x^3*x^n*e^(n*log(d*x + c) + n*log(x)) + c*x^2*x^n*e^(n*log(d*x + c) + n*log(x)))/(n + 1)","B",0
189,1,41,0,0.313521," ","integrate(x^(2*n)*(d*x+c)^n*(3*d*x^2+2*c*x),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{n} d x^{3} x^{2 \, n} + {\left(d x + c\right)}^{n} c x^{2} x^{2 \, n}}{n + 1}"," ",0,"((d*x + c)^n*d*x^3*x^(2*n) + (d*x + c)^n*c*x^2*x^(2*n))/(n + 1)","A",0
190,1,22,0,0.322642," ","integrate(x*(3*d*x+2*c)*(d*x^3+c*x^2+a)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2} + a\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2 + a)^(n + 1)/(n + 1)","A",0
191,1,21,0,0.398241," ","integrate(x*(3*d*x+2*c)*(d*x^3+c*x^2)^n,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2}\right)}^{n + 1}}{n + 1}"," ",0,"(d*x^3 + c*x^2)^(n + 1)/(n + 1)","A",0
192,1,160,0,0.298983," ","integrate((3*d*x^2+2*c*x+b)*(d*x^3+c*x^2+b*x+a)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2} + b x\right)}^{8} + {\left(d x^{3} + c x^{2} + b x\right)}^{7} a + \frac{7}{2} \, {\left(d x^{3} + c x^{2} + b x\right)}^{6} a^{2} + 7 \, {\left(d x^{3} + c x^{2} + b x\right)}^{5} a^{3} + \frac{35}{4} \, {\left(d x^{3} + c x^{2} + b x\right)}^{4} a^{4} + 7 \, {\left(d x^{3} + c x^{2} + b x\right)}^{3} a^{5} + \frac{7}{2} \, {\left(d x^{3} + c x^{2} + b x\right)}^{2} a^{6} + {\left(d x^{3} + c x^{2} + b x\right)} a^{7}"," ",0,"1/8*(d*x^3 + c*x^2 + b*x)^8 + (d*x^3 + c*x^2 + b*x)^7*a + 7/2*(d*x^3 + c*x^2 + b*x)^6*a^2 + 7*(d*x^3 + c*x^2 + b*x)^5*a^3 + 35/4*(d*x^3 + c*x^2 + b*x)^4*a^4 + 7*(d*x^3 + c*x^2 + b*x)^3*a^5 + 7/2*(d*x^3 + c*x^2 + b*x)^2*a^6 + (d*x^3 + c*x^2 + b*x)*a^7","B",0
193,1,18,0,0.313888," ","integrate((3*d*x^2+2*c*x+b)*(d*x^3+c*x^2+b*x)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2} + b x\right)}^{8}"," ",0,"1/8*(d*x^3 + c*x^2 + b*x)^8","A",0
194,1,18,0,0.296510," ","integrate(x^7*(d*x^2+c*x+b)^7*(3*d*x^2+2*c*x+b),x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2} + b x\right)}^{8}"," ",0,"1/8*(d*x^3 + c*x^2 + b*x)^8","A",0
195,1,120,0,0.412845," ","integrate((3*d*x^2+b)*(d*x^3+b*x+a)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + b x\right)}^{8} + {\left(d x^{3} + b x\right)}^{7} a + \frac{7}{2} \, {\left(d x^{3} + b x\right)}^{6} a^{2} + 7 \, {\left(d x^{3} + b x\right)}^{5} a^{3} + \frac{35}{4} \, {\left(d x^{3} + b x\right)}^{4} a^{4} + 7 \, {\left(d x^{3} + b x\right)}^{3} a^{5} + \frac{7}{2} \, {\left(d x^{3} + b x\right)}^{2} a^{6} + {\left(d x^{3} + b x\right)} a^{7}"," ",0,"1/8*(d*x^3 + b*x)^8 + (d*x^3 + b*x)^7*a + 7/2*(d*x^3 + b*x)^6*a^2 + 7*(d*x^3 + b*x)^5*a^3 + 35/4*(d*x^3 + b*x)^4*a^4 + 7*(d*x^3 + b*x)^3*a^5 + 7/2*(d*x^3 + b*x)^2*a^6 + (d*x^3 + b*x)*a^7","B",0
196,1,13,0,0.301148," ","integrate((3*d*x^2+b)*(d*x^3+b*x)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + b x\right)}^{8}"," ",0,"1/8*(d*x^3 + b*x)^8","A",0
197,1,13,0,0.267550," ","integrate(x^7*(d*x^2+b)^7*(3*d*x^2+b),x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + b x\right)}^{8}"," ",0,"1/8*(d*x^3 + b*x)^8","A",0
198,1,136,0,0.429803," ","integrate((3*d*x^2+2*c*x)*(d*x^3+c*x^2+a)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2}\right)}^{8} + {\left(d x^{3} + c x^{2}\right)}^{7} a + \frac{7}{2} \, {\left(d x^{3} + c x^{2}\right)}^{6} a^{2} + 7 \, {\left(d x^{3} + c x^{2}\right)}^{5} a^{3} + \frac{35}{4} \, {\left(d x^{3} + c x^{2}\right)}^{4} a^{4} + 7 \, {\left(d x^{3} + c x^{2}\right)}^{3} a^{5} + \frac{7}{2} \, {\left(d x^{3} + c x^{2}\right)}^{2} a^{6} + {\left(d x^{3} + c x^{2}\right)} a^{7}"," ",0,"1/8*(d*x^3 + c*x^2)^8 + (d*x^3 + c*x^2)^7*a + 7/2*(d*x^3 + c*x^2)^6*a^2 + 7*(d*x^3 + c*x^2)^5*a^3 + 35/4*(d*x^3 + c*x^2)^4*a^4 + 7*(d*x^3 + c*x^2)^3*a^5 + 7/2*(d*x^3 + c*x^2)^2*a^6 + (d*x^3 + c*x^2)*a^7","B",0
199,1,15,0,0.372521," ","integrate((3*d*x^2+2*c*x)*(d*x^3+c*x^2)^7,x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2}\right)}^{8}"," ",0,"1/8*(d*x^3 + c*x^2)^8","A",0
200,1,15,0,0.234105," ","integrate(x^7*(d*x^2+c*x)^7*(3*d*x^2+2*c*x),x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2}\right)}^{8}"," ",0,"1/8*(d*x^3 + c*x^2)^8","A",0
201,1,15,0,0.256015," ","integrate(x^14*(d*x+c)^7*(3*d*x^2+2*c*x),x, algorithm=""giac"")","\frac{1}{8} \, {\left(d x^{3} + c x^{2}\right)}^{8}"," ",0,"1/8*(d*x^3 + c*x^2)^8","A",0
202,1,488,0,0.317037," ","integrate(x*(3*d*x+2*c)*(d*x^3+c*x^2+a)^7,x, algorithm=""giac"")","\frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + a d^{7} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, a c d^{6} x^{20} + 7 \, c^{5} d^{3} x^{19} + 21 \, a c^{2} d^{5} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + 35 \, a c^{3} d^{4} x^{18} + \frac{7}{2} \, a^{2} d^{6} x^{18} + c^{7} d x^{17} + 35 \, a c^{4} d^{3} x^{17} + 21 \, a^{2} c d^{5} x^{17} + \frac{1}{8} \, c^{8} x^{16} + 21 \, a c^{5} d^{2} x^{16} + \frac{105}{2} \, a^{2} c^{2} d^{4} x^{16} + 7 \, a c^{6} d x^{15} + 70 \, a^{2} c^{3} d^{3} x^{15} + 7 \, a^{3} d^{5} x^{15} + a c^{7} x^{14} + \frac{105}{2} \, a^{2} c^{4} d^{2} x^{14} + 35 \, a^{3} c d^{4} x^{14} + 21 \, a^{2} c^{5} d x^{13} + 70 \, a^{3} c^{2} d^{3} x^{13} + \frac{7}{2} \, a^{2} c^{6} x^{12} + 70 \, a^{3} c^{3} d^{2} x^{12} + \frac{35}{4} \, a^{4} d^{4} x^{12} + 35 \, a^{3} c^{4} d x^{11} + 35 \, a^{4} c d^{3} x^{11} + 7 \, a^{3} c^{5} x^{10} + \frac{105}{2} \, a^{4} c^{2} d^{2} x^{10} + 35 \, a^{4} c^{3} d x^{9} + 7 \, a^{5} d^{3} x^{9} + \frac{35}{4} \, a^{4} c^{4} x^{8} + 21 \, a^{5} c d^{2} x^{8} + 21 \, a^{5} c^{2} d x^{7} + 7 \, a^{5} c^{3} x^{6} + \frac{7}{2} \, a^{6} d^{2} x^{6} + 7 \, a^{6} c d x^{5} + \frac{7}{2} \, a^{6} c^{2} x^{4} + a^{7} d x^{3} + a^{7} c x^{2}"," ",0,"1/8*d^8*x^24 + c*d^7*x^23 + 7/2*c^2*d^6*x^22 + 7*c^3*d^5*x^21 + a*d^7*x^21 + 35/4*c^4*d^4*x^20 + 7*a*c*d^6*x^20 + 7*c^5*d^3*x^19 + 21*a*c^2*d^5*x^19 + 7/2*c^6*d^2*x^18 + 35*a*c^3*d^4*x^18 + 7/2*a^2*d^6*x^18 + c^7*d*x^17 + 35*a*c^4*d^3*x^17 + 21*a^2*c*d^5*x^17 + 1/8*c^8*x^16 + 21*a*c^5*d^2*x^16 + 105/2*a^2*c^2*d^4*x^16 + 7*a*c^6*d*x^15 + 70*a^2*c^3*d^3*x^15 + 7*a^3*d^5*x^15 + a*c^7*x^14 + 105/2*a^2*c^4*d^2*x^14 + 35*a^3*c*d^4*x^14 + 21*a^2*c^5*d*x^13 + 70*a^3*c^2*d^3*x^13 + 7/2*a^2*c^6*x^12 + 70*a^3*c^3*d^2*x^12 + 35/4*a^4*d^4*x^12 + 35*a^3*c^4*d*x^11 + 35*a^4*c*d^3*x^11 + 7*a^3*c^5*x^10 + 105/2*a^4*c^2*d^2*x^10 + 35*a^4*c^3*d*x^9 + 7*a^5*d^3*x^9 + 35/4*a^4*c^4*x^8 + 21*a^5*c*d^2*x^8 + 21*a^5*c^2*d*x^7 + 7*a^5*c^3*x^6 + 7/2*a^6*d^2*x^6 + 7*a^6*c*d*x^5 + 7/2*a^6*c^2*x^4 + a^7*d*x^3 + a^7*c*x^2","B",0
203,1,88,0,0.305626," ","integrate(x*(3*d*x+2*c)*(d*x^3+c*x^2)^7,x, algorithm=""giac"")","\frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac{1}{8} \, c^{8} x^{16}"," ",0,"1/8*d^8*x^24 + c*d^7*x^23 + 7/2*c^2*d^6*x^22 + 7*c^3*d^5*x^21 + 35/4*c^4*d^4*x^20 + 7*c^5*d^3*x^19 + 7/2*c^6*d^2*x^18 + c^7*d*x^17 + 1/8*c^8*x^16","B",0
204,1,88,0,0.293562," ","integrate(x^8*(3*d*x+2*c)*(d*x^2+c*x)^7,x, algorithm=""giac"")","\frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac{1}{8} \, c^{8} x^{16}"," ",0,"1/8*d^8*x^24 + c*d^7*x^23 + 7/2*c^2*d^6*x^22 + 7*c^3*d^5*x^21 + 35/4*c^4*d^4*x^20 + 7*c^5*d^3*x^19 + 7/2*c^6*d^2*x^18 + c^7*d*x^17 + 1/8*c^8*x^16","B",0
205,1,88,0,0.242693," ","integrate(x^15*(d*x+c)^7*(3*d*x+2*c),x, algorithm=""giac"")","\frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac{1}{8} \, c^{8} x^{16}"," ",0,"1/8*d^8*x^24 + c*d^7*x^23 + 7/2*c^2*d^6*x^22 + 7*c^3*d^5*x^21 + 35/4*c^4*d^4*x^20 + 7*c^5*d^3*x^19 + 7/2*c^6*d^2*x^18 + c^7*d*x^17 + 1/8*c^8*x^16","B",0
206,1,24,0,0.366385," ","integrate((b*x+a)*(1+(a*x+1/2*b*x^2)^4),x, algorithm=""giac"")","\frac{1}{160} \, {\left(b x^{2} + 2 \, a x\right)}^{5} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/160*(b*x^2 + 2*a*x)^5 + 1/2*b*x^2 + a*x","A",0
207,1,88,0,0.366262," ","integrate((b*x+a)*(1+(c+a*x+1/2*b*x^2)^4),x, algorithm=""giac"")","\frac{1}{160} \, {\left(b x^{2} + 2 \, a x\right)}^{5} + \frac{1}{16} \, {\left(b x^{2} + 2 \, a x\right)}^{4} c + \frac{1}{4} \, {\left(b x^{2} + 2 \, a x\right)}^{3} c^{2} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)}^{2} c^{3} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} c^{4} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/160*(b*x^2 + 2*a*x)^5 + 1/16*(b*x^2 + 2*a*x)^4*c + 1/4*(b*x^2 + 2*a*x)^3*c^2 + 1/2*(b*x^2 + 2*a*x)^2*c^3 + 1/2*(b*x^2 + 2*a*x)*c^4 + 1/2*b*x^2 + a*x","B",0
208,1,30,0,0.402948," ","integrate((b*x+a)*(1+(a*x+1/2*b*x^2)^n),x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} + a x + \frac{{\left(\frac{1}{2} \, b x^{2} + a x\right)}^{n + 1}}{n + 1}"," ",0,"1/2*b*x^2 + a*x + (1/2*b*x^2 + a*x)^(n + 1)/(n + 1)","A",0
209,1,32,0,0.250754," ","integrate((b*x+a)*(1+(c+a*x+1/2*b*x^2)^n),x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} + a x + c + \frac{{\left(\frac{1}{2} \, b x^{2} + a x + c\right)}^{n + 1}}{n + 1}"," ",0,"1/2*b*x^2 + a*x + c + (1/2*b*x^2 + a*x + c)^(n + 1)/(n + 1)","A",0
210,1,24,0,0.219816," ","integrate((c*x^2+a)*(1+(a*x+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{4374} \, {\left(c x^{3} + 3 \, a x\right)}^{6} + \frac{1}{3} \, c x^{3} + a x"," ",0,"1/4374*(c*x^3 + 3*a*x)^6 + 1/3*c*x^3 + a*x","A",0
211,1,105,0,0.336377," ","integrate((c*x^2+a)*(1+(d+a*x+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{4374} \, {\left(c x^{3} + 3 \, a x\right)}^{6} + \frac{1}{243} \, {\left(c x^{3} + 3 \, a x\right)}^{5} d + \frac{5}{162} \, {\left(c x^{3} + 3 \, a x\right)}^{4} d^{2} + \frac{10}{81} \, {\left(c x^{3} + 3 \, a x\right)}^{3} d^{3} + \frac{5}{18} \, {\left(c x^{3} + 3 \, a x\right)}^{2} d^{4} + \frac{1}{3} \, {\left(c x^{3} + 3 \, a x\right)} d^{5} + \frac{1}{3} \, c x^{3} + a x"," ",0,"1/4374*(c*x^3 + 3*a*x)^6 + 1/243*(c*x^3 + 3*a*x)^5*d + 5/162*(c*x^3 + 3*a*x)^4*d^2 + 10/81*(c*x^3 + 3*a*x)^3*d^3 + 5/18*(c*x^3 + 3*a*x)^2*d^4 + 1/3*(c*x^3 + 3*a*x)*d^5 + 1/3*c*x^3 + a*x","B",0
212,1,30,0,0.293712," ","integrate((c*x^2+b*x)*(1+(1/2*b*x^2+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{279936} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{6} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}"," ",0,"1/279936*(2*c*x^3 + 3*b*x^2)^6 + 1/3*c*x^3 + 1/2*b*x^2","A",0
213,1,126,0,0.312271," ","integrate((c*x^2+b*x)*(1+(d+1/2*b*x^2+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{279936} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{6} + \frac{1}{7776} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{5} d + \frac{5}{2592} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{4} d^{2} + \frac{5}{324} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{3} d^{3} + \frac{5}{72} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)}^{2} d^{4} + \frac{1}{6} \, {\left(2 \, c x^{3} + 3 \, b x^{2}\right)} d^{5} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}"," ",0,"1/279936*(2*c*x^3 + 3*b*x^2)^6 + 1/7776*(2*c*x^3 + 3*b*x^2)^5*d + 5/2592*(2*c*x^3 + 3*b*x^2)^4*d^2 + 5/324*(2*c*x^3 + 3*b*x^2)^3*d^3 + 5/72*(2*c*x^3 + 3*b*x^2)^2*d^4 + 1/6*(2*c*x^3 + 3*b*x^2)*d^5 + 1/3*c*x^3 + 1/2*b*x^2","B",0
214,1,37,0,0.307259," ","integrate((c*x^2+b*x+a)*(1+(a*x+1/2*b*x^2+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{279936} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{6} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/279936*(2*c*x^3 + 3*b*x^2 + 6*a*x)^6 + 1/3*c*x^3 + 1/2*b*x^2 + a*x","A",0
215,1,153,0,0.441787," ","integrate((c*x^2+b*x+a)*(1+(d+a*x+1/2*b*x^2+1/3*c*x^3)^5),x, algorithm=""giac"")","\frac{1}{279936} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{6} + \frac{1}{7776} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{5} d + \frac{5}{2592} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{4} d^{2} + \frac{5}{324} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{3} d^{3} + \frac{5}{72} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)}^{2} d^{4} + \frac{1}{6} \, {\left(2 \, c x^{3} + 3 \, b x^{2} + 6 \, a x\right)} d^{5} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/279936*(2*c*x^3 + 3*b*x^2 + 6*a*x)^6 + 1/7776*(2*c*x^3 + 3*b*x^2 + 6*a*x)^5*d + 5/2592*(2*c*x^3 + 3*b*x^2 + 6*a*x)^4*d^2 + 5/324*(2*c*x^3 + 3*b*x^2 + 6*a*x)^3*d^3 + 5/72*(2*c*x^3 + 3*b*x^2 + 6*a*x)^2*d^4 + 1/6*(2*c*x^3 + 3*b*x^2 + 6*a*x)*d^5 + 1/3*c*x^3 + 1/2*b*x^2 + a*x","B",0
216,1,30,0,0.417403," ","integrate((c*x^2+a)*(1+(a*x+1/3*c*x^3)^n),x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + a x + \frac{{\left(\frac{1}{3} \, c x^{3} + a x\right)}^{n + 1}}{n + 1}"," ",0,"1/3*c*x^3 + a*x + (1/3*c*x^3 + a*x)^(n + 1)/(n + 1)","A",0
217,1,36,0,0.392009," ","integrate((c*x^2+b*x)*(1+(1/2*b*x^2+1/3*c*x^3)^n),x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + \frac{{\left(\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}\right)}^{n + 1}}{n + 1}"," ",0,"1/3*c*x^3 + 1/2*b*x^2 + (1/3*c*x^3 + 1/2*b*x^2)^(n + 1)/(n + 1)","A",0
218,1,42,0,0.391331," ","integrate((c*x^2+b*x+a)*(1+(a*x+1/2*b*x^2+1/3*c*x^3)^n),x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x + \frac{{\left(\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x\right)}^{n + 1}}{n + 1}"," ",0,"1/3*c*x^3 + 1/2*b*x^2 + a*x + (1/3*c*x^3 + 1/2*b*x^2 + a*x)^(n + 1)/(n + 1)","A",0
219,1,30,0,0.345566," ","integrate((x^2+4*x-4)*(x^3+6*x^2-12*x+5),x, algorithm=""giac"")","\frac{5}{3} \, x^{3} + \frac{1}{6} \, {\left(x^{3} + 6 \, x^{2} - 12 \, x\right)}^{2} + 10 \, x^{2} - 20 \, x"," ",0,"5/3*x^3 + 1/6*(x^3 + 6*x^2 - 12*x)^2 + 10*x^2 - 20*x","A",0
220,1,22,0,0.233274," ","integrate((x^3+2*x)*(x^4+4*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{1}{8} \, {\left(x^{4} + 4 \, x^{2}\right)}^{2} + x^{2}"," ",0,"1/4*x^4 + 1/8*(x^4 + 4*x^2)^2 + x^2","A",0
221,1,28,0,0.288131," ","integrate((1+2*x)*(x^2+x)^3*(-18+7*(x^2+x)^3)^2,x, algorithm=""giac"")","\frac{49}{10} \, {\left(x^{2} + x\right)}^{10} - 36 \, {\left(x^{2} + x\right)}^{7} + 81 \, {\left(x^{2} + x\right)}^{4}"," ",0,"49/10*(x^2 + x)^10 - 36*(x^2 + x)^7 + 81*(x^2 + x)^4","A",0
222,1,28,0,0.359956," ","integrate(x^3*(1+x)^3*(1+2*x)*(-18+7*x^3*(1+x)^3)^2,x, algorithm=""giac"")","\frac{49}{10} \, {\left(x^{2} + x\right)}^{10} - 36 \, {\left(x^{2} + x\right)}^{7} + 81 \, {\left(x^{2} + x\right)}^{4}"," ",0,"49/10*(x^2 + x)^10 - 36*(x^2 + x)^7 + 81*(x^2 + x)^4","A",0
223,1,12,0,0.316065," ","integrate((-x^2+2)/(x^3-6*x+1)^5,x, algorithm=""giac"")","\frac{1}{12 \, {\left(x^{3} - 6 \, x + 1\right)}^{4}}"," ",0,"1/12/(x^3 - 6*x + 1)^4","A",0
224,1,14,0,0.371203," ","integrate((x^2+2*x)/(x^3+3*x^2+4),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| x^{3} + 3 \, x^{2} + 4 \right|}\right)"," ",0,"1/3*log(abs(x^3 + 3*x^2 + 4))","A",0
225,1,18,0,0.270149," ","integrate((x^3+x+1)/(x^4+2*x^2+4*x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left(4 \, {\left| \frac{1}{4} \, x^{4} + \frac{1}{2} \, x^{2} + x \right|}\right)"," ",0,"1/4*log(4*abs(1/4*x^4 + 1/2*x^2 + x))","A",0
226,1,24,0,0.536457," ","integrate((-2*b*f*x^3-3*a*f*x^2-b*e*x^2-2*a*e*x-a*d+b*c)/(f*x^3+e*x^2+d*x+c)^2,x, algorithm=""giac"")","\frac{b x + a}{f x^{3} + x^{2} e + d x + c}"," ",0,"(b*x + a)/(f*x^3 + x^2*e + d*x + c)","A",0
227,-2,0,0,0.000000," ","integrate((D*x^3+C*x^2+B*x+A)/(a*x^4+b*x^3+c*x^2+b*x+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.16Not invertible Error: Bad Argument Value","F(-2)",0
228,1,58,0,0.274029," ","integrate((2*x^3-4*x^2+x+2)/(x^4-x^3+x^2-x+1),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{2} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) + \frac{1}{2} \, \log\left(x^{4} - x^{3} + x^{2} - x + 1\right)"," ",0,"-1/2*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/2*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) + 1/2*log(x^4 - x^3 + x^2 - x + 1)","A",0
229,1,13,0,0.289105," ","integrate((x^3+3*x^2+3*x)/(x^4+4*x^3+6*x^2+4*x+1),x, algorithm=""giac"")","\frac{1}{3 \, {\left(x + 1\right)}^{3}} + \log\left({\left| x + 1 \right|}\right)"," ",0,"1/3/(x + 1)^3 + log(abs(x + 1))","A",0
230,1,23,0,0.391828," ","integrate((x^3-3*x^2+3*x-1)/(x^4+4*x^3+6*x^2+4*x+1),x, algorithm=""giac"")","\frac{2 \, {\left(9 \, x^{2} + 9 \, x + 4\right)}}{3 \, {\left(x + 1\right)}^{3}} + \log\left({\left| x + 1 \right|}\right)"," ",0,"2/3*(9*x^2 + 9*x + 4)/(x + 1)^3 + log(abs(x + 1))","A",0
231,1,28,0,1.436094," ","integrate((-39*x^8+26*x^6+24*x^5+174*x^4-18*x^2-40*x+9)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","\frac{13 \, x^{5} - 4 \, x^{2} + 3 \, x + 2}{{\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"(13*x^5 - 4*x^2 + 3*x + 2)/(x^4 + 2*x^2 + 3)^2","A",0
232,1,11,0,0.330738," ","integrate((4*x^5-1)/(x^5+x+1)^2,x, algorithm=""giac"")","-\frac{x}{x^{5} + x + 1}"," ",0,"-x/(x^5 + x + 1)","A",0
233,1,134,0,0.372287," ","integrate((x^2+1)/(-x^6+7*x^4-7*x^2+1)^2,x, algorithm=""giac"")","\frac{1}{64} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} + 2 \right|}}\right) + \frac{1}{64} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} - 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} - 2 \right|}}\right) - \frac{7 \, x^{5} - 46 \, x^{3} + 31 \, x}{32 \, {\left(x^{6} - 7 \, x^{4} + 7 \, x^{2} - 1\right)}} + \frac{3}{128} \, \log\left({\left| x^{2} + 2 \, x - 1 \right|}\right) - \frac{3}{128} \, \log\left({\left| x^{2} - 2 \, x - 1 \right|}\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/64*sqrt(2)*log(abs(2*x - 2*sqrt(2) + 2)/abs(2*x + 2*sqrt(2) + 2)) + 1/64*sqrt(2)*log(abs(2*x - 2*sqrt(2) - 2)/abs(2*x + 2*sqrt(2) - 2)) - 1/32*(7*x^5 - 46*x^3 + 31*x)/(x^6 - 7*x^4 + 7*x^2 - 1) + 3/128*log(abs(x^2 + 2*x - 1)) - 3/128*log(abs(x^2 - 2*x - 1)) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
234,1,99,0,2.090159," ","integrate(x^m*(d*x^3+c*x^2+b*x+a)^p*(a*(1+m)+x*(b*(2+m+p)+x*(c*(3+m+2*p)+d*(4+m+3*p)*x))),x, algorithm=""giac"")","{\left(d x^{3} + c x^{2} + b x + a\right)}^{p} d x^{4} x^{m} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} c x^{3} x^{m} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} b x^{2} x^{m} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} a x x^{m}"," ",0,"(d*x^3 + c*x^2 + b*x + a)^p*d*x^4*x^m + (d*x^3 + c*x^2 + b*x + a)^p*c*x^3*x^m + (d*x^3 + c*x^2 + b*x + a)^p*b*x^2*x^m + (d*x^3 + c*x^2 + b*x + a)^p*a*x*x^m","B",0
235,1,89,0,1.886825," ","integrate(x^2*(d*x^3+c*x^2+b*x+a)^p*(3*a+b*(4+p)*x+c*(5+2*p)*x^2+d*(6+3*p)*x^3),x, algorithm=""giac"")","{\left(d x^{3} + c x^{2} + b x + a\right)}^{p} d x^{6} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} c x^{5} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} b x^{4} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} a x^{3}"," ",0,"(d*x^3 + c*x^2 + b*x + a)^p*d*x^6 + (d*x^3 + c*x^2 + b*x + a)^p*c*x^5 + (d*x^3 + c*x^2 + b*x + a)^p*b*x^4 + (d*x^3 + c*x^2 + b*x + a)^p*a*x^3","B",0
236,1,89,0,0.727576," ","integrate(x*(d*x^3+c*x^2+b*x+a)^p*(2*a+b*(3+p)*x+c*(4+2*p)*x^2+d*(5+3*p)*x^3),x, algorithm=""giac"")","{\left(d x^{3} + c x^{2} + b x + a\right)}^{p} d x^{5} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} c x^{4} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} b x^{3} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} a x^{2}"," ",0,"(d*x^3 + c*x^2 + b*x + a)^p*d*x^5 + (d*x^3 + c*x^2 + b*x + a)^p*c*x^4 + (d*x^3 + c*x^2 + b*x + a)^p*b*x^3 + (d*x^3 + c*x^2 + b*x + a)^p*a*x^2","B",0
237,1,87,0,1.082948," ","integrate((d*x^3+c*x^2+b*x+a)^p*(a+b*(2+p)*x+c*(3+2*p)*x^2+d*(4+3*p)*x^3),x, algorithm=""giac"")","{\left(d x^{3} + c x^{2} + b x + a\right)}^{p} d x^{4} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} c x^{3} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} b x^{2} + {\left(d x^{3} + c x^{2} + b x + a\right)}^{p} a x"," ",0,"(d*x^3 + c*x^2 + b*x + a)^p*d*x^4 + (d*x^3 + c*x^2 + b*x + a)^p*c*x^3 + (d*x^3 + c*x^2 + b*x + a)^p*b*x^2 + (d*x^3 + c*x^2 + b*x + a)^p*a*x","B",0
238,1,52,0,0.295724," ","integrate((d*x^3+c*x^2+b*x+a)^p*(b*(1+p)*x+c*(2+2*p)*x^2+d*(3+3*p)*x^3)/x,x, algorithm=""giac"")","\frac{{\left(d x^{3} + c x^{2} + b x + a\right)}^{p + 1} p}{p + 1} + \frac{{\left(d x^{3} + c x^{2} + b x + a\right)}^{p + 1}}{p + 1}"," ",0,"(d*x^3 + c*x^2 + b*x + a)^(p + 1)*p/(p + 1) + (d*x^3 + c*x^2 + b*x + a)^(p + 1)/(p + 1)","B",0
239,0,0,0,0.000000," ","integrate((d*x^3+c*x^2+b*x+a)^p*(-a+b*p*x+c*(1+2*p)*x^2+d*(2+3*p)*x^3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(d {\left(3 \, p + 2\right)} x^{3} + c {\left(2 \, p + 1\right)} x^{2} + b p x - a\right)} {\left(d x^{3} + c x^{2} + b x + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((d*(3*p + 2)*x^3 + c*(2*p + 1)*x^2 + b*p*x - a)*(d*x^3 + c*x^2 + b*x + a)^p/x^2, x)","F",0
240,0,0,0,0.000000," ","integrate((d*x^3+c*x^2+b*x+a)^p*(-2*a+b*(-1+p)*x+2*c*p*x^2+d*(1+3*p)*x^3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(d {\left(3 \, p + 1\right)} x^{3} + 2 \, c p x^{2} + b {\left(p - 1\right)} x - 2 \, a\right)} {\left(d x^{3} + c x^{2} + b x + a\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((d*(3*p + 1)*x^3 + 2*c*p*x^2 + b*(p - 1)*x - 2*a)*(d*x^3 + c*x^2 + b*x + a)^p/x^3, x)","F",0
241,0,0,0,0.000000," ","integrate((d*x^3+c*x^2+b*x+a)^p*(-3*a+b*(-2+p)*x+c*(-1+2*p)*x^2+3*d*p*x^3)/x^4,x, algorithm=""giac"")","\int \frac{{\left(3 \, d p x^{3} + c {\left(2 \, p - 1\right)} x^{2} + b {\left(p - 2\right)} x - 3 \, a\right)} {\left(d x^{3} + c x^{2} + b x + a\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((3*d*p*x^3 + c*(2*p - 1)*x^2 + b*(p - 2)*x - 3*a)*(d*x^3 + c*x^2 + b*x + a)^p/x^4, x)","F",0
242,1,73,0,0.309319," ","integrate(x^4*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{1}{3} \, x^{3} - \frac{3}{4} \, x^{2} - \frac{1}{72} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) - \frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{5}{4} \, x - \frac{13}{48} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{1}{3} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/4*x^4 + 1/3*x^3 - 3/4*x^2 - 1/72*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) - 10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 5/4*x - 13/48*log(2*x^2 - x + 2) + 1/3*log(x^2 + x + 1)","A",0
243,1,68,0,0.377525," ","integrate(x^3*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} - \frac{5}{36} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) + \frac{8}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{3}{2} \, x - \frac{1}{24} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{2}{3} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/3*x^3 + 1/2*x^2 - 5/36*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) + 8/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 3/2*x - 1/24*log(2*x^2 - x + 2) + 2/3*log(x^2 + x + 1)","A",0
244,1,61,0,0.391499," ","integrate(x^2*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{18} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x + \frac{1}{4} \, \log\left(2 \, x^{2} - x + 2\right) - \log\left(x^{2} + x + 1\right)"," ",0,"1/2*x^2 - 1/18*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) + 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x + 1/4*log(2*x^2 - x + 2) - log(x^2 + x + 1)","A",0
245,1,56,0,0.306678," ","integrate(x*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) - \frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x + \frac{1}{6} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{1}{3} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/9*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) - 10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x + 1/6*log(2*x^2 - x + 2) + 1/3*log(x^2 + x + 1)","A",0
246,1,55,0,0.287369," ","integrate((2*x^3+3*x^2+x+5)/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) + \frac{8}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{2}{3} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/9*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) + 8/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*log(2*x^2 - x + 2) + 2/3*log(x^2 + x + 1)","A",0
247,1,60,0,0.306988," ","integrate((2*x^3+3*x^2+x+5)/x/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","-\frac{1}{18} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{4} \, \log\left(2 \, x^{2} - x + 2\right) - \log\left(x^{2} + x + 1\right) + \frac{5}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-1/18*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) + 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/4*log(2*x^2 - x + 2) - log(x^2 + x + 1) + 5/2*log(abs(x))","A",0
248,1,65,0,0.256569," ","integrate((2*x^3+3*x^2+x+5)/x^2/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","-\frac{5}{36} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) - \frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{5}{2 \, x} + \frac{1}{24} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{1}{3} \, \log\left(x^{2} + x + 1\right) - \frac{3}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-5/36*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) - 10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 5/2/x + 1/24*log(2*x^2 - x + 2) + 1/3*log(x^2 + x + 1) - 3/4*log(abs(x))","A",0
249,1,70,0,0.285514," ","integrate((2*x^3+3*x^2+x+5)/x^3/(2*x^4+x^3+3*x^2+x+2),x, algorithm=""giac"")","-\frac{1}{72} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, x - 1\right)}\right) + \frac{8}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{3 \, x - 5}{4 \, x^{2}} + \frac{13}{48} \, \log\left(2 \, x^{2} - x + 2\right) + \frac{2}{3} \, \log\left(x^{2} + x + 1\right) - \frac{15}{8} \, \log\left({\left| x \right|}\right)"," ",0,"-1/72*sqrt(15)*arctan(1/15*sqrt(15)*(4*x - 1)) + 8/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/4*(3*x - 5)/x^2 + 13/48*log(2*x^2 - x + 2) + 2/3*log(x^2 + x + 1) - 15/8*log(abs(x))","A",0
250,0,0,0,0.000000," ","integrate(x^3*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 3 \, x^{2} + x + 5\right)} x^{3}}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)*x^3/(2*x^4 + x^3 + 5*x^2 + x + 2), x)","F",0
251,0,0,0,0.000000," ","integrate(x^2*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 3 \, x^{2} + x + 5\right)} x^{2}}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)*x^2/(2*x^4 + x^3 + 5*x^2 + x + 2), x)","F",0
252,0,0,0,0.000000," ","integrate(x*(2*x^3+3*x^2+x+5)/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 3 \, x^{2} + x + 5\right)} x}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)*x/(2*x^4 + x^3 + 5*x^2 + x + 2), x)","F",0
253,0,0,0,0.000000," ","integrate((2*x^3+3*x^2+x+5)/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 3 \, x^{2} + x + 5}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)/(2*x^4 + x^3 + 5*x^2 + x + 2), x)","F",0
254,0,0,0,0.000000," ","integrate((2*x^3+3*x^2+x+5)/x/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 3 \, x^{2} + x + 5}{{\left(2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2\right)} x}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)/((2*x^4 + x^3 + 5*x^2 + x + 2)*x), x)","F",0
255,0,0,0,0.000000," ","integrate((2*x^3+3*x^2+x+5)/x^2/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 3 \, x^{2} + x + 5}{{\left(2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)/((2*x^4 + x^3 + 5*x^2 + x + 2)*x^2), x)","F",0
256,0,0,0,0.000000," ","integrate((2*x^3+3*x^2+x+5)/x^3/(2*x^4+x^3+5*x^2+x+2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 3 \, x^{2} + x + 5}{{\left(2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^3 + 3*x^2 + x + 5)/((2*x^4 + x^3 + 5*x^2 + x + 2)*x^3), x)","F",0
257,1,87,0,4.080052," ","integrate(x^2*(b*x^2+3*a)/(c^2*x^6+b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{b}\right) + \arctan\left(-\frac{b c^{2} x^{5} + b^{3} x^{3} - a c^{2} x^{3} + a b^{2} x}{a^{2} c}\right) - \arctan\left(-\frac{b c^{2} x^{3} + b^{3} x - a c^{2} x}{a b c}\right)}{c}"," ",0,"(arctan(c*x/b) + arctan(-(b*c^2*x^5 + b^3*x^3 - a*c^2*x^3 + a*b^2*x)/(a^2*c)) - arctan(-(b*c^2*x^3 + b^3*x - a*c^2*x)/(a*b*c)))/c","B",0
258,1,34,0,0.254395," ","integrate((-3*x^4+1)/(-2+x)/(x^2+1)^2,x, algorithm=""giac"")","\frac{2 \, x - 1}{5 \, {\left(x^{2} + 1\right)}} - \frac{46}{25} \, \arctan\left(x\right) - \frac{14}{25} \, \log\left(x^{2} + 1\right) - \frac{47}{25} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"1/5*(2*x - 1)/(x^2 + 1) - 46/25*arctan(x) - 14/25*log(x^2 + 1) - 47/25*log(abs(x - 2))","A",0
259,1,18,0,0.311085," ","integrate((2*x^2-9*x-9)/(x^3-9*x),x, algorithm=""giac"")","2 \, \log\left({\left| x + 3 \right|}\right) - \log\left({\left| x - 3 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"2*log(abs(x + 3)) - log(abs(x - 3)) + log(abs(x))","A",0
260,1,24,0,0.254386," ","integrate((x^5+2*x^2+1)/(x^3-x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + x + \log\left({\left| x + 1 \right|}\right) + 2 \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"1/3*x^3 + x + log(abs(x + 1)) + 2*log(abs(x - 1)) - log(abs(x))","A",0
261,1,28,0,0.366142," ","integrate((2*x^2+3)/(-1+x)^2/x,x, algorithm=""giac"")","-\frac{5}{x - 1} + 2 \, \log\left({\left| x - 1 \right|}\right) + 3 \, \log\left({\left| -\frac{1}{x - 1} - 1 \right|}\right)"," ",0,"-5/(x - 1) + 2*log(abs(x - 1)) + 3*log(abs(-1/(x - 1) - 1))","A",0
262,1,22,0,0.286090," ","integrate((2*x^2-1)/(-1+4*x)/(x^2+1),x, algorithm=""giac"")","\frac{3}{17} \, \arctan\left(x\right) + \frac{6}{17} \, \log\left(x^{2} + 1\right) - \frac{7}{34} \, \log\left({\left| 4 \, x - 1 \right|}\right)"," ",0,"3/17*arctan(x) + 6/17*log(x^2 + 1) - 7/34*log(abs(4*x - 1))","A",0
263,1,17,0,0.269559," ","integrate((x^3-3*x^2+2*x-3)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 3 \, x + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"1/2*x^2 - 3*x + 1/2*log(x^2 + 1)","A",0
264,1,23,0,0.277597," ","integrate((x^4+6*x^3+10*x^2+x)/(x^2+6*x+10),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - 3 \, \arctan\left(x + 3\right) + \frac{1}{2} \, \log\left(x^{2} + 6 \, x + 10\right)"," ",0,"1/3*x^3 - 3*arctan(x + 3) + 1/2*log(x^2 + 6*x + 10)","A",0
265,1,29,0,0.317477," ","integrate(1/(x^4-3*x^3-7*x^2+27*x-18),x, algorithm=""giac"")","-\frac{1}{120} \, \log\left({\left| x + 3 \right|}\right) + \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right) - \frac{1}{5} \, \log\left({\left| x - 2 \right|}\right) + \frac{1}{12} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"-1/120*log(abs(x + 3)) + 1/8*log(abs(x - 1)) - 1/5*log(abs(x - 2)) + 1/12*log(abs(x - 3))","A",0
266,1,19,0,0.281334," ","integrate((x^3+1)/(-2+x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log\left({\left| x - 2 \right|}\right)"," ",0,"1/3*x^3 + x^2 + 4*x + 9*log(abs(x - 2))","A",0
267,1,13,0,0.341361," ","integrate((3*x^3-4*x^2+3*x)/(x^2+1),x, algorithm=""giac"")","\frac{3}{2} \, x^{2} - 4 \, x + 4 \, \arctan\left(x\right)"," ",0,"3/2*x^2 - 4*x + 4*arctan(x)","A",0
268,1,22,0,0.296934," ","integrate((5+3*x)/(x^3-x^2-x+1),x, algorithm=""giac"")","-\frac{4}{x - 1} + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-4/(x - 1) + 1/2*log(abs(x + 1)) - 1/2*log(abs(x - 1))","B",0
269,1,23,0,0.268664," ","integrate((x^4-x^3-x-1)/(x^3-x^2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{x} - 2 \, \log\left({\left| x - 1 \right|}\right) + 2 \, \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 - 1/x - 2*log(abs(x - 1)) + 2*log(abs(x))","A",0
270,1,11,0,0.308839," ","integrate((x^3+x^2+x+2)/(x^4+3*x^2+2),x, algorithm=""giac"")","\arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 2\right)"," ",0,"arctan(x) + 1/2*log(x^2 + 2)","A",0
271,1,30,0,0.328892," ","integrate((x^5-x^4+4*x^3-4*x^2+8*x-4)/(x^2+2)^3,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{1}{{\left(x^{2} + 2\right)}^{2}} + \frac{1}{2} \, \log\left(x^{2} + 2\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/(x^2 + 2)^2 + 1/2*log(x^2 + 2)","A",0
272,1,20,0,0.238720," ","integrate((x^2-3*x-1)/(x^3+x^2-2*x),x, algorithm=""giac"")","\frac{3}{2} \, \log\left({\left| x + 2 \right|}\right) - \log\left({\left| x - 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"3/2*log(abs(x + 2)) - log(abs(x - 1)) + 1/2*log(abs(x))","A",0
273,1,20,0,0.294684," ","integrate((x^4-2*x^3+3*x^2-x+3)/(x^3-2*x^2+3*x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{2} \, \log\left(x^{2} - 2 \, x + 3\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 - 1/2*log(x^2 - 2*x + 3) + log(abs(x))","A",0
274,1,23,0,0.374214," ","integrate((x^3+x-1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} - \frac{1}{2} \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-1/2*x/(x^2 + 1) - 1/2*arctan(x) + 1/2*log(x^2 + 1)","A",0
275,1,43,0,0.363210," ","integrate((x^4+8*x^3-x^2+2*x+1)/(x^2+x)/(x^3+1),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{3}{x + 1} + \log\left(x^{2} - x + 1\right) - 2 \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 3/(x + 1) + log(x^2 - x + 1) - 2*log(abs(x + 1)) + log(abs(x))","A",0
276,1,38,0,0.304124," ","integrate((x^3+x^2-5*x+15)/(x^2+5)/(x^2+2*x+3),x, algorithm=""giac"")","\frac{5}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x + 1\right)}\right) - \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) + \frac{1}{2} \, \log\left(x^{2} + 2 \, x + 3\right)"," ",0,"5/2*sqrt(2)*arctan(1/2*sqrt(2)*(x + 1)) - sqrt(5)*arctan(1/5*sqrt(5)*x) + 1/2*log(x^2 + 2*x + 3)","A",0
277,1,44,0,0.300884," ","integrate((x^6+7*x^5+15*x^4+32*x^3+23*x^2+25*x-3)/(x^2+1)^2/(x^2+x+2)^2,x, algorithm=""giac"")","-\frac{2 \, x^{2} + 3 \, x + 5}{x^{4} + x^{3} + 3 \, x^{2} + x + 2} - \log\left(x^{2} + x + 2\right) + \log\left(x^{2} + 1\right)"," ",0,"-(2*x^2 + 3*x + 5)/(x^4 + x^3 + 3*x^2 + x + 2) - log(x^2 + x + 2) + log(x^2 + 1)","A",0
278,1,11,0,0.288112," ","integrate(1/(x^2+1)/(x^2+4),x, algorithm=""giac"")","-\frac{1}{6} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"-1/6*arctan(1/2*x) + 1/3*arctan(x)","A",0
279,1,20,0,0.287649," ","integrate((b*x^3+a)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} + a \arctan\left(x\right) - \frac{1}{2} \, b \log\left(x^{2} + 1\right)"," ",0,"1/2*b*x^2 + a*arctan(x) - 1/2*b*log(x^2 + 1)","A",0
280,1,20,0,0.319480," ","integrate((x^2+x)/(4+x)/(x^2-4),x, algorithm=""giac"")","\log\left({\left| x + 4 \right|}\right) - \frac{1}{4} \, \log\left({\left| x + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"log(abs(x + 4)) - 1/4*log(abs(x + 2)) + 1/4*log(abs(x - 2))","A",0
281,1,17,0,0.375162," ","integrate((x^2+4)/(x^2+1)/(x^2+2),x, algorithm=""giac"")","-\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 3 \, \arctan\left(x\right)"," ",0,"-sqrt(2)*arctan(1/2*sqrt(2)*x) + 3*arctan(x)","A",0
282,1,60,0,0.286997," ","integrate((x^4+3*x^2-4*x+5)/(-1+x)^2/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \pi - 2 \, \pi \left \lfloor \frac{\pi + 4 \, \arctan\left(x\right)}{4 \, \pi} + \frac{1}{2} \right \rfloor + x - \frac{5}{2 \, {\left(x - 1\right)}} + 2 \, \arctan\left(x\right) + \frac{3}{4} \, \log\left(\frac{2}{x - 1} + \frac{2}{{\left(x - 1\right)}^{2}} + 1\right) + 2 \, \log\left({\left| x - 1 \right|}\right) - 1"," ",0,"1/2*pi - 2*pi*floor(1/4*(pi + 4*arctan(x))/pi + 1/2) + x - 5/2/(x - 1) + 2*arctan(x) + 3/4*log(2/(x - 1) + 2/(x - 1)^2 + 1) + 2*log(abs(x - 1)) - 1","B",0
283,1,21,0,0.308753," ","integrate((x^4+1)/(x^2+2),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{5}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - 2 \, x"," ",0,"1/3*x^3 + 5/2*sqrt(2)*arctan(1/2*sqrt(2)*x) - 2*x","A",0
284,1,11,0,0.287214," ","integrate((x^4+2*x+2)/(x^5+x^4),x, algorithm=""giac"")","-\frac{2}{3 \, x^{3}} + \log\left({\left| x + 1 \right|}\right)"," ",0,"-2/3/x^3 + log(abs(x + 1))","A",0
285,1,20,0,0.282111," ","integrate((2*x^2-5*x-1)/(x^3-2*x^2-x+2),x, algorithm=""giac"")","\log\left({\left| x + 1 \right|}\right) + 2 \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x - 2 \right|}\right)"," ",0,"log(abs(x + 1)) + 2*log(abs(x - 1)) - log(abs(x - 2))","A",0
286,1,20,0,0.282017," ","integrate((x^3+x+2)/(x^4+2*x^2+1),x, algorithm=""giac"")","\frac{x}{x^{2} + 1} + \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x/(x^2 + 1) + arctan(x) + 1/2*log(x^2 + 1)","A",0
287,1,20,0,0.404920," ","integrate((x^3+x^2+2*x+1)/(x^4+2*x^2+1),x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}} + \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-1/2/(x^2 + 1) + arctan(x) + 1/2*log(x^2 + 1)","A",0
288,1,33,0,0.245288," ","integrate((3+4*x)/(x^2+1)/(x^2+2),x, algorithm=""giac"")","-\frac{3}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 3 \, \arctan\left(x\right) - 2 \, \log\left(x^{2} + 2\right) + 2 \, \log\left(x^{2} + 1\right)"," ",0,"-3/2*sqrt(2)*arctan(1/2*sqrt(2)*x) + 3*arctan(x) - 2*log(x^2 + 2) + 2*log(x^2 + 1)","A",0
289,1,27,0,0.285259," ","integrate((2+x)/(x^2+1)/(x^2+4),x, algorithm=""giac"")","-\frac{1}{3} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{2}{3} \, \arctan\left(x\right) - \frac{1}{6} \, \log\left(x^{2} + 4\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"-1/3*arctan(1/2*x) + 2/3*arctan(x) - 1/6*log(x^2 + 4) + 1/6*log(x^2 + 1)","A",0
290,1,23,0,0.366756," ","integrate((x^3-x+2)/(x^2-6*x-7),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 6 \, x - \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) + \frac{169}{4} \, \log\left({\left| x - 7 \right|}\right)"," ",0,"1/2*x^2 + 6*x - 1/4*log(abs(x + 1)) + 169/4*log(abs(x - 7))","A",0
291,1,16,0,0.266118," ","integrate((x^5-1)/(x^2-1),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{1}{2} \, x^{2} + \log\left({\left| x + 1 \right|}\right)"," ",0,"1/4*x^4 + 1/2*x^2 + log(abs(x + 1))","A",0
292,1,34,0,0.287794," ","integrate((x^3-x^2+2*x+5)/(x^2+x+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{11}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - 2 \, x + \frac{3}{2} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/2*x^2 + 11/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 2*x + 3/2*log(x^2 + x + 1)","A",0
293,1,31,0,0.278491," ","integrate((x^4-2*x^3+x-3)/(2*x^2-8*x+10),x, algorithm=""giac"")","\frac{1}{6} \, x^{3} + \frac{1}{2} \, x^{2} + \frac{3}{2} \, x - 6 \, \arctan\left(x - 2\right) + \frac{3}{4} \, \log\left(x^{2} - 4 \, x + 5\right)"," ",0,"1/6*x^3 + 1/2*x^2 + 3/2*x - 6*arctan(x - 2) + 3/4*log(x^2 - 4*x + 5)","A",0
294,1,23,0,0.249871," ","integrate((x^3+3*x^2+2*x+1)/(-3+x)/(-2+x)/(-1+x),x, algorithm=""giac"")","x + \frac{7}{2} \, \log\left({\left| x - 1 \right|}\right) - 25 \, \log\left({\left| x - 2 \right|}\right) + \frac{61}{2} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"x + 7/2*log(abs(x - 1)) - 25*log(abs(x - 2)) + 61/2*log(abs(x - 3))","A",0
295,1,30,0,0.323681," ","integrate((x^4-x^3+x^2-7*x+2)/(x^3+x^2-14*x-24),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 2 \, x + 20 \, \log\left({\left| x + 3 \right|}\right) - \frac{22}{3} \, \log\left({\left| x + 2 \right|}\right) + \frac{13}{3} \, \log\left({\left| x - 4 \right|}\right)"," ",0,"1/2*x^2 - 2*x + 20*log(abs(x + 3)) - 22/3*log(abs(x + 2)) + 13/3*log(abs(x - 4))","A",0
296,1,34,0,0.387093," ","integrate((x^2+2)/(-1+x)^2/x/(1+x),x, algorithm=""giac"")","-\frac{3}{2 \, {\left(x - 1\right)}} + 2 \, \log\left({\left| -\frac{1}{x - 1} - 1 \right|}\right) - \frac{3}{4} \, \log\left({\left| -\frac{2}{x - 1} - 1 \right|}\right)"," ",0,"-3/2/(x - 1) + 2*log(abs(-1/(x - 1) - 1)) - 3/4*log(abs(-2/(x - 1) - 1))","A",0
297,1,33,0,0.297046," ","integrate((x^3+x^2+3)/(x^2+2)^2,x, algorithm=""giac"")","\frac{5}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{x + 4}{4 \, {\left(x^{2} + 2\right)}} + \frac{1}{2} \, \log\left(x^{2} + 2\right)"," ",0,"5/8*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/4*(x + 4)/(x^2 + 2) + 1/2*log(x^2 + 2)","A",0
298,1,37,0,0.315350," ","integrate((2*x^3-4*x^2+70*x-35)/(x^2-10*x+26)/(x^2-2*x+17),x, algorithm=""giac"")","\frac{15033}{1025} \, \arctan\left(x - 5\right) - \frac{4607}{4100} \, \arctan\left(\frac{1}{4} \, x - \frac{1}{4}\right) + \frac{22}{1025} \, \log\left(x^{2} - 2 \, x + 17\right) + \frac{1003}{1025} \, \log\left(x^{2} - 10 \, x + 26\right)"," ",0,"15033/1025*arctan(x - 5) - 4607/4100*arctan(1/4*x - 1/4) + 22/1025*log(x^2 - 2*x + 17) + 1003/1025*log(x^2 - 10*x + 26)","A",0
299,1,22,0,0.274772," ","integrate((x^2+2)/(-5+x)/(-3+x)/(4+x),x, algorithm=""giac"")","\frac{2}{7} \, \log\left({\left| x + 4 \right|}\right) - \frac{11}{14} \, \log\left({\left| x - 3 \right|}\right) + \frac{3}{2} \, \log\left({\left| x - 5 \right|}\right)"," ",0,"2/7*log(abs(x + 4)) - 11/14*log(abs(x - 3)) + 3/2*log(abs(x - 5))","A",0
300,1,34,0,0.317211," ","integrate(x^4/(-1+x)/(x^2+2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{2}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + x - \frac{2}{3} \, \log\left(x^{2} + 2\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 - 2/3*sqrt(2)*arctan(1/2*sqrt(2)*x) + x - 2/3*log(x^2 + 2) + 1/3*log(abs(x - 1))","A",0
301,1,15,0,0.396824," ","integrate((2*x^2+7*x-1)/(x^3+x^2-x-1),x, algorithm=""giac"")","-\frac{3}{x + 1} + 2 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-3/(x + 1) + 2*log(abs(x - 1))","A",0
302,1,12,0,0.301251," ","integrate((1+2*x)/(x^3-3*x^2+3*x-1),x, algorithm=""giac"")","-\frac{4 \, x - 1}{2 \, {\left(x - 1\right)}^{2}}"," ",0,"-1/2*(4*x - 1)/(x - 1)^2","A",0
303,1,30,0,0.262182," ","integrate((x^3+7*x^2-5*x+5)/(-1+x)^2/(1+x)^3,x, algorithm=""giac"")","-\frac{1}{x - 1} + \frac{\frac{4}{x - 1} + 1}{2 \, {\left(\frac{2}{x - 1} + 1\right)}^{2}}"," ",0,"-1/(x - 1) + 1/2*(4/(x - 1) + 1)/(2/(x - 1) + 1)^2","A",0
304,1,29,0,0.277896," ","integrate((3*x^2+3*x+1)/(x^3+2*x^2+2*x+1),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \log\left(x^{2} + x + 1\right) + \log\left({\left| x + 1 \right|}\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + log(x^2 + x + 1) + log(abs(x + 1))","A",0
305,1,22,0,0.286505," ","integrate((x^2+2*x-1)/(2*x^3+3*x^2-2*x),x, algorithm=""giac"")","\frac{1}{10} \, \log\left({\left| 2 \, x - 1 \right|}\right) - \frac{1}{10} \, \log\left({\left| x + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"1/10*log(abs(2*x - 1)) - 1/10*log(abs(x + 2)) + 1/2*log(abs(x))","A",0
306,1,26,0,0.276088," ","integrate((x^4-2*x^2+4*x+1)/(x^3-x^2-x+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + x - \frac{2}{x - 1} - \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 + x - 2/(x - 1) - log(abs(x + 1)) + log(abs(x - 1))","A",0
307,1,18,0,0.330584," ","integrate((2*x^2-x+4)/(x^3+4*x),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{1}{2} \, \log\left(x^{2} + 4\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/2*arctan(1/2*x) + 1/2*log(x^2 + 4) + log(abs(x))","A",0
308,1,74,0,0.343778," ","integrate((x^3+x^2+1)/(-1+x)/x/(x^2+1)^3/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{9 \, x^{3} - 6 \, x^{2} + 11 \, x - 4}{16 \, {\left(x^{2} + 1\right)}^{2}} + \frac{7}{16} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + x + 1\right) + \frac{15}{16} \, \log\left(x^{2} + 1\right) + \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/16*(9*x^3 - 6*x^2 + 11*x - 4)/(x^2 + 1)^2 + 7/16*arctan(x) - 1/2*log(x^2 + x + 1) + 15/16*log(x^2 + 1) + 1/8*log(abs(x - 1)) - log(abs(x))","A",0
309,1,25,0,0.317487," ","integrate((-x^3+2*x^2-3*x+1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{x - 2}{2 \, {\left(x^{2} + 1\right)}} + \frac{3}{2} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-1/2*(x - 2)/(x^2 + 1) + 3/2*arctan(x) - 1/2*log(x^2 + 1)","A",0
310,1,30,0,0.379373," ","integrate((-x^3+2*x^2-3*x+1)/x/(x^2+1)^2,x, algorithm=""giac"")","-\frac{2 \, x + 1}{2 \, {\left(x^{2} + 1\right)}} - 2 \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/2*(2*x + 1)/(x^2 + 1) - 2*arctan(x) - 1/2*log(x^2 + 1) + log(abs(x))","A",0
311,1,26,0,0.290797," ","integrate((x^4+x^3-x^2-x+1)/(x^3-x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + x + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 + x + 1/2*log(abs(x + 1)) + 1/2*log(abs(x - 1)) - log(abs(x))","A",0
312,1,31,0,0.336103," ","integrate((x^3-4*x^2+2)/(x^2+1)/(x^2+2),x, algorithm=""giac"")","-5 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 6 \, \arctan\left(x\right) + \log\left(x^{2} + 2\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-5*sqrt(2)*arctan(1/2*sqrt(2)*x) + 6*arctan(x) + log(x^2 + 2) - 1/2*log(x^2 + 1)","A",0
313,1,21,0,0.227126," ","integrate((x^4+x^2+1)/(x^2+1)/(x^2+4)^2,x, algorithm=""giac"")","-\frac{13 \, x}{24 \, {\left(x^{2} + 4\right)}} + \frac{25}{144} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{1}{9} \, \arctan\left(x\right)"," ",0,"-13/24*x/(x^2 + 4) + 25/144*arctan(1/2*x) + 1/9*arctan(x)","A",0
314,1,36,0,0.295500," ","integrate((x^3+x^2+1)/(x^4+x^3+2*x^2),x, algorithm=""giac"")","\frac{1}{28} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(2 \, x + 1\right)}\right) - \frac{1}{2 \, x} + \frac{5}{8} \, \log\left(x^{2} + x + 2\right) - \frac{1}{4} \, \log\left({\left| x \right|}\right)"," ",0,"1/28*sqrt(7)*arctan(1/7*sqrt(7)*(2*x + 1)) - 1/2/x + 5/8*log(x^2 + x + 2) - 1/4*log(abs(x))","A",0
315,1,20,0,0.284430," ","integrate((x^3+x^2-12*x+1)/(x^2+x-12),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{7} \, \log\left({\left| x + 4 \right|}\right) + \frac{1}{7} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"1/2*x^2 - 1/7*log(abs(x + 4)) + 1/7*log(abs(x - 3))","A",0
316,1,18,0,0.380928," ","integrate((6*x^2+5*x-3)/(x^3+2*x^2-3*x),x, algorithm=""giac"")","3 \, \log\left({\left| x + 3 \right|}\right) + 2 \, \log\left({\left| x - 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"3*log(abs(x + 3)) + 2*log(abs(x - 1)) + log(abs(x))","A",0
317,1,16,0,0.373219," ","integrate((5*x^2+3*x-2)/(x^3+2*x^2),x, algorithm=""giac"")","\frac{1}{x} + 3 \, \log\left({\left| x + 2 \right|}\right) + 2 \, \log\left({\left| x \right|}\right)"," ",0,"1/x + 3*log(abs(x + 2)) + 2*log(abs(x))","A",0
318,1,20,0,0.292227," ","integrate((-4*x^2-2*x+18)/(x^3+4*x^2+x-6),x, algorithm=""giac"")","-3 \, \log\left({\left| x + 3 \right|}\right) - 2 \, \log\left({\left| x + 2 \right|}\right) + \log\left({\left| x - 1 \right|}\right)"," ",0,"-3*log(abs(x + 3)) - 2*log(abs(x + 2)) + log(abs(x - 1))","A",0
319,1,17,0,0.364354," ","integrate((x^3-2*x^2+x+1)/(x^4+5*x^2+4),x, algorithm=""giac"")","-\frac{3}{2} \, \arctan\left(\frac{1}{2} \, x\right) + \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 4\right)"," ",0,"-3/2*arctan(1/2*x) + arctan(x) + 1/2*log(x^2 + 4)","A",0
320,1,53,0,0.306150," ","integrate((4*x^3-27*x^2+5*x-32)/(30*x^5-13*x^4+50*x^3-286*x^2-299*x-70),x, algorithm=""giac"")","\frac{3988}{260015} \, \sqrt{19} \arctan\left(\frac{1}{19} \, \sqrt{19} {\left(2 \, x + 1\right)}\right) + \frac{11049}{260015} \, \log\left(x^{2} + x + 5\right) + \frac{4822}{4879} \, \log\left({\left| 5 \, x + 2 \right|}\right) - \frac{3146}{80155} \, \log\left({\left| 3 \, x - 7 \right|}\right) - \frac{334}{323} \, \log\left({\left| 2 \, x + 1 \right|}\right)"," ",0,"3988/260015*sqrt(19)*arctan(1/19*sqrt(19)*(2*x + 1)) + 11049/260015*log(x^2 + x + 5) + 4822/4879*log(abs(5*x + 2)) - 3146/80155*log(abs(3*x - 7)) - 334/323*log(abs(2*x + 1))","A",0
321,1,59,0,0.236062," ","integrate((12*x^5-7*x^3-13*x^2+8)/(100*x^6-80*x^5+116*x^4-80*x^3+41*x^2-20*x+4),x, algorithm=""giac"")","\frac{503}{15972} \, \sqrt{2} \arctan\left(\sqrt{2} x\right) - \frac{36458 \, x^{2} + 4675 \, x + 2554}{12100 \, {\left(2 \, x^{2} + 1\right)} {\left(5 \, x - 2\right)}} + \frac{2843}{7986} \, \log\left(2 \, x^{2} + 1\right) - \frac{59096}{99825} \, \log\left({\left| 5 \, x - 2 \right|}\right)"," ",0,"503/15972*sqrt(2)*arctan(sqrt(2)*x) - 1/12100*(36458*x^2 + 4675*x + 2554)/((2*x^2 + 1)*(5*x - 2)) + 2843/7986*log(2*x^2 + 1) - 59096/99825*log(abs(5*x - 2))","A",0
322,1,13,0,0.302203," ","integrate((x^4+9)/x^2/(x^2+9),x, algorithm=""giac"")","x - \frac{1}{x} - \frac{10}{3} \, \arctan\left(\frac{1}{3} \, x\right)"," ",0,"x - 1/x - 10/3*arctan(1/3*x)","A",0
323,1,17,0,0.268642," ","integrate((x^4+2*x)/(x^2+1),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - x + \arctan\left(x\right) + \log\left(x^{2} + 1\right)"," ",0,"1/3*x^3 - x + arctan(x) + log(x^2 + 1)","A",0
324,1,28,0,0.291636," ","integrate((x^3-x)/(-1+x)^2/(x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \pi - \pi \left \lfloor \frac{\pi + 4 \, \arctan\left(x\right)}{4 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(x\right) + \log\left({\left| x - 1 \right|}\right)"," ",0,"1/4*pi - pi*floor(1/4*(pi + 4*arctan(x))/pi + 1/2) + arctan(x) + log(abs(x - 1))","B",0
325,1,12,0,0.294863," ","integrate((2*x^3+3*x^2+5*x+2)/(x^2+x+1),x, algorithm=""giac"")","x^{2} + x + \log\left(x^{2} + x + 1\right)"," ",0,"x^2 + x + log(x^2 + x + 1)","A",0
326,1,55,0,0.295232," ","integrate((3*x^3-5*x^2-4*x+3)/x^3/(x^2+x-1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x - \sqrt{5} + 1 \right|}}{{\left| 2 \, x + \sqrt{5} + 1 \right|}}\right) - \frac{2 \, x - 3}{2 \, x^{2}} - \frac{3}{2} \, \log\left({\left| x^{2} + x - 1 \right|}\right) + 3 \, \log\left({\left| x \right|}\right)"," ",0,"1/10*sqrt(5)*log(abs(2*x - sqrt(5) + 1)/abs(2*x + sqrt(5) + 1)) - 1/2*(2*x - 3)/x^2 - 3/2*log(abs(x^2 + x - 1)) + 3*log(abs(x))","A",0
327,1,28,0,0.284950," ","integrate((2*x^3+5*x^2+8*x+4)/(x^2+2*x+2)^2,x, algorithm=""giac"")","-\frac{1}{x^{2} + 2 \, x + 2} - \arctan\left(x + 1\right) + \log\left(x^{2} + 2 \, x + 2\right)"," ",0,"-1/(x^2 + 2*x + 2) - arctan(x + 1) + log(x^2 + 2*x + 2)","A",0
328,1,26,0,0.373539," ","integrate((-1+x)^4*x^4/(x^2+1),x, algorithm=""giac"")","\frac{1}{7} \, x^{7} - \frac{2}{3} \, x^{6} + x^{5} - \frac{4}{3} \, x^{3} + 4 \, x - 4 \, \arctan\left(x\right)"," ",0,"1/7*x^7 - 2/3*x^6 + x^5 - 4/3*x^3 + 4*x - 4*arctan(x)","A",0
329,1,27,0,0.307716," ","integrate((4*x^2-20*x)/(x^4-10*x^2+9),x, algorithm=""giac"")","-2 \, \log\left({\left| x + 3 \right|}\right) + \frac{3}{2} \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x - 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"-2*log(abs(x + 3)) + 3/2*log(abs(x + 1)) + log(abs(x - 1)) - 1/2*log(abs(x - 3))","A",0
330,1,23,0,0.292304," ","integrate((4*x^3+x-1)/(-1+x)/x^2/(x^2+1),x, algorithm=""giac"")","-\frac{1}{x} + \arctan\left(x\right) - \log\left(x^{2} + 1\right) + 2 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/x + arctan(x) - log(x^2 + 1) + 2*log(abs(x - 1))","A",0
331,1,19,0,0.390914," ","integrate((x^4-4*x^3+2*x^2-3*x+1)/(x^2+1)^3,x, algorithm=""giac"")","\frac{8 \, x^{2} + 7}{4 \, {\left(x^{2} + 1\right)}^{2}} + \arctan\left(x\right)"," ",0,"1/4*(8*x^2 + 7)/(x^2 + 1)^2 + arctan(x)","A",0
332,1,19,0,0.274070," ","integrate((x^4-4*x^3+2*x^2-3*x+1)/(x^6+3*x^4+3*x^2+1),x, algorithm=""giac"")","\frac{8 \, x^{2} + 7}{4 \, {\left(x^{2} + 1\right)}^{2}} + \arctan\left(x\right)"," ",0,"1/4*(8*x^2 + 7)/(x^2 + 1)^2 + arctan(x)","A",0
333,1,13,0,0.283462," ","integrate((2*x^3+2*x^2+x+1)/(x^4+x^3+x^2),x, algorithm=""giac"")","-\frac{1}{x} + \log\left(x^{2} + x + 1\right)"," ",0,"-1/x + log(x^2 + x + 1)","A",0
334,1,208,0,0.441998," ","integrate(x^2*(d*x+c)^2/(b*x^3+a),x, algorithm=""giac"")","\frac{c^{2} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b} - \frac{\sqrt{3} {\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c d - \left(-a b^{2}\right)^{\frac{2}{3}} 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 \, b^{3}} + \frac{b d^{2} x^{2} + 4 \, b c d x}{2 \, b^{2}} - \frac{{\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c d + \left(-a b^{2}\right)^{\frac{2}{3}} 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 \, b^{3}} + \frac{{\left(a b^{4} d^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b^{4} c 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^{5}}"," ",0,"1/3*c^2*log(abs(b*x^3 + a))/b - 1/3*sqrt(3)*(2*(-a*b^2)^(1/3)*b*c*d - (-a*b^2)^(2/3)*d^2)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^3 + 1/2*(b*d^2*x^2 + 4*b*c*d*x)/b^2 - 1/6*(2*(-a*b^2)^(1/3)*b*c*d + (-a*b^2)^(2/3)*d^2)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^3 + 1/3*(a*b^4*d^2*(-a/b)^(1/3) + 2*a*b^4*c*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5)","A",0
335,1,38,0,1.109330," ","integrate((4*x^5+2*x^3-x)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{9}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{7 \, x^{2} - 5}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"9/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 1/8*(7*x^2 - 5)/(x^4 + 2*x^2 + 3)","A",0
336,1,42,0,1.802551," ","integrate((x^5+x)/(2*x^4+2*x^2+1)^3,x, algorithm=""giac"")","\frac{32 \, x^{6} + 48 \, x^{4} + 36 \, x^{2} + 11}{16 \, {\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{2}} + \arctan\left(2 \, x^{2} + 1\right)"," ",0,"1/16*(32*x^6 + 48*x^4 + 36*x^2 + 11)/(2*x^4 + 2*x^2 + 1)^2 + arctan(2*x^2 + 1)","A",0
337,1,1587,0,4.697380," ","integrate((c*x^2+b*x+a)/(f*x^4+e*x^2+d),x, algorithm=""giac"")","\frac{{\left(4 \, d f^{3} - f^{4} + 2 \, f^{3} e - f^{2} e^{2}\right)} \sqrt{-4 \, d f + e^{2}} b \log\left(x^{2} + \frac{\sqrt{-4 \, d f + e^{2}} + e}{2 \, f}\right)}{2 \, {\left(16 \, d^{2} f^{2} - 4 \, d f^{3} + 8 \, d f^{2} e - 8 \, d f e^{2} + f^{2} e^{2} - 2 \, f e^{3} + e^{4}\right)} f^{2}} - \frac{{\left(4 \, d f^{3} - f^{4} + 2 \, f^{3} e - f^{2} e^{2}\right)} \sqrt{-4 \, d f + e^{2}} b \log\left(x^{2} - \frac{\sqrt{-4 \, d f + e^{2}} - e}{2 \, f}\right)}{2 \, {\left(16 \, d^{2} f^{2} - 4 \, d f^{3} + 8 \, d f^{2} e - 8 \, d f e^{2} + f^{2} e^{2} - 2 \, f e^{3} + e^{4}\right)} f^{2}} + \frac{{\left({\left(16 \, \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d^{2} f^{2} - 4 \, \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f^{3} - 32 \, d^{2} f^{3} + 8 \, \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f^{2} e - 8 \, d f^{3} e + 4 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f e - \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} f^{2} e + 8 \, {\left(4 \, d f - e^{2}\right)} d f^{2} - 8 \, \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f e^{2} + \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} f^{2} e^{2} + 16 \, d f^{2} e^{2} + 2 \, {\left(4 \, d f - e^{2}\right)} f^{2} e + 2 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} f e^{2} - 2 \, \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} f e^{3} + 2 \, f^{2} e^{3} - 2 \, {\left(4 \, d f - e^{2}\right)} f e^{2} - \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} e^{3} + \sqrt{2} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} e^{4} - 2 \, f e^{4}\right)} a + 2 \, {\left(8 \, d^{2} f^{3} - 4 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d^{2} f + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d f e - 2 \, {\left(4 \, d f - e^{2}\right)} d f^{2} - 2 \, d f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e + \sqrt{-4 \, d f + e^{2}} f} d e^{2}\right)} c\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{\sqrt{-4 \, d f + e^{2}} + e}{f}}}\right)}{4 \, {\left(16 \, d^{3} f^{2} - 4 \, d^{2} f^{3} + 8 \, d^{2} f^{2} e - 8 \, d^{2} f e^{2} + d f^{2} e^{2} - 2 \, d f e^{3} + d e^{4}\right)} {\left| f \right|}} + \frac{{\left({\left(16 \, \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d^{2} f^{2} - 4 \, \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f^{3} + 32 \, d^{2} f^{3} + 8 \, \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f^{2} e + 8 \, d f^{3} e - 4 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f e + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} f^{2} e - 8 \, {\left(4 \, d f - e^{2}\right)} d f^{2} - 8 \, \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f e^{2} + \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} f^{2} e^{2} - 16 \, d f^{2} e^{2} - 2 \, {\left(4 \, d f - e^{2}\right)} f^{2} e - 2 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} f e^{2} - 2 \, \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} f e^{3} - 2 \, f^{2} e^{3} + 2 \, {\left(4 \, d f - e^{2}\right)} f e^{2} + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} e^{3} + \sqrt{2} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} e^{4} + 2 \, f e^{4}\right)} a - 2 \, {\left(8 \, d^{2} f^{3} - 4 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d^{2} f + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d f e - 2 \, {\left(4 \, d f - e^{2}\right)} d f^{2} - 2 \, d f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d f + e^{2}} \sqrt{f e - \sqrt{-4 \, d f + e^{2}} f} d e^{2}\right)} c\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{\sqrt{-4 \, d f + e^{2}} - e}{f}}}\right)}{4 \, {\left(16 \, d^{3} f^{2} - 4 \, d^{2} f^{3} + 8 \, d^{2} f^{2} e - 8 \, d^{2} f e^{2} + d f^{2} e^{2} - 2 \, d f e^{3} + d e^{4}\right)} {\left| f \right|}}"," ",0,"1/2*(4*d*f^3 - f^4 + 2*f^3*e - f^2*e^2)*sqrt(-4*d*f + e^2)*b*log(x^2 + 1/2*(sqrt(-4*d*f + e^2) + e)/f)/((16*d^2*f^2 - 4*d*f^3 + 8*d*f^2*e - 8*d*f*e^2 + f^2*e^2 - 2*f*e^3 + e^4)*f^2) - 1/2*(4*d*f^3 - f^4 + 2*f^3*e - f^2*e^2)*sqrt(-4*d*f + e^2)*b*log(x^2 - 1/2*(sqrt(-4*d*f + e^2) - e)/f)/((16*d^2*f^2 - 4*d*f^3 + 8*d*f^2*e - 8*d*f*e^2 + f^2*e^2 - 2*f*e^3 + e^4)*f^2) + 1/4*((16*sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d^2*f^2 - 4*sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f^3 - 32*d^2*f^3 + 8*sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f^2*e - 8*d*f^3*e + 4*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f*e - sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*f^2*e + 8*(4*d*f - e^2)*d*f^2 - 8*sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f*e^2 + sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*f^2*e^2 + 16*d*f^2*e^2 + 2*(4*d*f - e^2)*f^2*e + 2*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*f*e^2 - 2*sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*f*e^3 + 2*f^2*e^3 - 2*(4*d*f - e^2)*f*e^2 - sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*e^3 + sqrt(2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*e^4 - 2*f*e^4)*a + 2*(8*d^2*f^3 - 4*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d^2*f + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f^2 - 2*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*f*e - 2*(4*d*f - e^2)*d*f^2 - 2*d*f^2*e^2 + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e + sqrt(-4*d*f + e^2)*f)*d*e^2)*c)*arctan(2*sqrt(1/2)*x/sqrt((sqrt(-4*d*f + e^2) + e)/f))/((16*d^3*f^2 - 4*d^2*f^3 + 8*d^2*f^2*e - 8*d^2*f*e^2 + d*f^2*e^2 - 2*d*f*e^3 + d*e^4)*abs(f)) + 1/4*((16*sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d^2*f^2 - 4*sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f^3 + 32*d^2*f^3 + 8*sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f^2*e + 8*d*f^3*e - 4*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f*e + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*f^2*e - 8*(4*d*f - e^2)*d*f^2 - 8*sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f*e^2 + sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*f^2*e^2 - 16*d*f^2*e^2 - 2*(4*d*f - e^2)*f^2*e - 2*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*f*e^2 - 2*sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*f*e^3 - 2*f^2*e^3 + 2*(4*d*f - e^2)*f*e^2 + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*e^3 + sqrt(2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*e^4 + 2*f*e^4)*a - 2*(8*d^2*f^3 - 4*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d^2*f + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f^2 - 2*sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*f*e - 2*(4*d*f - e^2)*d*f^2 - 2*d*f^2*e^2 + sqrt(2)*sqrt(-4*d*f + e^2)*sqrt(f*e - sqrt(-4*d*f + e^2)*f)*d*e^2)*c)*arctan(2*sqrt(1/2)*x/sqrt(-(sqrt(-4*d*f + e^2) - e)/f))/((16*d^3*f^2 - 4*d^2*f^3 + 8*d^2*f^2*e - 8*d^2*f*e^2 + d*f^2*e^2 - 2*d*f*e^3 + d*e^4)*abs(f))","B",0
338,1,1625,0,4.563237," ","integrate((e*x+d)^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"-(b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c)*d*e*log(x^2 + 1/2*(b + sqrt(b^2 - 4*a*c))/c)/((b^4 - 8*a*b^2*c - 2*b^3*c + 16*a^2*c^2 + 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*c^2) + (b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c)*d*e*log(x^2 + 1/2*(b - sqrt(b^2 - 4*a*c))/c)/((b^4 - 8*a*b^2*c - 2*b^3*c + 16*a^2*c^2 + 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*c^2) + 1/4*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*d^2 + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/4*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*d^2 + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
339,1,62,0,0.313458," ","integrate(x^2/(b*x+a)/(d*x+c),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x + a \right|}\right)}{b^{3} c - a b^{2} d} - \frac{c^{2} \log\left({\left| d x + c \right|}\right)}{b c d^{2} - a d^{3}} + \frac{x}{b d}"," ",0,"a^2*log(abs(b*x + a))/(b^3*c - a*b^2*d) - c^2*log(abs(d*x + c))/(b*c*d^2 - a*d^3) + x/(b*d)","A",0
340,1,85,0,0.256514," ","integrate(x^2/(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{a d \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c^{2} + a b d^{2}\right)}} + \frac{c^{2} \log\left({\left| d x + c \right|}\right)}{b c^{2} d + a d^{3}} - \frac{a c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b c^{2} + a d^{2}\right)} \sqrt{a b}}"," ",0,"1/2*a*d*log(b*x^2 + a)/(b^2*c^2 + a*b*d^2) + c^2*log(abs(d*x + c))/(b*c^2*d + a*d^3) - a*c*arctan(b*x/sqrt(a*b))/((b*c^2 + a*d^2)*sqrt(a*b))","A",0
341,1,320,0,0.301516," ","integrate(x^2/(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{c^{2} d \log\left({\left| d x + c \right|}\right)}{b c^{3} d - a d^{4}} + \frac{c^{2} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, {\left(b c^{3} - a d^{3}\right)}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} d \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} b^{2} c^{2} - \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} b c d + \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} d^{2}} + \frac{{\left(a b^{2} c^{3} d^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b d^{5} \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} c^{4} d + a^{2} b c 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 \, {\left(a b^{3} c^{6} - 2 \, a^{2} b^{2} c^{3} d^{3} + a^{3} b d^{6}\right)}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b c d - \left(-a b^{2}\right)^{\frac{2}{3}} 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(b^{3} c^{3} - a b^{2} d^{3}\right)}}"," ",0,"-c^2*d*log(abs(d*x + c))/(b*c^3*d - a*d^4) + 1/3*c^2*log(abs(b*x^3 + a))/(b*c^3 - a*d^3) + (-a*b^2)^(1/3)*d*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(sqrt(3)*b^2*c^2 - sqrt(3)*(-a*b^2)^(1/3)*b*c*d + sqrt(3)*(-a*b^2)^(2/3)*d^2) + 1/3*(a*b^2*c^3*d^2*(-a/b)^(1/3) - a^2*b*d^5*(-a/b)^(1/3) - a*b^2*c^4*d + a^2*b*c*d^4)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^3*c^6 - 2*a^2*b^2*c^3*d^3 + a^3*b*d^6) + 1/6*((-a*b^2)^(1/3)*b*c*d - (-a*b^2)^(2/3)*d^2)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(b^3*c^3 - a*b^2*d^3)","A",0
342,1,401,0,0.566517," ","integrate(x^2/(d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{c^{2} d^{2} \log\left({\left| d x + c \right|}\right)}{b c^{4} d + a d^{5}} - \frac{c^{2} d \log\left({\left| b x^{4} + a \right|}\right)}{4 \, {\left(b c^{4} + a d^{4}\right)}} + \frac{{\left(\sqrt{2} \sqrt{a b} b d + \left(a b^{3}\right)^{\frac{1}{4}} b c\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)}{2 \, {\left(\sqrt{2} a b^{2} d^{2} + \sqrt{2} \sqrt{a b} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{3}{4}} c d\right)}} + \frac{{\left(\sqrt{2} \sqrt{a b} b d + \left(a b^{3}\right)^{\frac{1}{4}} b c\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)}{2 \, {\left(\sqrt{2} a b^{2} d^{2} + \sqrt{2} \sqrt{a b} b^{2} c^{2} + 2 \, \left(a b^{3}\right)^{\frac{3}{4}} c d\right)}} - \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} a b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} c^{3}\right)} \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^{3} c^{4} + \sqrt{2} a^{2} b^{2} d^{4}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} a b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} c^{3}\right)} \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^{3} c^{4} + \sqrt{2} a^{2} b^{2} d^{4}\right)}}"," ",0,"c^2*d^2*log(abs(d*x + c))/(b*c^4*d + a*d^5) - 1/4*c^2*d*log(abs(b*x^4 + a))/(b*c^4 + a*d^4) + 1/2*(sqrt(2)*sqrt(a*b)*b*d + (a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b^2*d^2 + sqrt(2)*sqrt(a*b)*b^2*c^2 - 2*(a*b^3)^(3/4)*c*d) + 1/2*(sqrt(2)*sqrt(a*b)*b*d + (a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b^2*d^2 + sqrt(2)*sqrt(a*b)*b^2*c^2 + 2*(a*b^3)^(3/4)*c*d) - 1/4*((a*b^3)^(1/4)*a*b*c*d^2 + (a*b^3)^(3/4)*c^3)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b^3*c^4 + sqrt(2)*a^2*b^2*d^4) + 1/4*((a*b^3)^(1/4)*a*b*c*d^2 + (a*b^3)^(3/4)*c^3)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b^3*c^4 + sqrt(2)*a^2*b^2*d^4)","A",0
343,1,21,0,0.239464," ","integrate(x/(1-x)/(1+x)^2,x, algorithm=""giac"")","\frac{1}{2 \, {\left(x + 1\right)}} - \frac{1}{4} \, \log\left({\left| -\frac{2}{x + 1} + 1 \right|}\right)"," ",0,"1/2/(x + 1) - 1/4*log(abs(-2/(x + 1) + 1))","A",0
344,1,30,0,0.303433," ","integrate(x^2/(-x^2+1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x + \frac{1}{x}\right)}} + \frac{1}{16} \, \log\left({\left| x + \frac{1}{x} + 2 \right|}\right) - \frac{1}{16} \, \log\left({\left| x + \frac{1}{x} - 2 \right|}\right)"," ",0,"-1/4/(x + 1/x) + 1/16*log(abs(x + 1/x + 2)) - 1/16*log(abs(x + 1/x - 2))","A",0
345,1,77,0,0.313560," ","integrate(x^3/(-x^3+1)/(x^3+1)^2,x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{36} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{x}{6 \, {\left(x^{3} + 1\right)}} + \frac{1}{24} \, \log\left(x^{2} + x + 1\right) + \frac{1}{72} \, \log\left(x^{2} - x + 1\right) - \frac{1}{36} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{12} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/36*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*x/(x^3 + 1) + 1/24*log(x^2 + x + 1) + 1/72*log(x^2 - x + 1) - 1/36*log(abs(x + 1)) - 1/12*log(abs(x - 1))","A",0
346,1,13,0,0.289243," ","integrate((x^3+3*x^2+x+9)/(x^2+1)/(x^2+3),x, algorithm=""giac"")","3 \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 3\right)"," ",0,"3*arctan(x) + 1/2*log(x^2 + 3)","A",0
347,1,11,0,0.297842," ","integrate((x^3+x^2+x+3)/(x^2+1)/(x^2+3),x, algorithm=""giac"")","\arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 3\right)"," ",0,"arctan(x) + 1/2*log(x^2 + 3)","A",0
348,1,24,0,0.258635," ","integrate((3*x^3-x^2+6*x-4)/(x^2+1)/(x^2+2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - 3 \, \arctan\left(x\right) + \frac{3}{2} \, \log\left(x^{2} + 1\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*x) - 3*arctan(x) + 3/2*log(x^2 + 1)","A",0
349,1,14,0,0.253052," ","integrate(1/(x^2-4*x+4)/(x^2-4*x+5),x, algorithm=""giac"")","-\frac{1}{x - 2} - \arctan\left(x - 2\right)"," ",0,"-1/(x - 2) - arctan(x - 2)","A",0
350,1,11,0,0.418144," ","integrate((x^2+x-3)/(-3+x)/x^2,x, algorithm=""giac"")","-\frac{1}{x} + \log\left({\left| x - 3 \right|}\right)"," ",0,"-1/x + log(abs(x - 3))","A",0
351,1,10,0,0.291688," ","integrate((4*x^2+x+1)/(4*x^3+x),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(2 \, x\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*arctan(2*x) + log(abs(x))","A",0
352,1,11,0,0.384234," ","integrate((3*x^2-x+1)/(x^3-x^2),x, algorithm=""giac"")","\frac{1}{x} + 3 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/x + 3*log(abs(x - 1))","A",0
353,1,14,0,0.228980," ","integrate((x^2+3*x+4)/(x^2+x),x, algorithm=""giac"")","x - 2 \, \log\left({\left| x + 1 \right|}\right) + 4 \, \log\left({\left| x \right|}\right)"," ",0,"x - 2*log(abs(x + 1)) + 4*log(abs(x))","A",0
354,1,16,0,0.243175," ","integrate((3*x^2+x+4)/(x^3+x),x, algorithm=""giac"")","\arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + 4 \, \log\left({\left| x \right|}\right)"," ",0,"arctan(x) - 1/2*log(x^2 + 1) + 4*log(abs(x))","A",0
355,1,14,0,0.342962," ","integrate((8*x^2-4*x+7)/(1+4*x)/(x^2+1),x, algorithm=""giac"")","-\arctan\left(x\right) + 2 \, \log\left({\left| 4 \, x + 1 \right|}\right)"," ",0,"-arctan(x) + 2*log(abs(4*x + 1))","A",0
356,1,22,0,0.297318," ","integrate(x^2/(-1+x)/(x^2+2*x+1),x, algorithm=""giac"")","\frac{1}{2 \, {\left(x + 1\right)}} + \frac{3}{4} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2/(x + 1) + 3/4*log(abs(x + 1)) + 1/4*log(abs(x - 1))","A",0
357,1,43,0,0.297877," ","integrate((x^2+3*x-4)/(-1+2*x)^2/(3+2*x),x, algorithm=""giac"")","\frac{9}{32 \, {\left(2 \, x - 1\right)}} - \frac{1}{8} \, \log\left(\frac{{\left| 2 \, x - 1 \right|}}{2 \, {\left(2 \, x - 1\right)}^{2}}\right) - \frac{25}{128} \, \log\left({\left| -\frac{4}{2 \, x - 1} - 1 \right|}\right)"," ",0,"9/32/(2*x - 1) - 1/8*log(1/2*abs(2*x - 1)/(2*x - 1)^2) - 25/128*log(abs(-4/(2*x - 1) - 1))","A",0
358,1,20,0,0.310303," ","integrate((3*x^2-4*x+5)/(-1+x)/(x^2+1),x, algorithm=""giac"")","-3 \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right) + 2 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-3*arctan(x) + 1/2*log(x^2 + 1) + 2*log(abs(x - 1))","A",0
359,1,47,0,0.302911," ","integrate((x^2-2*x-1)/(-1+x)^2/(x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \pi - \pi \left \lfloor \frac{\pi + 4 \, \arctan\left(x\right)}{4 \, \pi} + \frac{1}{2} \right \rfloor + \frac{1}{x - 1} + \arctan\left(x\right) - \frac{1}{2} \, \log\left(\frac{2}{x - 1} + \frac{2}{{\left(x - 1\right)}^{2}} + 1\right)"," ",0,"1/4*pi - pi*floor(1/4*(pi + 4*arctan(x))/pi + 1/2) + 1/(x - 1) + arctan(x) - 1/2*log(2/(x - 1) + 2/(x - 1)^2 + 1)","B",0
360,1,39,0,0.283423," ","integrate((x^3+5)/(x^2-6*x+10)/(1/2-x+x^2),x, algorithm=""giac"")","\frac{261}{221} \, \arctan\left(2 \, x - 1\right) + \frac{1026}{221} \, \arctan\left(x - 3\right) + \frac{109}{442} \, \log\left(2 \, x^{2} - 2 \, x + 1\right) + \frac{56}{221} \, \log\left(x^{2} - 6 \, x + 10\right)"," ",0,"261/221*arctan(2*x - 1) + 1026/221*arctan(x - 3) + 109/442*log(2*x^2 - 2*x + 1) + 56/221*log(x^2 - 6*x + 10)","A",0
361,1,22,0,0.392017," ","integrate((x^2+3*x+4)/(-3+x)/(-2+x)/(-1+x),x, algorithm=""giac"")","4 \, \log\left({\left| x - 1 \right|}\right) - 14 \, \log\left({\left| x - 2 \right|}\right) + 11 \, \log\left({\left| x - 3 \right|}\right)"," ",0,"4*log(abs(x - 1)) - 14*log(abs(x - 2)) + 11*log(abs(x - 3))","A",0
362,1,60,0,0.343287," ","integrate((1+16*x)/(5+x)^2/(-3+2*x)/(x^2+x+1),x, algorithm=""giac"")","\frac{451}{8379} \, \sqrt{3} \arctan\left(-\sqrt{3} {\left(\frac{14}{x + 5} - 3\right)}\right) - \frac{79}{273 \, {\left(x + 5\right)}} - \frac{481}{5586} \, \log\left(-\frac{9}{x + 5} + \frac{21}{{\left(x + 5\right)}^{2}} + 1\right) + \frac{200}{3211} \, \log\left({\left| -\frac{13}{x + 5} + 2 \right|}\right)"," ",0,"451/8379*sqrt(3)*arctan(-sqrt(3)*(14/(x + 5) - 3)) - 79/273/(x + 5) - 481/5586*log(-9/(x + 5) + 21/(x + 5)^2 + 1) + 200/3211*log(abs(-13/(x + 5) + 2))","A",0
363,1,9,0,0.227024," ","integrate((x^3-1)/(x^2+x+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - x"," ",0,"1/2*x^2 - x","A",0
364,1,23,0,0.354866," ","integrate((x^3-3)/(x^2-6*x-7),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 6 \, x + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \frac{85}{2} \, \log\left({\left| x - 7 \right|}\right)"," ",0,"1/2*x^2 + 6*x + 1/2*log(abs(x + 1)) + 85/2*log(abs(x - 7))","A",0
365,1,37,0,0.299182," ","integrate((x^3+1)/(x^2+4*x+13)^2,x, algorithm=""giac"")","\frac{47 \, x + 67}{18 \, {\left(x^{2} + 4 \, x + 13\right)}} - \frac{61}{54} \, \arctan\left(\frac{1}{3} \, x + \frac{2}{3}\right) + \frac{1}{2} \, \log\left(x^{2} + 4 \, x + 13\right)"," ",0,"1/18*(47*x + 67)/(x^2 + 4*x + 13) - 61/54*arctan(1/3*x + 2/3) + 1/2*log(x^2 + 4*x + 13)","A",0
366,1,29,0,0.324683," ","integrate((3*x^5-10*x^4+21*x^3-42*x^2+36*x-32)/x/(x^2+1)/(x^2+4)^2,x, algorithm=""giac"")","\frac{1}{x^{2} + 4} + \frac{1}{2} \, \arctan\left(\frac{1}{2} \, x\right) + 2 \, \arctan\left(x\right) + \log\left(x^{2} + 4\right) - 2 \, \log\left({\left| x \right|}\right)"," ",0,"1/(x^2 + 4) + 1/2*arctan(1/2*x) + 2*arctan(x) + log(x^2 + 4) - 2*log(abs(x))","A",0
367,1,122,0,0.388304," ","integrate((x^9+7*x^5+x^4-1)/(x^8+6*x^4-7),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{1}{28} \cdot 28^{\frac{1}{4}} \arctan\left(\frac{1}{14} \cdot 7^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 7^{\frac{1}{4}} \sqrt{2}\right)}\right) + \frac{1}{28} \cdot 28^{\frac{1}{4}} \arctan\left(\frac{1}{14} \cdot 7^{\frac{3}{4}} \sqrt{2} {\left(2 \, x - 7^{\frac{1}{4}} \sqrt{2}\right)}\right) + \frac{1}{56} \cdot 28^{\frac{1}{4}} \log\left(x^{2} + 7^{\frac{1}{4}} \sqrt{2} x + \sqrt{7}\right) - \frac{1}{56} \cdot 28^{\frac{1}{4}} \log\left(x^{2} - 7^{\frac{1}{4}} \sqrt{2} x + \sqrt{7}\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right) + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 + 1/28*28^(1/4)*arctan(1/14*7^(3/4)*sqrt(2)*(2*x + 7^(1/4)*sqrt(2))) + 1/28*28^(1/4)*arctan(1/14*7^(3/4)*sqrt(2)*(2*x - 7^(1/4)*sqrt(2))) + 1/56*28^(1/4)*log(x^2 + 7^(1/4)*sqrt(2)*x + sqrt(7)) - 1/56*28^(1/4)*log(x^2 - 7^(1/4)*sqrt(2)*x + sqrt(7)) - 1/4*log(x^2 + 1) + 1/4*log(abs(x + 1)) + 1/4*log(abs(x - 1))","A",0
368,1,92,0,0.389851," ","integrate((x^6+x^3+1)/(x^5+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{1}{4} \, {\left(\sqrt{2} + 2\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{4} \, {\left(\sqrt{2} - 2\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{4} \, \log\left(x^{4} + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 + 1/4*(sqrt(2) + 2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/4*(sqrt(2) - 2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/8*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/8*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*log(x^4 + 1) + log(abs(x))","A",0
369,1,14,0,0.261646," ","integrate((x^2+1)/(x^2-x),x, algorithm=""giac"")","x + 2 \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"x + 2*log(abs(x - 1)) - log(abs(x))","A",0
370,1,12,0,0.371729," ","integrate((x^3+1)/(x^3-x),x, algorithm=""giac"")","x + \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"x + log(abs(x - 1)) - log(abs(x))","A",0
371,1,17,0,0.318847," ","integrate((x^3+1)/(x^3-x^2),x, algorithm=""giac"")","x + \frac{1}{x} + 2 \, \log\left({\left| x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"x + 1/x + 2*log(abs(x - 1)) - log(abs(x))","A",0
372,1,17,0,0.260181," ","integrate((x^5-1)/(x^3-x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + x - \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"1/3*x^3 + x - log(abs(x + 1)) + log(abs(x))","A",0
373,1,23,0,0.267197," ","integrate((x^4+1)/(x^5+x^3),x, algorithm=""giac"")","\frac{x^{2} - 1}{2 \, x^{2}} + \log\left(x^{2} + 1\right) - \frac{1}{2} \, \log\left(x^{2}\right)"," ",0,"1/2*(x^2 - 1)/x^2 + log(x^2 + 1) - 1/2*log(x^2)","A",0
374,1,11,0,0.361405," ","integrate((x^2+1)/(x^3+2*x^2+x),x, algorithm=""giac"")","\frac{2}{x + 1} + \log\left({\left| x \right|}\right)"," ",0,"2/(x + 1) + log(abs(x))","A",0
375,1,33,0,0.287230," ","integrate((x^5+1)/(x^3-3*x^2-10*x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} + 19 \, x - \frac{31}{14} \, \log\left({\left| x + 2 \right|}\right) + \frac{3126}{35} \, \log\left({\left| x - 5 \right|}\right) - \frac{1}{10} \, \log\left({\left| x \right|}\right)"," ",0,"1/3*x^3 + 3/2*x^2 + 19*x - 31/14*log(abs(x + 2)) + 3126/35*log(abs(x - 5)) - 1/10*log(abs(x))","A",0
376,1,38,0,0.355159," ","integrate((x^3+x^2-5*x+15)/(x^2+5)/(x^2+2*x+3),x, algorithm=""giac"")","\frac{5}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x + 1\right)}\right) - \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) + \frac{1}{2} \, \log\left(x^{2} + 2 \, x + 3\right)"," ",0,"5/2*sqrt(2)*arctan(1/2*sqrt(2)*(x + 1)) - sqrt(5)*arctan(1/5*sqrt(5)*x) + 1/2*log(x^2 + 2*x + 3)","A",0
377,1,17,0,0.281203," ","integrate(1/(x^2+1)/(3+10*x/(x^2+1)),x, algorithm=""giac"")","\frac{1}{8} \, \log\left({\left| 3 \, x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x + 3 \right|}\right)"," ",0,"1/8*log(abs(3*x + 1)) - 1/8*log(abs(x + 3))","A",0
378,1,32,0,0.284438," ","integrate(x^3/(13+2/x+15*x),x, algorithm=""giac"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{16}{567} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(abs(5*x + 1)) - 16/567*log(abs(3*x + 2))","A",0
379,1,27,0,0.343172," ","integrate(x^2/(13+2/x+15*x),x, algorithm=""giac"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{8}{189} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(abs(5*x + 1)) + 8/189*log(abs(3*x + 2))","A",0
380,1,22,0,0.269588," ","integrate(x/(13+2/x+15*x),x, algorithm=""giac"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{4}{63} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/15*x + 1/175*log(abs(5*x + 1)) - 4/63*log(abs(3*x + 2))","A",0
381,1,19,0,0.285817," ","integrate(1/(13+2/x+15*x),x, algorithm=""giac"")","-\frac{1}{35} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{2}{21} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"-1/35*log(abs(5*x + 1)) + 2/21*log(abs(3*x + 2))","A",0
382,1,19,0,0.274548," ","integrate(1/x/(13+2/x+15*x),x, algorithm=""giac"")","\frac{1}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{1}{7} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/7*log(abs(5*x + 1)) - 1/7*log(abs(3*x + 2))","A",0
383,1,24,0,0.373240," ","integrate(1/x^2/(13+2/x+15*x),x, algorithm=""giac"")","-\frac{5}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{3}{14} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-5/7*log(abs(5*x + 1)) + 3/14*log(abs(3*x + 2)) + 1/2*log(abs(x))","A",0
384,1,29,0,0.266468," ","integrate(1/x^3/(13+2/x+15*x),x, algorithm=""giac"")","-\frac{1}{2 \, x} + \frac{25}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{9}{28} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{13}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2/x + 25/7*log(abs(5*x + 1)) - 9/28*log(abs(3*x + 2)) - 13/4*log(abs(x))","A",0
385,1,34,0,0.276327," ","integrate(1/x^4/(13+2/x+15*x),x, algorithm=""giac"")","\frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{27}{56} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{139}{8} \, \log\left({\left| x \right|}\right)"," ",0,"1/4*(13*x - 1)/x^2 - 125/7*log(abs(5*x + 1)) + 27/56*log(abs(3*x + 2)) + 139/8*log(abs(x))","A",0
386,1,39,0,0.238073," ","integrate(1/x^5/(13+2/x+15*x),x, algorithm=""giac"")","-\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{81}{112} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{1417}{16} \, \log\left({\left| x \right|}\right)"," ",0,"-1/24*(417*x^2 - 39*x + 4)/x^3 + 625/7*log(abs(5*x + 1)) - 81/112*log(abs(3*x + 2)) - 1417/16*log(abs(x))","A",0
387,0,0,0,0.000000," ","integrate(x^2/(2-(x^2+1)^4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(x^{2} + 1\right)}^{4} - 2}\,{d x}"," ",0,"integrate(-x^2/((x^2 + 1)^4 - 2), x)","F",0
388,0,0,0,0.000000," ","integrate(x^2/(2-(-x^2+1)^4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(x^{2} - 1\right)}^{4} - 2}\,{d x}"," ",0,"integrate(-x^2/((x^2 - 1)^4 - 2), x)","F",0
389,0,0,0,0.000000," ","integrate(x^2/(2+(x^2+1)^4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{2} + 1\right)}^{4} + 2}\,{d x}"," ",0,"integrate(x^2/((x^2 + 1)^4 + 2), x)","F",0
390,0,0,0,0.000000," ","integrate(x^2/(2+(-x^2+1)^4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{2} - 1\right)}^{4} + 2}\,{d x}"," ",0,"integrate(x^2/((x^2 - 1)^4 + 2), x)","F",0
391,0,0,0,0.000000," ","integrate((-x^2+1)/(a+b*(-x^2+1)^4),x, algorithm=""giac"")","\int -\frac{x^{2} - 1}{{\left(x^{2} - 1\right)}^{4} b + a}\,{d x}"," ",0,"integrate(-(x^2 - 1)/((x^2 - 1)^4*b + a), x)","F",0
392,0,0,0,0.000000," ","integrate((-x^2+1)/(a+b*(x^2-1)^4),x, algorithm=""giac"")","\int -\frac{x^{2} - 1}{{\left(x^{2} - 1\right)}^{4} b + a}\,{d x}"," ",0,"integrate(-(x^2 - 1)/((x^2 - 1)^4*b + a), x)","F",0
393,0,0,0,0.000000," ","integrate((x^2+1)^2/(a*x^6+b*(x^2+1)^3),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2}}{a x^{6} + {\left(x^{2} + 1\right)}^{3} b}\,{d x}"," ",0,"integrate((x^2 + 1)^2/(a*x^6 + (x^2 + 1)^3*b), x)","F",0
394,1,311,0,0.360932," ","integrate((e*x+d)^3/(c*x^4+a),x, algorithm=""giac"")","\frac{e^{3} \log\left({\left| c x^{4} + a \right|}\right)}{4 \, c} + \frac{\sqrt{2} {\left(3 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(3 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"1/4*e^3*log(abs(c*x^4 + a))/c + 1/4*sqrt(2)*(3*sqrt(2)*sqrt(a*c)*c^2*d^2*e + (a*c^3)^(1/4)*c^2*d^3 + 3*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*(3*sqrt(2)*sqrt(a*c)*c^2*d^2*e + (a*c^3)^(1/4)*c^2*d^3 + 3*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^3 - 3*(a*c^3)^(3/4)*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^3 - 3*(a*c^3)^(3/4)*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
395,1,285,0,0.336179," ","integrate((e*x+d)^2/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c^{2} d e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c^{2} d e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"1/4*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c^2*d*e + (a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c^2*d*e + (a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
396,1,215,0,0.315589," ","integrate((e*x+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a c} c e - \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{2}} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a c} c e - \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{2}}"," ",0,"1/8*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c) - 1/8*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*c)*c*e - (a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^2) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*c)*c*e - (a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^2)","A",0
397,1,179,0,0.325013," ","integrate(1/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c}"," ",0,"1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c) - 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c)","A",0
398,1,371,0,0.421763," ","integrate(1/(e*x+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{\left(a c^{3}\right)^{\frac{1}{4}} c d \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{2} d^{2} - 2 \, \left(a c^{3}\right)^{\frac{1}{4}} a c d e + \sqrt{2} \sqrt{a c} a c e^{2}\right)}} + \frac{\left(a c^{3}\right)^{\frac{1}{4}} c d \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{2} d^{2} + 2 \, \left(a c^{3}\right)^{\frac{1}{4}} a c d e + \sqrt{2} \sqrt{a c} a c e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{4} + \sqrt{2} a^{2} c^{2} e^{4}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{4} + \sqrt{2} a^{2} c^{2} e^{4}\right)}} - \frac{e^{3} \log\left({\left| c x^{4} + a \right|}\right)}{4 \, {\left(c d^{4} + a e^{4}\right)}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{c d^{4} e + a e^{5}}"," ",0,"1/2*(a*c^3)^(1/4)*c*d*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^2*d^2 - 2*(a*c^3)^(1/4)*a*c*d*e + sqrt(2)*sqrt(a*c)*a*c*e^2) + 1/2*(a*c^3)^(1/4)*c*d*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^2*d^2 + 2*(a*c^3)^(1/4)*a*c*d*e + sqrt(2)*sqrt(a*c)*a*c*e^2) + 1/4*((a*c^3)^(1/4)*c^2*d^3 - (a*c^3)^(3/4)*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^4 + sqrt(2)*a^2*c^2*e^4) - 1/4*((a*c^3)^(1/4)*c^2*d^3 - (a*c^3)^(3/4)*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^4 + sqrt(2)*a^2*c^2*e^4) - 1/4*e^3*log(abs(c*x^4 + a))/(c*d^4 + a*e^4) + e^4*log(abs(x*e + d))/(c*d^4*e + a*e^5)","A",0
399,1,646,0,2.779847," ","integrate(1/(e*x+d)^2/(c*x^4+a),x, algorithm=""giac"")","-\frac{c d^{3} e^{3} \log\left({\left| c x^{4} + a \right|}\right)}{c^{2} d^{8} + 2 \, a c d^{4} e^{4} + a^{2} e^{8}} + \frac{4 \, c d^{3} e^{4} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{8} e + 2 \, a c d^{4} e^{5} + a^{2} e^{9}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{4} - 4 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{3} e + 4 \, \sqrt{2} \sqrt{a c} a c^{2} d^{2} e^{2} + \sqrt{2} a^{2} c^{2} e^{4} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{4} + 4 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{3} e + 4 \, \sqrt{2} \sqrt{a c} a c^{2} d^{2} e^{2} + \sqrt{2} a^{2} c^{2} e^{4} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)}} + \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{6} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{4} e^{2} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{4} + \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a e^{6}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{4} e^{4} + a^{3} c^{2} e^{8}\right)}} - \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{6} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{4} e^{2} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{4} + \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a e^{6}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{4} e^{4} + a^{3} c^{2} e^{8}\right)}} - \frac{c d^{4} e^{3} + a e^{7}}{{\left(c d^{4} + a e^{4}\right)}^{2} {\left(x e + d\right)}}"," ",0,"-c*d^3*e^3*log(abs(c*x^4 + a))/(c^2*d^8 + 2*a*c*d^4*e^4 + a^2*e^8) + 4*c*d^3*e^4*log(abs(x*e + d))/(c^2*d^8*e + 2*a*c*d^4*e^5 + a^2*e^9) + 1/2*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^4 - 4*(a*c^3)^(1/4)*a*c^2*d^3*e + 4*sqrt(2)*sqrt(a*c)*a*c^2*d^2*e^2 + sqrt(2)*a^2*c^2*e^4 - 4*(a*c^3)^(3/4)*a*d*e^3) + 1/2*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^4 + 4*(a*c^3)^(1/4)*a*c^2*d^3*e + 4*sqrt(2)*sqrt(a*c)*a*c^2*d^2*e^2 + sqrt(2)*a^2*c^2*e^4 + 4*(a*c^3)^(3/4)*a*d*e^3) + 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^3*d^6 - 3*sqrt(2)*(a*c^3)^(3/4)*c*d^4*e^2 - 3*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^2*e^4 + sqrt(2)*(a*c^3)^(3/4)*a*e^6)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4*d^8 + 2*a^2*c^3*d^4*e^4 + a^3*c^2*e^8) - 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^3*d^6 - 3*sqrt(2)*(a*c^3)^(3/4)*c*d^4*e^2 - 3*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^2*e^4 + sqrt(2)*(a*c^3)^(3/4)*a*e^6)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4*d^8 + 2*a^2*c^3*d^4*e^4 + a^3*c^2*e^8) - (c*d^4*e^3 + a*e^7)/((c*d^4 + a*e^4)^2*(x*e + d))","A",0
400,1,901,0,0.892472," ","integrate(1/(e*x+d)^3/(c*x^4+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 2 \, a c^{2} e^{3} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(a c^{3} d^{6} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{5} e + 9 \, \sqrt{a c} a c^{2} d^{4} e^{2} + 9 \, a^{2} c^{2} d^{2} e^{4} - 8 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d^{3} e^{3} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c d e^{5} + \sqrt{a c} a^{2} c e^{6}\right)}} + \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - 2 \, a c^{2} e^{3} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(a c^{3} d^{6} + 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{5} e - 9 \, \sqrt{a c} a c^{2} d^{4} e^{2} + 9 \, a^{2} c^{2} d^{2} e^{4} + 8 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d^{3} e^{3} + 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c d e^{5} + \sqrt{a c} a^{2} c e^{6}\right)}} + \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{9} - 6 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{7} e^{2} - 12 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{5} e^{4} + 10 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d^{3} e^{6} + 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c d e^{8}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{4} d^{12} + 3 \, a^{2} c^{3} d^{8} e^{4} + 3 \, a^{3} c^{2} d^{4} e^{8} + a^{4} c e^{12}\right)}} - \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{9} - 6 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{7} e^{2} - 12 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{5} e^{4} + 10 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d^{3} e^{6} + 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c d e^{8}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{4} d^{12} + 3 \, a^{2} c^{3} d^{8} e^{4} + 3 \, a^{3} c^{2} d^{4} e^{8} + a^{4} c e^{12}\right)}} - \frac{{\left(5 \, c^{2} d^{6} e^{3} - 3 \, a c d^{2} e^{7}\right)} \log\left({\left| c x^{4} + a \right|}\right)}{2 \, {\left(c^{3} d^{12} + 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{4} e^{8} + a^{3} e^{12}\right)}} + \frac{2 \, {\left(5 \, c^{2} d^{6} e^{4} - 3 \, a c d^{2} e^{8}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{12} e + 3 \, a c^{2} d^{8} e^{5} + 3 \, a^{2} c d^{4} e^{9} + a^{3} e^{13}} - \frac{9 \, c^{2} d^{8} e^{3} + 10 \, a c d^{4} e^{7} + a^{2} e^{11} + 8 \, {\left(c^{2} d^{7} e^{4} + a c d^{3} e^{8}\right)} x}{2 \, {\left(c d^{4} + a e^{4}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/4*(sqrt(2)*(a*c^3)^(1/4)*c^2*d^3 + 2*a*c^2*e^3 - 3*sqrt(2)*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3*d^6 - 3*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^5*e + 9*sqrt(a*c)*a*c^2*d^4*e^2 + 9*a^2*c^2*d^2*e^4 - 8*sqrt(2)*(a*c^3)^(3/4)*a*d^3*e^3 - 3*sqrt(2)*(a*c^3)^(1/4)*a^2*c*d*e^5 + sqrt(a*c)*a^2*c*e^6) + 1/4*(sqrt(2)*(a*c^3)^(1/4)*c^2*d^3 - 2*a*c^2*e^3 - 3*sqrt(2)*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3*d^6 + 3*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^5*e - 9*sqrt(a*c)*a*c^2*d^4*e^2 + 9*a^2*c^2*d^2*e^4 + 8*sqrt(2)*(a*c^3)^(3/4)*a*d^3*e^3 + 3*sqrt(2)*(a*c^3)^(1/4)*a^2*c*d*e^5 + sqrt(a*c)*a^2*c*e^6) + 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^3*d^9 - 6*sqrt(2)*(a*c^3)^(3/4)*c*d^7*e^2 - 12*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^5*e^4 + 10*sqrt(2)*(a*c^3)^(3/4)*a*d^3*e^6 + 3*sqrt(2)*(a*c^3)^(1/4)*a^2*c*d*e^8)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4*d^12 + 3*a^2*c^3*d^8*e^4 + 3*a^3*c^2*d^4*e^8 + a^4*c*e^12) - 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^3*d^9 - 6*sqrt(2)*(a*c^3)^(3/4)*c*d^7*e^2 - 12*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^5*e^4 + 10*sqrt(2)*(a*c^3)^(3/4)*a*d^3*e^6 + 3*sqrt(2)*(a*c^3)^(1/4)*a^2*c*d*e^8)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4*d^12 + 3*a^2*c^3*d^8*e^4 + 3*a^3*c^2*d^4*e^8 + a^4*c*e^12) - 1/2*(5*c^2*d^6*e^3 - 3*a*c*d^2*e^7)*log(abs(c*x^4 + a))/(c^3*d^12 + 3*a*c^2*d^8*e^4 + 3*a^2*c*d^4*e^8 + a^3*e^12) + 2*(5*c^2*d^6*e^4 - 3*a*c*d^2*e^8)*log(abs(x*e + d))/(c^3*d^12*e + 3*a*c^2*d^8*e^5 + 3*a^2*c*d^4*e^9 + a^3*e^13) - 1/2*(9*c^2*d^8*e^3 + 10*a*c*d^4*e^7 + a^2*e^11 + 8*(c^2*d^7*e^4 + a*c*d^3*e^8)*x)/((c*d^4 + a*e^4)^3*(x*e + d)^2)","A",0
401,1,342,0,0.341694," ","integrate((e*x+d)^3/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, c d x^{3} e^{2} + 3 \, c d^{2} x^{2} e + c d^{3} x - a e^{3}}{4 \, {\left(c x^{4} + a\right)} a c} + \frac{3 \, \sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{3 \, \sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}} - \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}}"," ",0,"1/4*(3*c*d*x^3*e^2 + 3*c*d^2*x^2*e + c*d^3*x - a*e^3)/((c*x^4 + a)*a*c) + 3/16*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c^2*d^2*e + (a*c^3)^(1/4)*c^2*d^3 + (a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 3/16*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c^2*d^2*e + (a*c^3)^(1/4)*c^2*d^3 + (a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 3/32*sqrt(2)*((a*c^3)^(1/4)*c^2*d^3 - (a*c^3)^(3/4)*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3) - 3/32*sqrt(2)*((a*c^3)^(1/4)*c^2*d^3 - (a*c^3)^(3/4)*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3)","A",0
402,1,323,0,0.364223," ","integrate((e*x+d)^2/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{3} e^{2} + 2 \, d x^{2} e + d^{2} x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a c} c^{2} d e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a c} c^{2} d e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}}"," ",0,"1/4*(x^3*e^2 + 2*d*x^2*e + d^2*x)/((c*x^4 + a)*a) + 1/16*sqrt(2)*(4*sqrt(2)*sqrt(a*c)*c^2*d*e + 3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*(4*sqrt(2)*sqrt(a*c)*c^2*d*e + 3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3) - 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(3/4)*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3)","A",0
403,1,241,0,0.338915," ","integrate((e*x+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c} + \frac{x^{2} e + d x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{2}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a c} c e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{2}}"," ",0,"3/32*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c) - 3/32*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c) + 1/4*(x^2*e + d*x)/((c*x^4 + a)*a) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c*e + 3*(a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*c)*c*e + 3*(a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2)","A",0
404,1,194,0,0.246282," ","integrate(1/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c}"," ",0,"1/4*x/((c*x^4 + a)*a) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c) - 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c)","A",0
405,1,771,0,0.504301," ","integrate(1/(e*x+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(4 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{3} d^{4} - 4 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{3} e + 4 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} d^{2} e^{2} + \sqrt{2} a^{3} c^{2} e^{4} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d e^{3}\right)}} + \frac{{\left(4 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{3} d^{4} + 4 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{3} e + 4 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} d^{2} e^{2} + \sqrt{2} a^{3} c^{2} e^{4} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d e^{3}\right)}} + \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{7} - \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{5} e^{2} + 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{3} e^{4} - 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d e^{6}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{4} e^{4} + a^{4} c^{2} e^{8}\right)}} - \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{7} - \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{5} e^{2} + 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{3} e^{4} - 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d e^{6}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{4} e^{4} + a^{4} c^{2} e^{8}\right)}} - \frac{e^{7} \log\left({\left| c x^{4} + a \right|}\right)}{4 \, {\left(c^{2} d^{8} + 2 \, a c d^{4} e^{4} + a^{2} e^{8}\right)}} + \frac{e^{8} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{8} e + 2 \, a c d^{4} e^{5} + a^{2} e^{9}} + \frac{a c d^{4} e^{3} + {\left(c^{2} d^{5} e^{2} + a c d e^{6}\right)} x^{3} - {\left(c^{2} d^{6} e + a c d^{2} e^{5}\right)} x^{2} + a^{2} e^{7} + {\left(c^{2} d^{7} + a c d^{3} e^{4}\right)} x}{4 \, {\left(c d^{4} + a e^{4}\right)}^{2} {\left(c x^{4} + a\right)} a}"," ",0,"1/8*(4*sqrt(2)*sqrt(a*c)*c^2*d^2*e + 3*(a*c^3)^(1/4)*c^2*d^3 + 5*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^3*d^4 - 4*(a*c^3)^(1/4)*a^2*c^2*d^3*e + 4*sqrt(2)*sqrt(a*c)*a^2*c^2*d^2*e^2 + sqrt(2)*a^3*c^2*e^4 - 4*(a*c^3)^(3/4)*a^2*d*e^3) + 1/8*(4*sqrt(2)*sqrt(a*c)*c^2*d^2*e + 3*(a*c^3)^(1/4)*c^2*d^3 + 5*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^3*d^4 + 4*(a*c^3)^(1/4)*a^2*c^2*d^3*e + 4*sqrt(2)*sqrt(a*c)*a^2*c^2*d^2*e^2 + sqrt(2)*a^3*c^2*e^4 + 4*(a*c^3)^(3/4)*a^2*d*e^3) + 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^3*d^7 - sqrt(2)*(a*c^3)^(3/4)*c*d^5*e^2 + 7*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^3*e^4 - 5*sqrt(2)*(a*c^3)^(3/4)*a*d*e^6)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4*d^8 + 2*a^3*c^3*d^4*e^4 + a^4*c^2*e^8) - 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^3*d^7 - sqrt(2)*(a*c^3)^(3/4)*c*d^5*e^2 + 7*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^3*e^4 - 5*sqrt(2)*(a*c^3)^(3/4)*a*d*e^6)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4*d^8 + 2*a^3*c^3*d^4*e^4 + a^4*c^2*e^8) - 1/4*e^7*log(abs(c*x^4 + a))/(c^2*d^8 + 2*a*c*d^4*e^4 + a^2*e^8) + e^8*log(abs(x*e + d))/(c^2*d^8*e + 2*a*c*d^4*e^5 + a^2*e^9) + 1/4*(a*c*d^4*e^3 + (c^2*d^5*e^2 + a*c*d*e^6)*x^3 - (c^2*d^6*e + a*c*d^2*e^5)*x^2 + a^2*e^7 + (c^2*d^7 + a*c*d^3*e^4)*x)/((c*d^4 + a*e^4)^2*(c*x^4 + a)*a)","A",0
406,1,1104,0,103.635529," ","integrate(1/(e*x+d)^2/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{2 \, c d^{3} e^{7} \log\left({\left| c x^{4} + a \right|}\right)}{c^{3} d^{12} + 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{4} e^{8} + a^{3} e^{12}} + \frac{8 \, c d^{3} e^{8} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{12} e + 3 \, a c^{2} d^{8} e^{5} + 3 \, a^{2} c d^{4} e^{9} + a^{3} e^{13}} + \frac{{\left(5 \, \sqrt{2} \sqrt{a c} c^{2} d^{3} e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{4} + 3 \, \sqrt{2} a c^{2} d e^{3} + 6 \, \left(a c^{3}\right)^{\frac{3}{4}} d^{2} e^{2} - 5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c e^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{3} d^{6} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{5} e + 9 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} d^{4} e^{2} + 9 \, \sqrt{2} a^{3} c^{2} d^{2} e^{4} - 16 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d^{3} e^{3} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c d e^{5} + \sqrt{2} \sqrt{a c} a^{3} c e^{6}\right)}} + \frac{{\left(5 \, \sqrt{2} \sqrt{a c} c^{2} d^{3} e + 3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{4} - 3 \, \sqrt{2} a c^{2} d e^{3} + 6 \, \left(a c^{3}\right)^{\frac{3}{4}} d^{2} e^{2} - 5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c e^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{3} d^{6} + 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{5} e + 9 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} d^{4} e^{2} + 9 \, \sqrt{2} a^{3} c^{2} d^{2} e^{4} + 16 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d^{3} e^{3} + 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c d e^{5} + \sqrt{2} \sqrt{a c} a^{3} c e^{6}\right)}} + \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{10} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{8} e^{2} + 14 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{6} e^{4} - 30 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{4} e^{6} - 21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{2} e^{8} + 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} e^{10}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{5} d^{12} + 3 \, a^{3} c^{4} d^{8} e^{4} + 3 \, a^{4} c^{3} d^{4} e^{8} + a^{5} c^{2} e^{12}\right)}} - \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{10} - 3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{8} e^{2} + 14 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{6} e^{4} - 30 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{4} e^{6} - 21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{2} e^{8} + 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} e^{10}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{5} d^{12} + 3 \, a^{3} c^{4} d^{8} e^{4} + 3 \, a^{4} c^{3} d^{4} e^{8} + a^{5} c^{2} e^{12}\right)}} + \frac{3 \, c^{2} d^{4} x^{4} e^{3} + c^{2} d^{5} x^{3} e^{2} - c^{2} d^{6} x^{2} e + c^{2} d^{7} x - 5 \, a c x^{4} e^{7} + a c d x^{3} e^{6} - a c d^{2} x^{2} e^{5} + a c d^{3} x e^{4} + 4 \, a c d^{4} e^{3} - 4 \, a^{2} e^{7}}{4 \, {\left(a c^{2} d^{8} + 2 \, a^{2} c d^{4} e^{4} + a^{3} e^{8}\right)} {\left(c x^{5} e + c d x^{4} + a x e + a d\right)}}"," ",0,"-2*c*d^3*e^7*log(abs(c*x^4 + a))/(c^3*d^12 + 3*a*c^2*d^8*e^4 + 3*a^2*c*d^4*e^8 + a^3*e^12) + 8*c*d^3*e^8*log(abs(x*e + d))/(c^3*d^12*e + 3*a*c^2*d^8*e^5 + 3*a^2*c*d^4*e^9 + a^3*e^13) + 1/8*(5*sqrt(2)*sqrt(a*c)*c^2*d^3*e + 3*(a*c^3)^(1/4)*c^2*d^4 + 3*sqrt(2)*a*c^2*d*e^3 + 6*(a*c^3)^(3/4)*d^2*e^2 - 5*(a*c^3)^(1/4)*a*c*e^4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^3*d^6 - 6*(a*c^3)^(1/4)*a^2*c^2*d^5*e + 9*sqrt(2)*sqrt(a*c)*a^2*c^2*d^4*e^2 + 9*sqrt(2)*a^3*c^2*d^2*e^4 - 16*(a*c^3)^(3/4)*a^2*d^3*e^3 - 6*(a*c^3)^(1/4)*a^3*c*d*e^5 + sqrt(2)*sqrt(a*c)*a^3*c*e^6) + 1/8*(5*sqrt(2)*sqrt(a*c)*c^2*d^3*e + 3*(a*c^3)^(1/4)*c^2*d^4 - 3*sqrt(2)*a*c^2*d*e^3 + 6*(a*c^3)^(3/4)*d^2*e^2 - 5*(a*c^3)^(1/4)*a*c*e^4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^3*d^6 + 6*(a*c^3)^(1/4)*a^2*c^2*d^5*e + 9*sqrt(2)*sqrt(a*c)*a^2*c^2*d^4*e^2 + 9*sqrt(2)*a^3*c^2*d^2*e^4 + 16*(a*c^3)^(3/4)*a^2*d^3*e^3 + 6*(a*c^3)^(1/4)*a^3*c*d*e^5 + sqrt(2)*sqrt(a*c)*a^3*c*e^6) + 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^4*d^10 - 3*sqrt(2)*(a*c^3)^(3/4)*c^2*d^8*e^2 + 14*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^6*e^4 - 30*sqrt(2)*(a*c^3)^(3/4)*a*c*d^4*e^6 - 21*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^2*e^8 + 5*sqrt(2)*(a*c^3)^(3/4)*a^2*e^10)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^5*d^12 + 3*a^3*c^4*d^8*e^4 + 3*a^4*c^3*d^4*e^8 + a^5*c^2*e^12) - 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^4*d^10 - 3*sqrt(2)*(a*c^3)^(3/4)*c^2*d^8*e^2 + 14*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^6*e^4 - 30*sqrt(2)*(a*c^3)^(3/4)*a*c*d^4*e^6 - 21*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^2*e^8 + 5*sqrt(2)*(a*c^3)^(3/4)*a^2*e^10)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^5*d^12 + 3*a^3*c^4*d^8*e^4 + 3*a^4*c^3*d^4*e^8 + a^5*c^2*e^12) + 1/4*(3*c^2*d^4*x^4*e^3 + c^2*d^5*x^3*e^2 - c^2*d^6*x^2*e + c^2*d^7*x - 5*a*c*x^4*e^7 + a*c*d*x^3*e^6 - a*c*d^2*x^2*e^5 + a*c*d^3*x*e^4 + 4*a*c*d^4*e^3 - 4*a^2*e^7)/((a*c^2*d^8 + 2*a^2*c*d^4*e^4 + a^3*e^8)*(c*x^5*e + c*d*x^4 + a*x*e + a*d))","A",0
407,1,1488,0,1.148449," ","integrate(1/(e*x+d)^3/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, \sqrt{2} \sqrt{a c} c^{3} d^{4} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{5} + 4 \, \sqrt{2} a c^{3} d^{2} e^{3} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e^{2} - 9 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{4} + 2 \, \sqrt{2} \sqrt{a c} a c^{2} e^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{8} - 8 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{3} d^{7} e + 16 \, \sqrt{2} \sqrt{a c} a^{2} c^{3} d^{6} e^{2} + 34 \, \sqrt{2} a^{3} c^{3} d^{4} e^{4} - 40 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} c d^{5} e^{3} - 40 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{3} e^{5} + 16 \, \sqrt{2} \sqrt{a c} a^{3} c^{2} d^{2} e^{6} + \sqrt{2} a^{4} c^{2} e^{8} - 8 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d e^{7}\right)}} + \frac{3 \, {\left(2 \, \sqrt{2} \sqrt{a c} c^{3} d^{4} e + \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{5} - 4 \, \sqrt{2} a c^{3} d^{2} e^{3} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e^{2} - 9 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{4} + 2 \, \sqrt{2} \sqrt{a c} a c^{2} e^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{8} + 8 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{3} d^{7} e + 16 \, \sqrt{2} \sqrt{a c} a^{2} c^{3} d^{6} e^{2} + 34 \, \sqrt{2} a^{3} c^{3} d^{4} e^{4} + 40 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{2} c d^{5} e^{3} + 40 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{3} e^{5} + 16 \, \sqrt{2} \sqrt{a c} a^{3} c^{2} d^{2} e^{6} + \sqrt{2} a^{4} c^{2} e^{8} + 8 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d e^{7}\right)}} + \frac{3 \, {\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{13} - 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{11} e^{2} + 9 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{9} e^{4} - 36 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{7} e^{6} - 49 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{5} e^{8} + 30 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d^{3} e^{10} + 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c d e^{12}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{5} d^{16} + 4 \, a^{3} c^{4} d^{12} e^{4} + 6 \, a^{4} c^{3} d^{8} e^{8} + 4 \, a^{5} c^{2} d^{4} e^{12} + a^{6} c e^{16}\right)}} - \frac{3 \, {\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{13} - 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{11} e^{2} + 9 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{9} e^{4} - 36 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{7} e^{6} - 49 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{5} e^{8} + 30 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d^{3} e^{10} + 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c d e^{12}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{5} d^{16} + 4 \, a^{3} c^{4} d^{12} e^{4} + 6 \, a^{4} c^{3} d^{8} e^{8} + 4 \, a^{5} c^{2} d^{4} e^{12} + a^{6} c e^{16}\right)}} - \frac{3 \, {\left(3 \, c^{2} d^{6} e^{7} - a c d^{2} e^{11}\right)} \log\left({\left| c x^{4} + a \right|}\right)}{c^{4} d^{16} + 4 \, a c^{3} d^{12} e^{4} + 6 \, a^{2} c^{2} d^{8} e^{8} + 4 \, a^{3} c d^{4} e^{12} + a^{4} e^{16}} + \frac{12 \, {\left(3 \, c^{2} d^{6} e^{8} - a c d^{2} e^{12}\right)} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{16} e + 4 \, a c^{3} d^{12} e^{5} + 6 \, a^{2} c^{2} d^{8} e^{9} + 4 \, a^{3} c d^{4} e^{13} + a^{4} e^{17}} + \frac{10 \, a c^{3} d^{12} e^{3} - 30 \, a^{2} c^{2} d^{8} e^{7} - 42 \, a^{3} c d^{4} e^{11} + 6 \, {\left(c^{4} d^{11} e^{4} - 6 \, a c^{3} d^{7} e^{8} - 7 \, a^{2} c^{2} d^{3} e^{12}\right)} x^{5} + 3 \, {\left(3 \, c^{4} d^{12} e^{3} - 11 \, a c^{3} d^{8} e^{7} - 15 \, a^{2} c^{2} d^{4} e^{11} - a^{3} c e^{15}\right)} x^{4} - 2 \, a^{4} e^{15} + {\left(c^{4} d^{13} e^{2} + 3 \, a c^{3} d^{9} e^{6} + 3 \, a^{2} c^{2} d^{5} e^{10} + a^{3} c d e^{14}\right)} x^{3} - {\left(c^{4} d^{14} e + 3 \, a c^{3} d^{10} e^{5} + 3 \, a^{2} c^{2} d^{6} e^{9} + a^{3} c d^{2} e^{13}\right)} x^{2} + {\left(c^{4} d^{15} + 9 \, a c^{3} d^{11} e^{4} - 33 \, a^{2} c^{2} d^{7} e^{8} - 41 \, a^{3} c d^{3} e^{12}\right)} x}{4 \, {\left(c d^{4} + a e^{4}\right)}^{4} {\left(c x^{4} + a\right)} {\left(x e + d\right)}^{2} a}"," ",0,"3/8*(2*sqrt(2)*sqrt(a*c)*c^3*d^4*e + (a*c^3)^(1/4)*c^3*d^5 + 4*sqrt(2)*a*c^3*d^2*e^3 + 2*(a*c^3)^(3/4)*c*d^3*e^2 - 9*(a*c^3)^(1/4)*a*c^2*d*e^4 + 2*sqrt(2)*sqrt(a*c)*a*c^2*e^5)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^8 - 8*(a*c^3)^(1/4)*a^2*c^3*d^7*e + 16*sqrt(2)*sqrt(a*c)*a^2*c^3*d^6*e^2 + 34*sqrt(2)*a^3*c^3*d^4*e^4 - 40*(a*c^3)^(3/4)*a^2*c*d^5*e^3 - 40*(a*c^3)^(1/4)*a^3*c^2*d^3*e^5 + 16*sqrt(2)*sqrt(a*c)*a^3*c^2*d^2*e^6 + sqrt(2)*a^4*c^2*e^8 - 8*(a*c^3)^(3/4)*a^3*d*e^7) + 3/8*(2*sqrt(2)*sqrt(a*c)*c^3*d^4*e + (a*c^3)^(1/4)*c^3*d^5 - 4*sqrt(2)*a*c^3*d^2*e^3 + 2*(a*c^3)^(3/4)*c*d^3*e^2 - 9*(a*c^3)^(1/4)*a*c^2*d*e^4 + 2*sqrt(2)*sqrt(a*c)*a*c^2*e^5)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^8 + 8*(a*c^3)^(1/4)*a^2*c^3*d^7*e + 16*sqrt(2)*sqrt(a*c)*a^2*c^3*d^6*e^2 + 34*sqrt(2)*a^3*c^3*d^4*e^4 + 40*(a*c^3)^(3/4)*a^2*c*d^5*e^3 + 40*(a*c^3)^(1/4)*a^3*c^2*d^3*e^5 + 16*sqrt(2)*sqrt(a*c)*a^3*c^2*d^2*e^6 + sqrt(2)*a^4*c^2*e^8 + 8*(a*c^3)^(3/4)*a^3*d*e^7) + 3/32*(sqrt(2)*(a*c^3)^(1/4)*c^4*d^13 - 2*sqrt(2)*(a*c^3)^(3/4)*c^2*d^11*e^2 + 9*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^9*e^4 - 36*sqrt(2)*(a*c^3)^(3/4)*a*c*d^7*e^6 - 49*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^5*e^8 + 30*sqrt(2)*(a*c^3)^(3/4)*a^2*d^3*e^10 + 7*sqrt(2)*(a*c^3)^(1/4)*a^3*c*d*e^12)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^5*d^16 + 4*a^3*c^4*d^12*e^4 + 6*a^4*c^3*d^8*e^8 + 4*a^5*c^2*d^4*e^12 + a^6*c*e^16) - 3/32*(sqrt(2)*(a*c^3)^(1/4)*c^4*d^13 - 2*sqrt(2)*(a*c^3)^(3/4)*c^2*d^11*e^2 + 9*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^9*e^4 - 36*sqrt(2)*(a*c^3)^(3/4)*a*c*d^7*e^6 - 49*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^5*e^8 + 30*sqrt(2)*(a*c^3)^(3/4)*a^2*d^3*e^10 + 7*sqrt(2)*(a*c^3)^(1/4)*a^3*c*d*e^12)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^5*d^16 + 4*a^3*c^4*d^12*e^4 + 6*a^4*c^3*d^8*e^8 + 4*a^5*c^2*d^4*e^12 + a^6*c*e^16) - 3*(3*c^2*d^6*e^7 - a*c*d^2*e^11)*log(abs(c*x^4 + a))/(c^4*d^16 + 4*a*c^3*d^12*e^4 + 6*a^2*c^2*d^8*e^8 + 4*a^3*c*d^4*e^12 + a^4*e^16) + 12*(3*c^2*d^6*e^8 - a*c*d^2*e^12)*log(abs(x*e + d))/(c^4*d^16*e + 4*a*c^3*d^12*e^5 + 6*a^2*c^2*d^8*e^9 + 4*a^3*c*d^4*e^13 + a^4*e^17) + 1/4*(10*a*c^3*d^12*e^3 - 30*a^2*c^2*d^8*e^7 - 42*a^3*c*d^4*e^11 + 6*(c^4*d^11*e^4 - 6*a*c^3*d^7*e^8 - 7*a^2*c^2*d^3*e^12)*x^5 + 3*(3*c^4*d^12*e^3 - 11*a*c^3*d^8*e^7 - 15*a^2*c^2*d^4*e^11 - a^3*c*e^15)*x^4 - 2*a^4*e^15 + (c^4*d^13*e^2 + 3*a*c^3*d^9*e^6 + 3*a^2*c^2*d^5*e^10 + a^3*c*d*e^14)*x^3 - (c^4*d^14*e + 3*a*c^3*d^10*e^5 + 3*a^2*c^2*d^6*e^9 + a^3*c*d^2*e^13)*x^2 + (c^4*d^15 + 9*a*c^3*d^11*e^4 - 33*a^2*c^2*d^7*e^8 - 41*a^3*c*d^3*e^12)*x)/((c*d^4 + a*e^4)^4*(c*x^4 + a)*(x*e + d)^2*a)","A",0
408,1,389,0,0.353626," ","integrate((e*x+d)^3/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} + \frac{3 \, \sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a c} c^{2} d^{2} e + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}} - \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{3} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}} + \frac{15 \, c^{2} d x^{7} e^{2} + 18 \, c^{2} d^{2} x^{6} e + 7 \, c^{2} d^{3} x^{5} + 27 \, a c d x^{3} e^{2} + 30 \, a c d^{2} x^{2} e + 11 \, a c d^{3} x - 4 \, a^{2} e^{3}}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2} c}"," ",0,"3/128*sqrt(2)*(12*sqrt(2)*sqrt(a*c)*c^2*d^2*e + 7*(a*c^3)^(1/4)*c^2*d^3 + 5*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) + 3/128*sqrt(2)*(12*sqrt(2)*sqrt(a*c)*c^2*d^2*e + 7*(a*c^3)^(1/4)*c^2*d^3 + 5*(a*c^3)^(3/4)*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) + 3/256*sqrt(2)*(7*(a*c^3)^(1/4)*c^2*d^3 - 5*(a*c^3)^(3/4)*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3) - 3/256*sqrt(2)*(7*(a*c^3)^(1/4)*c^2*d^3 - 5*(a*c^3)^(3/4)*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3) + 1/32*(15*c^2*d*x^7*e^2 + 18*c^2*d^2*x^6*e + 7*c^2*d^3*x^5 + 27*a*c*d*x^3*e^2 + 30*a*c*d^2*x^2*e + 11*a*c*d^3*x - 4*a^2*e^3)/((c*x^4 + a)^2*a^2*c)","A",0
409,1,356,0,0.433299," ","integrate((e*x+d)^2/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{5 \, c x^{7} e^{2} + 12 \, c d x^{6} e + 7 \, c d^{2} x^{5} + 9 \, a x^{3} e^{2} + 20 \, a d x^{2} e + 11 \, a d^{2} x}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2}} + \frac{\sqrt{2} {\left(24 \, \sqrt{2} \sqrt{a c} c^{2} d e + 21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(24 \, \sqrt{2} \sqrt{a c} c^{2} d e + 21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}}"," ",0,"1/32*(5*c*x^7*e^2 + 12*c*d*x^6*e + 7*c*d^2*x^5 + 9*a*x^3*e^2 + 20*a*d*x^2*e + 11*a*d^2*x)/((c*x^4 + a)^2*a^2) + 1/128*sqrt(2)*(24*sqrt(2)*sqrt(a*c)*c^2*d*e + 21*(a*c^3)^(1/4)*c^2*d^2 + 5*(a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) + 1/128*sqrt(2)*(24*sqrt(2)*sqrt(a*c)*c^2*d*e + 21*(a*c^3)^(1/4)*c^2*d^2 + 5*(a*c^3)^(3/4)*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) + 1/256*sqrt(2)*(21*(a*c^3)^(1/4)*c^2*d^2 - 5*(a*c^3)^(3/4)*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3) - 1/256*sqrt(2)*(21*(a*c^3)^(1/4)*c^2*d^2 - 5*(a*c^3)^(3/4)*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3)","A",0
410,1,260,0,0.319744," ","integrate((e*x+d)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} - \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a c} c e + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{2}} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a c} c e + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} c d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{2}} + \frac{6 \, c x^{6} e + 7 \, c d x^{5} + 10 \, a x^{2} e + 11 \, a d x}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"21/256*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) - 21/256*sqrt(2)*(a*c^3)^(1/4)*d*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(a*c)*c*e + 7*(a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^2) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(a*c)*c*e + 7*(a*c^3)^(1/4)*c*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^2) + 1/32*(6*c*x^6*e + 7*c*d*x^5 + 10*a*x^2*e + 11*a*d*x)/((c*x^4 + a)^2*a^2)","A",0
411,1,204,0,0.357675," ","integrate(1/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} - \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} + \frac{7 \, c x^{5} + 11 \, a x}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"21/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c) + 21/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c) + 21/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) - 21/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) + 1/32*(7*c*x^5 + 11*a*x)/((c*x^4 + a)^2*a^2)","A",0
412,1,1259,0,0.909538," ","integrate(1/(e*x+d)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{{\left(51 \, \sqrt{2} \sqrt{a c} c^{2} d^{4} e + 21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{5} - 75 \, \sqrt{2} a c^{2} d^{2} e^{3} + 122 \, \left(a c^{3}\right)^{\frac{3}{4}} d^{3} e^{2} + 45 \, \left(a c^{3}\right)^{\frac{1}{4}} a c d e^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, {\left(\sqrt{2} a^{3} c^{3} d^{6} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{5} e + 9 \, \sqrt{2} \sqrt{a c} a^{3} c^{2} d^{4} e^{2} + 9 \, \sqrt{2} a^{4} c^{2} d^{2} e^{4} - 16 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d^{3} e^{3} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c d e^{5} + \sqrt{2} \sqrt{a c} a^{4} c e^{6}\right)}} + \frac{{\left(51 \, \sqrt{2} \sqrt{a c} c^{2} d^{4} e + 21 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{5} + 75 \, \sqrt{2} a c^{2} d^{2} e^{3} + 122 \, \left(a c^{3}\right)^{\frac{3}{4}} d^{3} e^{2} + 45 \, \left(a c^{3}\right)^{\frac{1}{4}} a c d e^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, {\left(\sqrt{2} a^{3} c^{3} d^{6} + 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{5} e + 9 \, \sqrt{2} \sqrt{a c} a^{3} c^{2} d^{4} e^{2} + 9 \, \sqrt{2} a^{4} c^{2} d^{2} e^{4} + 16 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d^{3} e^{3} + 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c d e^{5} + \sqrt{2} \sqrt{a c} a^{4} c e^{6}\right)}} + \frac{{\left(21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{11} - 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{9} e^{2} + 66 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{7} e^{4} - 18 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{5} e^{6} + 77 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{3} e^{8} - 45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d e^{10}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, {\left(a^{3} c^{5} d^{12} + 3 \, a^{4} c^{4} d^{8} e^{4} + 3 \, a^{5} c^{3} d^{4} e^{8} + a^{6} c^{2} e^{12}\right)}} - \frac{{\left(21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{4} d^{11} - 5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{9} e^{2} + 66 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{7} e^{4} - 18 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c d^{5} e^{6} + 77 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d^{3} e^{8} - 45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} d e^{10}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, {\left(a^{3} c^{5} d^{12} + 3 \, a^{4} c^{4} d^{8} e^{4} + 3 \, a^{5} c^{3} d^{4} e^{8} + a^{6} c^{2} e^{12}\right)}} - \frac{e^{11} \log\left({\left| c x^{4} + a \right|}\right)}{4 \, {\left(c^{3} d^{12} + 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{4} e^{8} + a^{3} e^{12}\right)}} + \frac{e^{12} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{12} e + 3 \, a c^{2} d^{8} e^{5} + 3 \, a^{2} c d^{4} e^{9} + a^{3} e^{13}} + \frac{4 \, a^{2} c^{2} d^{8} e^{3} + 16 \, a^{3} c d^{4} e^{7} + {\left(5 \, c^{4} d^{9} e^{2} + 18 \, a c^{3} d^{5} e^{6} + 13 \, a^{2} c^{2} d e^{10}\right)} x^{7} - 2 \, {\left(3 \, c^{4} d^{10} e + 10 \, a c^{3} d^{6} e^{5} + 7 \, a^{2} c^{2} d^{2} e^{9}\right)} x^{6} + {\left(7 \, c^{4} d^{11} + 22 \, a c^{3} d^{7} e^{4} + 15 \, a^{2} c^{2} d^{3} e^{8}\right)} x^{5} + 8 \, {\left(a^{2} c^{2} d^{4} e^{7} + a^{3} c e^{11}\right)} x^{4} + 12 \, a^{4} e^{11} + {\left(9 \, a c^{3} d^{9} e^{2} + 26 \, a^{2} c^{2} d^{5} e^{6} + 17 \, a^{3} c d e^{10}\right)} x^{3} - 2 \, {\left(5 \, a c^{3} d^{10} e + 14 \, a^{2} c^{2} d^{6} e^{5} + 9 \, a^{3} c d^{2} e^{9}\right)} x^{2} + {\left(11 \, a c^{3} d^{11} + 30 \, a^{2} c^{2} d^{7} e^{4} + 19 \, a^{3} c d^{3} e^{8}\right)} x}{32 \, {\left(c d^{4} + a e^{4}\right)}^{3} {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"1/64*(51*sqrt(2)*sqrt(a*c)*c^2*d^4*e + 21*(a*c^3)^(1/4)*c^2*d^5 - 75*sqrt(2)*a*c^2*d^2*e^3 + 122*(a*c^3)^(3/4)*d^3*e^2 + 45*(a*c^3)^(1/4)*a*c*d*e^4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^6 - 6*(a*c^3)^(1/4)*a^3*c^2*d^5*e + 9*sqrt(2)*sqrt(a*c)*a^3*c^2*d^4*e^2 + 9*sqrt(2)*a^4*c^2*d^2*e^4 - 16*(a*c^3)^(3/4)*a^3*d^3*e^3 - 6*(a*c^3)^(1/4)*a^4*c*d*e^5 + sqrt(2)*sqrt(a*c)*a^4*c*e^6) + 1/64*(51*sqrt(2)*sqrt(a*c)*c^2*d^4*e + 21*(a*c^3)^(1/4)*c^2*d^5 + 75*sqrt(2)*a*c^2*d^2*e^3 + 122*(a*c^3)^(3/4)*d^3*e^2 + 45*(a*c^3)^(1/4)*a*c*d*e^4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^6 + 6*(a*c^3)^(1/4)*a^3*c^2*d^5*e + 9*sqrt(2)*sqrt(a*c)*a^3*c^2*d^4*e^2 + 9*sqrt(2)*a^4*c^2*d^2*e^4 + 16*(a*c^3)^(3/4)*a^3*d^3*e^3 + 6*(a*c^3)^(1/4)*a^4*c*d*e^5 + sqrt(2)*sqrt(a*c)*a^4*c*e^6) + 1/256*(21*sqrt(2)*(a*c^3)^(1/4)*c^4*d^11 - 5*sqrt(2)*(a*c^3)^(3/4)*c^2*d^9*e^2 + 66*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^7*e^4 - 18*sqrt(2)*(a*c^3)^(3/4)*a*c*d^5*e^6 + 77*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^3*e^8 - 45*sqrt(2)*(a*c^3)^(3/4)*a^2*d*e^10)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^5*d^12 + 3*a^4*c^4*d^8*e^4 + 3*a^5*c^3*d^4*e^8 + a^6*c^2*e^12) - 1/256*(21*sqrt(2)*(a*c^3)^(1/4)*c^4*d^11 - 5*sqrt(2)*(a*c^3)^(3/4)*c^2*d^9*e^2 + 66*sqrt(2)*(a*c^3)^(1/4)*a*c^3*d^7*e^4 - 18*sqrt(2)*(a*c^3)^(3/4)*a*c*d^5*e^6 + 77*sqrt(2)*(a*c^3)^(1/4)*a^2*c^2*d^3*e^8 - 45*sqrt(2)*(a*c^3)^(3/4)*a^2*d*e^10)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^5*d^12 + 3*a^4*c^4*d^8*e^4 + 3*a^5*c^3*d^4*e^8 + a^6*c^2*e^12) - 1/4*e^11*log(abs(c*x^4 + a))/(c^3*d^12 + 3*a*c^2*d^8*e^4 + 3*a^2*c*d^4*e^8 + a^3*e^12) + e^12*log(abs(x*e + d))/(c^3*d^12*e + 3*a*c^2*d^8*e^5 + 3*a^2*c*d^4*e^9 + a^3*e^13) + 1/32*(4*a^2*c^2*d^8*e^3 + 16*a^3*c*d^4*e^7 + (5*c^4*d^9*e^2 + 18*a*c^3*d^5*e^6 + 13*a^2*c^2*d*e^10)*x^7 - 2*(3*c^4*d^10*e + 10*a*c^3*d^6*e^5 + 7*a^2*c^2*d^2*e^9)*x^6 + (7*c^4*d^11 + 22*a*c^3*d^7*e^4 + 15*a^2*c^2*d^3*e^8)*x^5 + 8*(a^2*c^2*d^4*e^7 + a^3*c*e^11)*x^4 + 12*a^4*e^11 + (9*a*c^3*d^9*e^2 + 26*a^2*c^2*d^5*e^6 + 17*a^3*c*d*e^10)*x^3 - 2*(5*a*c^3*d^10*e + 14*a^2*c^2*d^6*e^5 + 9*a^3*c*d^2*e^9)*x^2 + (11*a*c^3*d^11 + 30*a^2*c^2*d^7*e^4 + 19*a^3*c*d^3*e^8)*x)/((c*d^4 + a*e^4)^3*(c*x^4 + a)^2*a^2)","A",0
413,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^4+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,1,2119,0,1.534453," ","integrate(1/(e*x+d)^3/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(23 \, \sqrt{2} a c^{4} d^{6} e - 65 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{5} e^{2} + 30 \, \sqrt{2} \sqrt{a c} a c^{3} d^{4} e^{3} - 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{7} - 115 \, \sqrt{2} a^{2} c^{3} d^{2} e^{5} + 65 \, \left(a c^{3}\right)^{\frac{3}{4}} a c d^{3} e^{4} + 123 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d e^{6} + 20 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} e^{7}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, {\left(\sqrt{2} \sqrt{a c} a^{3} c^{4} d^{10} - 25 \, \sqrt{2} a^{4} c^{4} d^{8} e^{2} + 10 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} c^{2} d^{9} e + 80 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c^{3} d^{7} e^{3} + 90 \, \sqrt{2} \sqrt{a c} a^{4} c^{3} d^{6} e^{4} - 90 \, \sqrt{2} a^{5} c^{3} d^{4} e^{6} + 148 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{4} c d^{5} e^{5} + 80 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{5} c^{2} d^{3} e^{7} + 25 \, \sqrt{2} \sqrt{a c} a^{5} c^{2} d^{2} e^{8} - \sqrt{2} a^{6} c^{2} e^{10} + 10 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{5} d e^{9}\right)}} - \frac{3 \, {\left(23 \, \sqrt{2} a c^{4} d^{6} e + 65 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{3} d^{5} e^{2} - 30 \, \sqrt{2} \sqrt{a c} a c^{3} d^{4} e^{3} + 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c^{2} d^{7} - 115 \, \sqrt{2} a^{2} c^{3} d^{2} e^{5} - 65 \, \left(a c^{3}\right)^{\frac{3}{4}} a c d^{3} e^{4} - 123 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{2} d e^{6} - 20 \, \sqrt{2} \sqrt{a c} a^{2} c^{2} e^{7}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, {\left(\sqrt{2} \sqrt{a c} a^{3} c^{4} d^{10} - 25 \, \sqrt{2} a^{4} c^{4} d^{8} e^{2} - 10 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{3} c^{2} d^{9} e - 80 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c^{3} d^{7} e^{3} + 90 \, \sqrt{2} \sqrt{a c} a^{4} c^{3} d^{6} e^{4} - 90 \, \sqrt{2} a^{5} c^{3} d^{4} e^{6} - 148 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{4} c d^{5} e^{5} - 80 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{5} c^{2} d^{3} e^{7} + 25 \, \sqrt{2} \sqrt{a c} a^{5} c^{2} d^{2} e^{8} - \sqrt{2} a^{6} c^{2} e^{10} - 10 \, \left(a c^{3}\right)^{\frac{3}{4}} a^{5} d e^{9}\right)}} + \frac{3 \, {\left(7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{5} d^{17} - 10 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{3} d^{15} e^{2} + 50 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{4} d^{13} e^{4} - 78 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c^{2} d^{11} e^{6} + 220 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{3} d^{9} e^{8} - 702 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} c d^{7} e^{10} - 770 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{5} e^{12} + 390 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d^{3} e^{14} + 77 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c d e^{16}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, {\left(a^{3} c^{6} d^{20} + 5 \, a^{4} c^{5} d^{16} e^{4} + 10 \, a^{5} c^{4} d^{12} e^{8} + 10 \, a^{6} c^{3} d^{8} e^{12} + 5 \, a^{7} c^{2} d^{4} e^{16} + a^{8} c e^{20}\right)}} - \frac{3 \, {\left(7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{5} d^{17} - 10 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c^{3} d^{15} e^{2} + 50 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{4} d^{13} e^{4} - 78 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a c^{2} d^{11} e^{6} + 220 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c^{3} d^{9} e^{8} - 702 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{2} c d^{7} e^{10} - 770 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2} d^{5} e^{12} + 390 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a^{3} d^{3} e^{14} + 77 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{4} c d e^{16}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, {\left(a^{3} c^{6} d^{20} + 5 \, a^{4} c^{5} d^{16} e^{4} + 10 \, a^{5} c^{4} d^{12} e^{8} + 10 \, a^{6} c^{3} d^{8} e^{12} + 5 \, a^{7} c^{2} d^{4} e^{16} + a^{8} c e^{20}\right)}} - \frac{3 \, {\left(13 \, c^{2} d^{6} e^{11} - 3 \, a c d^{2} e^{15}\right)} \log\left({\left| c x^{4} + a \right|}\right)}{2 \, {\left(c^{5} d^{20} + 5 \, a c^{4} d^{16} e^{4} + 10 \, a^{2} c^{3} d^{12} e^{8} + 10 \, a^{3} c^{2} d^{8} e^{12} + 5 \, a^{4} c d^{4} e^{16} + a^{5} e^{20}\right)}} + \frac{6 \, {\left(13 \, c^{2} d^{6} e^{12} - 3 \, a c d^{2} e^{16}\right)} \log\left({\left| x e + d \right|}\right)}{c^{5} d^{20} e + 5 \, a c^{4} d^{16} e^{5} + 10 \, a^{2} c^{3} d^{12} e^{9} + 10 \, a^{3} c^{2} d^{8} e^{13} + 5 \, a^{4} c d^{4} e^{17} + a^{5} e^{21}} + \frac{30 \, c^{5} d^{11} x^{9} e^{4} + 42 \, c^{5} d^{12} x^{8} e^{3} + c^{5} d^{13} x^{7} e^{2} - 4 \, c^{5} d^{14} x^{6} e + 7 \, c^{5} d^{15} x^{5} + 204 \, a c^{4} d^{7} x^{9} e^{8} + 294 \, a c^{4} d^{8} x^{8} e^{7} + 19 \, a c^{4} d^{9} x^{7} e^{6} - 28 \, a c^{4} d^{10} x^{6} e^{5} + 97 \, a c^{4} d^{11} x^{5} e^{4} + 78 \, a c^{4} d^{12} x^{4} e^{3} + 5 \, a c^{4} d^{13} x^{3} e^{2} - 8 \, a c^{4} d^{14} x^{2} e + 11 \, a c^{4} d^{15} x - 594 \, a^{2} c^{3} d^{3} x^{9} e^{12} - 546 \, a^{2} c^{3} d^{4} x^{8} e^{11} + 35 \, a^{2} c^{3} d^{5} x^{7} e^{10} - 44 \, a^{2} c^{3} d^{6} x^{6} e^{9} + 461 \, a^{2} c^{3} d^{7} x^{5} e^{8} + 586 \, a^{2} c^{3} d^{8} x^{4} e^{7} + 31 \, a^{2} c^{3} d^{9} x^{3} e^{6} - 40 \, a^{2} c^{3} d^{10} x^{2} e^{5} + 79 \, a^{2} c^{3} d^{11} x e^{4} + 40 \, a^{2} c^{3} d^{12} e^{3} - 30 \, a^{3} c^{2} x^{8} e^{15} + 17 \, a^{3} c^{2} d x^{7} e^{14} - 20 \, a^{3} c^{2} d^{2} x^{6} e^{13} - 1165 \, a^{3} c^{2} d^{3} x^{5} e^{12} - 1078 \, a^{3} c^{2} d^{4} x^{4} e^{11} + 47 \, a^{3} c^{2} d^{5} x^{3} e^{10} - 56 \, a^{3} c^{2} d^{6} x^{2} e^{9} + 269 \, a^{3} c^{2} d^{7} x e^{8} + 304 \, a^{3} c^{2} d^{8} e^{7} - 50 \, a^{4} c x^{4} e^{15} + 21 \, a^{4} c d x^{3} e^{14} - 24 \, a^{4} c d^{2} x^{2} e^{13} - 567 \, a^{4} c d^{3} x e^{12} - 520 \, a^{4} c d^{4} e^{11} - 16 \, a^{5} e^{15}}{32 \, {\left(a^{2} c^{4} d^{16} + 4 \, a^{3} c^{3} d^{12} e^{4} + 6 \, a^{4} c^{2} d^{8} e^{8} + 4 \, a^{5} c d^{4} e^{12} + a^{6} e^{16}\right)} {\left(c x^{5} e + c d x^{4} + a x e + a d\right)}^{2}}"," ",0,"3/64*(23*sqrt(2)*a*c^4*d^6*e - 65*(a*c^3)^(1/4)*a*c^3*d^5*e^2 + 30*sqrt(2)*sqrt(a*c)*a*c^3*d^4*e^3 - 7*(a*c^3)^(3/4)*c^2*d^7 - 115*sqrt(2)*a^2*c^3*d^2*e^5 + 65*(a*c^3)^(3/4)*a*c*d^3*e^4 + 123*(a*c^3)^(1/4)*a^2*c^2*d*e^6 + 20*sqrt(2)*sqrt(a*c)*a^2*c^2*e^7)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*sqrt(a*c)*a^3*c^4*d^10 - 25*sqrt(2)*a^4*c^4*d^8*e^2 + 10*(a*c^3)^(3/4)*a^3*c^2*d^9*e + 80*(a*c^3)^(1/4)*a^4*c^3*d^7*e^3 + 90*sqrt(2)*sqrt(a*c)*a^4*c^3*d^6*e^4 - 90*sqrt(2)*a^5*c^3*d^4*e^6 + 148*(a*c^3)^(3/4)*a^4*c*d^5*e^5 + 80*(a*c^3)^(1/4)*a^5*c^2*d^3*e^7 + 25*sqrt(2)*sqrt(a*c)*a^5*c^2*d^2*e^8 - sqrt(2)*a^6*c^2*e^10 + 10*(a*c^3)^(3/4)*a^5*d*e^9) - 3/64*(23*sqrt(2)*a*c^4*d^6*e + 65*(a*c^3)^(1/4)*a*c^3*d^5*e^2 - 30*sqrt(2)*sqrt(a*c)*a*c^3*d^4*e^3 + 7*(a*c^3)^(3/4)*c^2*d^7 - 115*sqrt(2)*a^2*c^3*d^2*e^5 - 65*(a*c^3)^(3/4)*a*c*d^3*e^4 - 123*(a*c^3)^(1/4)*a^2*c^2*d*e^6 - 20*sqrt(2)*sqrt(a*c)*a^2*c^2*e^7)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*sqrt(a*c)*a^3*c^4*d^10 - 25*sqrt(2)*a^4*c^4*d^8*e^2 - 10*(a*c^3)^(3/4)*a^3*c^2*d^9*e - 80*(a*c^3)^(1/4)*a^4*c^3*d^7*e^3 + 90*sqrt(2)*sqrt(a*c)*a^4*c^3*d^6*e^4 - 90*sqrt(2)*a^5*c^3*d^4*e^6 - 148*(a*c^3)^(3/4)*a^4*c*d^5*e^5 - 80*(a*c^3)^(1/4)*a^5*c^2*d^3*e^7 + 25*sqrt(2)*sqrt(a*c)*a^5*c^2*d^2*e^8 - sqrt(2)*a^6*c^2*e^10 - 10*(a*c^3)^(3/4)*a^5*d*e^9) + 3/256*(7*sqrt(2)*(a*c^3)^(1/4)*c^5*d^17 - 10*sqrt(2)*(a*c^3)^(3/4)*c^3*d^15*e^2 + 50*sqrt(2)*(a*c^3)^(1/4)*a*c^4*d^13*e^4 - 78*sqrt(2)*(a*c^3)^(3/4)*a*c^2*d^11*e^6 + 220*sqrt(2)*(a*c^3)^(1/4)*a^2*c^3*d^9*e^8 - 702*sqrt(2)*(a*c^3)^(3/4)*a^2*c*d^7*e^10 - 770*sqrt(2)*(a*c^3)^(1/4)*a^3*c^2*d^5*e^12 + 390*sqrt(2)*(a*c^3)^(3/4)*a^3*d^3*e^14 + 77*sqrt(2)*(a*c^3)^(1/4)*a^4*c*d*e^16)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^6*d^20 + 5*a^4*c^5*d^16*e^4 + 10*a^5*c^4*d^12*e^8 + 10*a^6*c^3*d^8*e^12 + 5*a^7*c^2*d^4*e^16 + a^8*c*e^20) - 3/256*(7*sqrt(2)*(a*c^3)^(1/4)*c^5*d^17 - 10*sqrt(2)*(a*c^3)^(3/4)*c^3*d^15*e^2 + 50*sqrt(2)*(a*c^3)^(1/4)*a*c^4*d^13*e^4 - 78*sqrt(2)*(a*c^3)^(3/4)*a*c^2*d^11*e^6 + 220*sqrt(2)*(a*c^3)^(1/4)*a^2*c^3*d^9*e^8 - 702*sqrt(2)*(a*c^3)^(3/4)*a^2*c*d^7*e^10 - 770*sqrt(2)*(a*c^3)^(1/4)*a^3*c^2*d^5*e^12 + 390*sqrt(2)*(a*c^3)^(3/4)*a^3*d^3*e^14 + 77*sqrt(2)*(a*c^3)^(1/4)*a^4*c*d*e^16)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^6*d^20 + 5*a^4*c^5*d^16*e^4 + 10*a^5*c^4*d^12*e^8 + 10*a^6*c^3*d^8*e^12 + 5*a^7*c^2*d^4*e^16 + a^8*c*e^20) - 3/2*(13*c^2*d^6*e^11 - 3*a*c*d^2*e^15)*log(abs(c*x^4 + a))/(c^5*d^20 + 5*a*c^4*d^16*e^4 + 10*a^2*c^3*d^12*e^8 + 10*a^3*c^2*d^8*e^12 + 5*a^4*c*d^4*e^16 + a^5*e^20) + 6*(13*c^2*d^6*e^12 - 3*a*c*d^2*e^16)*log(abs(x*e + d))/(c^5*d^20*e + 5*a*c^4*d^16*e^5 + 10*a^2*c^3*d^12*e^9 + 10*a^3*c^2*d^8*e^13 + 5*a^4*c*d^4*e^17 + a^5*e^21) + 1/32*(30*c^5*d^11*x^9*e^4 + 42*c^5*d^12*x^8*e^3 + c^5*d^13*x^7*e^2 - 4*c^5*d^14*x^6*e + 7*c^5*d^15*x^5 + 204*a*c^4*d^7*x^9*e^8 + 294*a*c^4*d^8*x^8*e^7 + 19*a*c^4*d^9*x^7*e^6 - 28*a*c^4*d^10*x^6*e^5 + 97*a*c^4*d^11*x^5*e^4 + 78*a*c^4*d^12*x^4*e^3 + 5*a*c^4*d^13*x^3*e^2 - 8*a*c^4*d^14*x^2*e + 11*a*c^4*d^15*x - 594*a^2*c^3*d^3*x^9*e^12 - 546*a^2*c^3*d^4*x^8*e^11 + 35*a^2*c^3*d^5*x^7*e^10 - 44*a^2*c^3*d^6*x^6*e^9 + 461*a^2*c^3*d^7*x^5*e^8 + 586*a^2*c^3*d^8*x^4*e^7 + 31*a^2*c^3*d^9*x^3*e^6 - 40*a^2*c^3*d^10*x^2*e^5 + 79*a^2*c^3*d^11*x*e^4 + 40*a^2*c^3*d^12*e^3 - 30*a^3*c^2*x^8*e^15 + 17*a^3*c^2*d*x^7*e^14 - 20*a^3*c^2*d^2*x^6*e^13 - 1165*a^3*c^2*d^3*x^5*e^12 - 1078*a^3*c^2*d^4*x^4*e^11 + 47*a^3*c^2*d^5*x^3*e^10 - 56*a^3*c^2*d^6*x^2*e^9 + 269*a^3*c^2*d^7*x*e^8 + 304*a^3*c^2*d^8*e^7 - 50*a^4*c*x^4*e^15 + 21*a^4*c*d*x^3*e^14 - 24*a^4*c*d^2*x^2*e^13 - 567*a^4*c*d^3*x*e^12 - 520*a^4*c*d^4*e^11 - 16*a^5*e^15)/((a^2*c^4*d^16 + 4*a^3*c^3*d^12*e^4 + 6*a^4*c^2*d^8*e^8 + 4*a^5*c*d^4*e^12 + a^6*e^16)*(c*x^5*e + c*d*x^4 + a*x*e + a*d)^2)","A",0
415,1,28,0,0.294896," ","integrate((-1+x)/(x^2-x+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*log(x^2 - x + 1)","A",0
416,1,28,0,0.379652," ","integrate((x^2-1)/(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*log(x^2 - x + 1)","A",0
417,1,26,0,0.387705," ","integrate((-4+3*x)/(x^2-2*x+4),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x - 1\right)}\right) + \frac{3}{2} \, \log\left(x^{2} - 2 \, x + 4\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(x - 1)) + 3/2*log(x^2 - 2*x + 4)","A",0
418,1,26,0,0.334995," ","integrate((3*x^2+2*x-8)/(x^3+8),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x - 1\right)}\right) + \frac{3}{2} \, \log\left(x^{2} - 2 \, x + 4\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(x - 1)) + 3/2*log(x^2 - 2*x + 4)","A",0
419,1,44,0,0.415480," ","integrate((2+x)/(x^2+2*x-1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} + 2 \right|}}\right) + \frac{1}{2} \, \log\left({\left| x^{2} + 2 \, x - 1 \right|}\right)"," ",0,"1/4*sqrt(2)*log(abs(2*x - 2*sqrt(2) + 2)/abs(2*x + 2*sqrt(2) + 2)) + 1/2*log(abs(x^2 + 2*x - 1))","A",0
420,1,44,0,0.314653," ","integrate((x^2-4)/(x^3-5*x+2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} + 2 \right|}}\right) + \frac{1}{2} \, \log\left({\left| x^{2} + 2 \, x - 1 \right|}\right)"," ",0,"1/4*sqrt(2)*log(abs(2*x - 2*sqrt(2) + 2)/abs(2*x + 2*sqrt(2) + 2)) + 1/2*log(abs(x^2 + 2*x - 1))","A",0
421,1,15,0,0.309898," ","integrate(2/(4*x^2-1),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| x + \frac{1}{2} \right|}\right) + \frac{1}{2} \, \log\left({\left| x - \frac{1}{2} \right|}\right)"," ",0,"-1/2*log(abs(x + 1/2)) + 1/2*log(abs(x - 1/2))","B",0
422,1,19,0,0.415875," ","integrate(1/(-1+2*x)-1/(1+2*x),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| 2 \, x + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| 2 \, x - 1 \right|}\right)"," ",0,"-1/2*log(abs(2*x + 1)) + 1/2*log(abs(2*x - 1))","A",0
423,1,9,0,0.334981," ","integrate(x/(-x^2+1)^5,x, algorithm=""giac"")","\frac{1}{8 \, {\left(x^{2} - 1\right)}^{4}}"," ",0,"1/8/(x^2 - 1)^4","A",0
424,1,57,0,0.312332," ","integrate(-1/32/(-1+x)^5+3/64/(-1+x)^4-5/128/(-1+x)^3+5/256/(-1+x)^2-1/32/(1+x)^5-3/64/(1+x)^4-5/128/(1+x)^3-5/256/(1+x)^2,x, algorithm=""giac"")","\frac{5}{256 \, {\left(x + 1\right)}} - \frac{5}{256 \, {\left(x - 1\right)}} + \frac{5}{256 \, {\left(x + 1\right)}^{2}} + \frac{5}{256 \, {\left(x - 1\right)}^{2}} + \frac{1}{64 \, {\left(x + 1\right)}^{3}} - \frac{1}{64 \, {\left(x - 1\right)}^{3}} + \frac{1}{128 \, {\left(x + 1\right)}^{4}} + \frac{1}{128 \, {\left(x - 1\right)}^{4}}"," ",0,"5/256/(x + 1) - 5/256/(x - 1) + 5/256/(x + 1)^2 + 5/256/(x - 1)^2 + 1/64/(x + 1)^3 - 1/64/(x - 1)^3 + 1/128/(x + 1)^4 + 1/128/(x - 1)^4","B",0
425,1,68,0,0.293361," ","integrate((x^6+1)/(x^6-1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + x - \frac{1}{6} \, \log\left(x^{2} + x + 1\right) + \frac{1}{6} \, \log\left(x^{2} - x + 1\right) - \frac{1}{3} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + x - 1/6*log(x^2 + x + 1) + 1/6*log(x^2 - x + 1) - 1/3*log(abs(x + 1)) + 1/3*log(abs(x - 1))","A",0
426,1,68,0,0.307252," ","integrate((1/x^3+x^3)/(-1/x^3+x^3),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + x - \frac{1}{6} \, \log\left(x^{2} + x + 1\right) + \frac{1}{6} \, \log\left(x^{2} - x + 1\right) - \frac{1}{3} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + x - 1/6*log(x^2 + x + 1) + 1/6*log(x^2 - x + 1) - 1/3*log(abs(x + 1)) + 1/3*log(abs(x - 1))","A",0
427,1,21,0,0.307213," ","integrate((x^3-x)/(6+2*x),x, algorithm=""giac"")","\frac{1}{6} \, x^{3} - \frac{3}{4} \, x^{2} + 4 \, x - 12 \, \log\left({\left| x + 3 \right|}\right)"," ",0,"1/6*x^3 - 3/4*x^2 + 4*x - 12*log(abs(x + 3))","A",0
428,1,21,0,0.295129," ","integrate((x^3+x)/(-1+x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + 2 \, x + 2 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*x^3 + 1/2*x^2 + 2*x + 2*log(abs(x - 1))","A",0
429,1,15,0,0.387616," ","integrate(a*c+(b*c+d)*x,x, algorithm=""giac"")","a c x + \frac{1}{2} \, {\left(b c + d\right)} x^{2}"," ",0,"a*c*x + 1/2*(b*c + d)*x^2","A",0
430,1,20,0,0.367942," ","integrate(d*x+c*(b*x+a),x, algorithm=""giac"")","\frac{1}{2} \, d x^{2} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} c"," ",0,"1/2*d*x^2 + 1/2*(b*x^2 + 2*a*x)*c","A",0
431,1,23,0,0.392734," ","integrate((4+4*x)/x^2/(x^2+1),x, algorithm=""giac"")","-\frac{4}{x} - 4 \, \arctan\left(x\right) - 2 \, \log\left(x^{2} + 1\right) + 4 \, \log\left({\left| x \right|}\right)"," ",0,"-4/x - 4*arctan(x) - 2*log(x^2 + 1) + 4*log(abs(x))","A",0
432,1,18,0,0.326591," ","integrate((24+8*x)/x/(x^2-4),x, algorithm=""giac"")","\log\left({\left| x + 2 \right|}\right) + 5 \, \log\left({\left| x - 2 \right|}\right) - 6 \, \log\left({\left| x \right|}\right)"," ",0,"log(abs(x + 2)) + 5*log(abs(x - 2)) - 6*log(abs(x))","A",0
433,1,16,0,0.305076," ","integrate((x^2-1)/(x^3-2*x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left(x^{2}\right) + \frac{1}{4} \, \log\left({\left| x^{2} - 2 \right|}\right)"," ",0,"1/4*log(x^2) + 1/4*log(abs(x^2 - 2))","A",0
434,1,13,0,0.397993," ","integrate((x^2+1)/(x^3+3*x),x, algorithm=""giac"")","\frac{1}{3} \, \log\left(3 \, {\left| \frac{1}{3} \, x^{3} + x \right|}\right)"," ",0,"1/3*log(3*abs(1/3*x^3 + x))","A",0
435,1,11,0,0.332117," ","integrate((3*b*x^2+a)/(b*x^3+a*x),x, algorithm=""giac"")","\log\left({\left| b x^{3} + a x \right|}\right)"," ",0,"log(abs(b*x^3 + a*x))","A",0
436,1,18,0,0.355931," ","integrate((-2+4*x)/(x^3-x),x, algorithm=""giac"")","-3 \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x - 1 \right|}\right) + 2 \, \log\left({\left| x \right|}\right)"," ",0,"-3*log(abs(x + 1)) + log(abs(x - 1)) + 2*log(abs(x))","A",0
437,1,18,0,0.376181," ","integrate((4+x)/(x^3+4*x),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(\frac{1}{2} \, x\right) - \frac{1}{2} \, \log\left(x^{2} + 4\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*arctan(1/2*x) - 1/2*log(x^2 + 4) + log(abs(x))","A",0
438,1,13,0,0.277750," ","integrate((2*x^3-x)/(x^4-x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(x^{4} - x^{2} + 1\right)"," ",0,"1/2*log(x^4 - x^2 + 1)","A",0
439,1,20,0,0.369324," ","integrate((-3+x)/(x^3+3*x^2+2*x),x, algorithm=""giac"")","-\frac{5}{2} \, \log\left({\left| x + 2 \right|}\right) + 4 \, \log\left({\left| x + 1 \right|}\right) - \frac{3}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-5/2*log(abs(x + 2)) + 4*log(abs(x + 1)) - 3/2*log(abs(x))","A",0
440,1,9,0,0.260918," ","integrate((2+4*x)/(x^4+2*x^3+x^2),x, algorithm=""giac"")","-\frac{2}{x^{2} + x}"," ",0,"-2/(x^2 + x)","A",0
441,1,20,0,0.362000," ","integrate((1+x)/(x^3+x^2-6*x),x, algorithm=""giac"")","-\frac{2}{15} \, \log\left({\left| x + 3 \right|}\right) + \frac{3}{10} \, \log\left({\left| x - 2 \right|}\right) - \frac{1}{6} \, \log\left({\left| x \right|}\right)"," ",0,"-2/15*log(abs(x + 3)) + 3/10*log(abs(x - 2)) - 1/6*log(abs(x))","A",0
442,1,14,0,0.251946," ","integrate((x^3+4*x^2)/(x^3+x),x, algorithm=""giac"")","x - \arctan\left(x\right) + 2 \, \log\left(x^{2} + 1\right)"," ",0,"x - arctan(x) + 2*log(x^2 + 1)","A",0
443,1,11,0,0.371304," ","integrate((2*x^3+x)/(x^4+x^2)^3,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{4} + x^{2}\right)}^{2}}"," ",0,"-1/4/(x^4 + x^2)^2","A",0
444,1,27,0,0.283139," ","integrate((b*x^3+a*x^2)/(d*x^3+c*x^2),x, algorithm=""giac"")","\frac{b x}{d} - \frac{{\left(b c - a d\right)} \log\left({\left| d x + c \right|}\right)}{d^{2}}"," ",0,"b*x/d - (b*c - a*d)*log(abs(d*x + c))/d^2","A",0
445,1,5,0,0.280188," ","integrate((x^2+x)/(x^3-x^2-2*x),x, algorithm=""giac"")","\log\left({\left| x - 2 \right|}\right)"," ",0,"log(abs(x - 2))","A",0
446,1,27,0,0.381316," ","integrate((-5*x^2+1)/x^3/(x^2+1),x, algorithm=""giac"")","\frac{6 \, x^{2} - 1}{2 \, x^{2}} + 3 \, \log\left(x^{2} + 1\right) - 3 \, \log\left(x^{2}\right)"," ",0,"1/2*(6*x^2 - 1)/x^2 + 3*log(x^2 + 1) - 3*log(x^2)","A",0
447,1,28,0,0.388559," ","integrate(2*x/(-1+x)/(x^2+5),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) - \frac{1}{6} \, \log\left(x^{2} + 5\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*sqrt(5)*arctan(1/5*sqrt(5)*x) - 1/6*log(x^2 + 5) + 1/3*log(abs(x - 1))","A",0
448,1,16,0,0.366582," ","integrate((x^2+2)/(2+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 2 \, x + 6 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/2*x^2 - 2*x + 6*log(abs(x + 2))","A",0
449,1,22,0,0.273782," ","integrate(1/(-3+x)/(x^2+4),x, algorithm=""giac"")","-\frac{3}{26} \, \arctan\left(\frac{1}{2} \, x\right) - \frac{1}{26} \, \log\left(x^{2} + 4\right) + \frac{1}{13} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"-3/26*arctan(1/2*x) - 1/26*log(x^2 + 4) + 1/13*log(abs(x - 3))","A",0
450,1,17,0,0.407724," ","integrate((3*x^6-2)/x/(2*x^6+5),x, algorithm=""giac"")","\frac{19}{60} \, \log\left(2 \, x^{6} + 5\right) - \frac{1}{15} \, \log\left(x^{6}\right)"," ",0,"19/60*log(2*x^6 + 5) - 1/15*log(x^6)","A",0
451,1,11,0,0.286973," ","integrate((3+2*x)/(-2+x)/(5+x),x, algorithm=""giac"")","\log\left({\left| x + 5 \right|}\right) + \log\left({\left| x - 2 \right|}\right)"," ",0,"log(abs(x + 5)) + log(abs(x - 2))","A",0
452,1,12,0,0.371131," ","integrate(x^4/(x^4+5*x^2+4),x, algorithm=""giac"")","x - \frac{8}{3} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"x - 8/3*arctan(1/2*x) + 1/3*arctan(x)","A",0
453,1,52,0,0.362775," ","integrate(1/(1+x)/(2+x)^2/(3+x)^3,x, algorithm=""giac"")","\frac{1}{x + 2} - \frac{\frac{7}{x + 2} + 6}{4 \, {\left(\frac{1}{x + 2} + 1\right)}^{2}} + \frac{1}{8} \, \log\left({\left| -\frac{1}{x + 2} + 1 \right|}\right) - \frac{17}{8} \, \log\left({\left| -\frac{1}{x + 2} - 1 \right|}\right)"," ",0,"1/(x + 2) - 1/4*(7/(x + 2) + 6)/(1/(x + 2) + 1)^2 + 1/8*log(abs(-1/(x + 2) + 1)) - 17/8*log(abs(-1/(x + 2) - 1))","A",0
454,1,9,0,0.274530," ","integrate(x/(x^2-1),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/2*log(abs(x^2 - 1))","A",0
455,1,25,0,0.271444," ","integrate(1/(x^2-1)^2,x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{2} - 1\right)}} + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*x/(x^2 - 1) + 1/4*log(abs(x + 1)) - 1/4*log(abs(x - 1))","A",0
456,1,15,0,0.290463," ","integrate(x^2/(x^2+1)^2,x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-1/2*x/(x^2 + 1) + 1/2*arctan(x)","A",0
457,1,9,0,0.381768," ","integrate(1/(2+3*x),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/3*log(abs(3*x + 2))","A",0
458,1,10,0,0.260539," ","integrate(1/(a^2+x^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{x}{a}\right)}{a}"," ",0,"arctan(x/a)/a","A",0
459,1,15,0,0.379245," ","integrate(1/(b*x^2+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"arctan(b*x/sqrt(a*b))/sqrt(a*b)","A",0
460,1,16,0,0.380142," ","integrate(1/(x^2-x+2),x, algorithm=""giac"")","\frac{2}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(2 \, x - 1\right)}\right)"," ",0,"2/7*sqrt(7)*arctan(1/7*sqrt(7)*(2*x - 1))","A",0
461,1,16,0,0.310385," ","integrate(x^2*(-x^2+4)^2,x, algorithm=""giac"")","\frac{1}{7} \, x^{7} - \frac{8}{5} \, x^{5} + \frac{16}{3} \, x^{3}"," ",0,"1/7*x^7 - 8/5*x^5 + 16/3*x^3","A",0
462,1,16,0,0.287173," ","integrate(x*(-x^3+1)^2,x, algorithm=""giac"")","\frac{1}{8} \, x^{8} - \frac{2}{5} \, x^{5} + \frac{1}{2} \, x^{2}"," ",0,"1/8*x^8 - 2/5*x^5 + 1/2*x^2","A",0
463,1,14,0,0.306256," ","integrate((x^3+5*x^2-4)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 5 \, x + \frac{4}{x}"," ",0,"1/2*x^2 + 5*x + 4/x","A",0
464,1,30,0,0.265672," ","integrate((-1+x)/(3*x^2-4*x+3),x, algorithm=""giac"")","-\frac{1}{15} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} {\left(3 \, x - 2\right)}\right) + \frac{1}{6} \, \log\left(3 \, x^{2} - 4 \, x + 3\right)"," ",0,"-1/15*sqrt(5)*arctan(1/5*sqrt(5)*(3*x - 2)) + 1/6*log(3*x^2 - 4*x + 3)","A",0
465,1,12,0,0.363924," ","integrate((x^3+2)^2,x, algorithm=""giac"")","\frac{1}{7} \, x^{7} + x^{4} + 4 \, x"," ",0,"1/7*x^7 + x^4 + 4*x","A",0
466,1,9,0,0.286024," ","integrate((x^2-4)/(2+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 2 \, x"," ",0,"1/2*x^2 - 2*x","A",0
467,1,20,0,0.365339," ","integrate(1/(2+x)/(x^2+1),x, algorithm=""giac"")","\frac{2}{5} \, \arctan\left(x\right) - \frac{1}{10} \, \log\left(x^{2} + 1\right) + \frac{1}{5} \, \log\left({\left| x + 2 \right|}\right)"," ",0,"2/5*arctan(x) - 1/10*log(x^2 + 1) + 1/5*log(abs(x + 2))","A",0
468,1,20,0,0.292278," ","integrate(1/(1+x)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(x\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right) + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*arctan(x) - 1/4*log(x^2 + 1) + 1/2*log(abs(x + 1))","A",0
469,1,20,0,0.249228," ","integrate(x/(1+x)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left(x^{2} + 1\right) - \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*arctan(x) + 1/4*log(x^2 + 1) - 1/2*log(abs(x + 1))","A",0
470,1,8,0,0.297929," ","integrate((x^2+2*x)/(1+x)^2,x, algorithm=""giac"")","x + \frac{1}{x + 1} + 1"," ",0,"x + 1/(x + 1) + 1","A",0
471,1,16,0,0.292119," ","integrate((x^2-10)/(2*x^4+9*x^2+4),x, algorithm=""giac"")","-\frac{3}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right) + \arctan\left(\frac{1}{2} \, x\right)"," ",0,"-3/2*sqrt(2)*arctan(sqrt(2)*x) + arctan(1/2*x)","A",0
472,1,30,0,0.383773," ","integrate((31+5*x)/(3*x^2-4*x+11),x, algorithm=""giac"")","\frac{103}{87} \, \sqrt{29} \arctan\left(\frac{1}{29} \, \sqrt{29} {\left(3 \, x - 2\right)}\right) + \frac{5}{6} \, \log\left(3 \, x^{2} - 4 \, x + 11\right)"," ",0,"103/87*sqrt(29)*arctan(1/29*sqrt(29)*(3*x - 2)) + 5/6*log(3*x^2 - 4*x + 11)","A",0
473,1,16,0,0.269315," ","integrate((x^3+x^2-2)/x^4,x, algorithm=""giac"")","-\frac{3 \, x^{2} - 2}{3 \, x^{3}} + \log\left({\left| x \right|}\right)"," ",0,"-1/3*(3*x^2 - 2)/x^3 + log(abs(x))","A",0
474,1,14,0,0.280365," ","integrate((x^3+x+1)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{x} + \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 - 1/x + log(abs(x))","A",0
475,1,13,0,0.286575," ","integrate((x^2-2)/x/(x^2+2),x, algorithm=""giac"")","\log\left(x^{2} + 2\right) - \frac{1}{2} \, \log\left(x^{2}\right)"," ",0,"log(x^2 + 2) - 1/2*log(x^2)","A",0
476,1,17,0,0.355822," ","integrate((-3+x)*(4*x^2-7),x, algorithm=""giac"")","x^{4} - 4 \, x^{3} - \frac{7}{2} \, x^{2} + 21 \, x"," ",0,"x^4 - 4*x^3 - 7/2*x^2 + 21*x","A",0
477,1,9,0,0.216007," ","integrate((-2+7*x)^3,x, algorithm=""giac"")","\frac{1}{28} \, {\left(7 \, x - 2\right)}^{4}"," ",0,"1/28*(7*x - 2)^4","A",0
478,1,14,0,0.360999," ","integrate((4*x^2-7)/(3+2*x),x, algorithm=""giac"")","x^{2} - 3 \, x + \log\left({\left| 2 \, x + 3 \right|}\right)"," ",0,"x^2 - 3*x + log(abs(2*x + 3))","A",0
479,1,16,0,0.360178," ","integrate((1+x)/(-1+x)/x^2,x, algorithm=""giac"")","\frac{1}{x} + 2 \, \log\left({\left| x - 1 \right|}\right) - 2 \, \log\left({\left| x \right|}\right)"," ",0,"1/x + 2*log(abs(x - 1)) - 2*log(abs(x))","A",0
480,1,27,0,0.379051," ","integrate(1/(x^4+4*x^3+4*x^2),x, algorithm=""giac"")","-\frac{x + 1}{2 \, {\left(x^{2} + 2 \, x\right)}} + \frac{1}{4} \, \log\left({\left| x + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2*(x + 1)/(x^2 + 2*x) + 1/4*log(abs(x + 2)) - 1/4*log(abs(x))","A",0
481,1,16,0,0.357314," ","integrate((x^2+1)/(1+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - x + 2 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*x^2 - x + 2*log(abs(x + 1))","A",0
482,1,17,0,0.371001," ","integrate((x^3-3*x^2+3*x-1)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 3 \, x + \frac{1}{x} + 3 \, \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 - 3*x + 1/x + 3*log(abs(x))","A",0
483,1,14,0,0.351162," ","integrate((x+3/2-1/2*37^(1/2))*(x+3/2+1/2*37^(1/2)),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} - 7 \, x"," ",0,"1/3*x^3 + 3/2*x^2 - 7*x","A",0
484,1,25,0,0.369406," ","integrate((2*x^3+3*x^2+4)/(1+x)^4,x, algorithm=""giac"")","\frac{9 \, x^{2} + 18 \, x + 4}{3 \, {\left(x + 1\right)}^{3}} + 2 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/3*(9*x^2 + 18*x + 4)/(x + 1)^3 + 2*log(abs(x + 1))","A",0
485,1,32,0,0.261951," ","integrate(x/(1+x)^2/(x^2+1),x, algorithm=""giac"")","-\frac{1}{8} \, \pi - \frac{1}{2} \, \pi \left \lfloor -\frac{\pi - 4 \, \arctan\left(x\right)}{4 \, \pi} + \frac{1}{2} \right \rfloor + \frac{1}{2 \, {\left(x + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-1/8*pi - 1/2*pi*floor(-1/4*(pi - 4*arctan(x))/pi + 1/2) + 1/2/(x + 1) + 1/2*arctan(x)","B",0
486,1,26,0,0.282962," ","integrate((x^4-x^3+3*x^2-2*x+7)/(2+x),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} - x^{3} + \frac{9}{2} \, x^{2} - 20 \, x + 47 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/4*x^4 - x^3 + 9/2*x^2 - 20*x + 47*log(abs(x + 2))","A",0
487,1,12,0,0.348186," ","integrate((x^3-1)/(-1+x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x"," ",0,"1/3*x^3 + 1/2*x^2 + x","A",0
488,1,12,0,0.237272," ","integrate((2+2*x)/(-1+x)^3/(x^2+1),x, algorithm=""giac"")","\frac{x - 2}{{\left(x - 1\right)}^{2}} + \arctan\left(x\right)"," ",0,"(x - 2)/(x - 1)^2 + arctan(x)","A",0
489,1,48,0,0.281173," ","integrate(1/(b*x+c*(e*x+d)^2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x e^{2} + 2 \, c d e + b}{\sqrt{-4 \, b c d e - b^{2}}}\right)}{\sqrt{-4 \, b c d e - b^{2}}}"," ",0,"2*arctan((2*c*x*e^2 + 2*c*d*e + b)/sqrt(-4*b*c*d*e - b^2))/sqrt(-4*b*c*d*e - b^2)","A",0
490,1,60,0,0.357826," ","integrate(1/(a+b*x+c*(e*x+d)^2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x e^{2} + 2 \, c d e + b}{\sqrt{-4 \, b c d e + 4 \, a c e^{2} - b^{2}}}\right)}{\sqrt{-4 \, b c d e + 4 \, a c e^{2} - b^{2}}}"," ",0,"2*arctan((2*c*x*e^2 + 2*c*d*e + b)/sqrt(-4*b*c*d*e + 4*a*c*e^2 - b^2))/sqrt(-4*b*c*d*e + 4*a*c*e^2 - b^2)","A",0
491,1,147,0,1.488341," ","integrate(x^2/(1+(x^2-1)^2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x + 2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x - 2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(x^{2} + 2^{\frac{1}{4}} x \sqrt{\sqrt{2} + 2} + \sqrt{2}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(x^{2} - 2^{\frac{1}{4}} x \sqrt{\sqrt{2} + 2} + \sqrt{2}\right)"," ",0,"1/4*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2*x + 2^(1/4)*sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/4*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2*x - 2^(1/4)*sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(2*sqrt(2) - 2)*log(x^2 + 2^(1/4)*x*sqrt(sqrt(2) + 2) + sqrt(2)) + 1/8*sqrt(2*sqrt(2) - 2)*log(x^2 - 2^(1/4)*x*sqrt(sqrt(2) + 2) + sqrt(2))","A",0
492,1,30,0,0.397021," ","integrate((30*x^9-8*x^7-15*x^6-140*x^5+34*x^4-12*x^3-5*x^2+36*x-15)/(x^4+x+3)^4,x, algorithm=""giac"")","-\frac{5 \, x^{6} - x^{4} - 5 \, x^{2} + 3 \, x - 2}{{\left(x^{4} + x + 3\right)}^{3}}"," ",0,"-(5*x^6 - x^4 - 5*x^2 + 3*x - 2)/(x^4 + x + 3)^3","A",0
493,1,197,0,0.396830," ","integrate(3*(19*x^3+120*x^2+228*x-47)/(x^4+x+3)^4+(-8*x^3-75*x^2-320*x+42)/(x^4+x+3)^3+30*x/(x^4+x+3)^2,x, algorithm=""giac"")","\frac{1}{195075} \, x {\left(\frac{377432 \, x^{2} - 2808656 \, x + 703551}{x^{4} + x + 3} - \frac{255032 \, x^{2} - 1829456 \, x + 680601}{x^{4} + x + 3} - \frac{7650 \, {\left(16 \, x^{2} - 128 \, x + 3\right)}}{x^{4} + x + 3}\right)} - \frac{2 \, {\left(16 \, x^{3} - 64 \, x^{2} + x + 12\right)}}{51 \, {\left(x^{4} + x + 3\right)}} + \frac{754864 \, x^{7} - 2808656 \, x^{6} + 469034 \, x^{5} + 1321012 \, x^{4} - 417584 \, x^{3} - 13339729 \, x^{2} + 2696430 \, x + 2183454}{390150 \, {\left(x^{4} + x + 3\right)}^{2}} - \frac{510064 \, x^{11} - 1829456 \, x^{10} + 453734 \, x^{9} + 1402676 \, x^{8} - 472048 \, x^{7} - 13501313 \, x^{6} + 4720744 \, x^{5} + 3747556 \, x^{4} - 10935781 \, x^{3} - 30736107 \, x^{2} + 10203894 \, x + 4117662}{390150 \, {\left(x^{4} + x + 3\right)}^{3}}"," ",0,"1/195075*x*((377432*x^2 - 2808656*x + 703551)/(x^4 + x + 3) - (255032*x^2 - 1829456*x + 680601)/(x^4 + x + 3) - 7650*(16*x^2 - 128*x + 3)/(x^4 + x + 3)) - 2/51*(16*x^3 - 64*x^2 + x + 12)/(x^4 + x + 3) + 1/390150*(754864*x^7 - 2808656*x^6 + 469034*x^5 + 1321012*x^4 - 417584*x^3 - 13339729*x^2 + 2696430*x + 2183454)/(x^4 + x + 3)^2 - 1/390150*(510064*x^11 - 1829456*x^10 + 453734*x^9 + 1402676*x^8 - 472048*x^7 - 13501313*x^6 + 4720744*x^5 + 3747556*x^4 - 10935781*x^3 - 30736107*x^2 + 10203894*x + 4117662)/(x^4 + x + 3)^3","B",0
494,1,111,0,0.446796," ","integrate((-30*x^5+4*x^3+10*x-3)/(x^4+x+3)^3-3*(4*x^3+1)*(-5*x^6+x^4+5*x^2-3*x+2)/(x^4+x+3)^4,x, algorithm=""giac"")","\frac{69136 \, x^{7} - 147344 \, x^{6} - 30784 \, x^{5} + 120988 \, x^{4} + 137584 \, x^{3} + 1167854 \, x^{2} - 100680 \, x + 18621}{390150 \, {\left(x^{4} + x + 3\right)}^{2}} - \frac{69136 \, x^{11} - 147344 \, x^{10} - 30784 \, x^{9} + 190124 \, x^{8} + 197648 \, x^{7} + 2645788 \, x^{6} - 72044 \, x^{5} + 129019 \, x^{4} + 1580606 \, x^{3} + 1452132 \, x^{2} + 887031 \, x - 724437}{390150 \, {\left(x^{4} + x + 3\right)}^{3}}"," ",0,"1/390150*(69136*x^7 - 147344*x^6 - 30784*x^5 + 120988*x^4 + 137584*x^3 + 1167854*x^2 - 100680*x + 18621)/(x^4 + x + 3)^2 - 1/390150*(69136*x^11 - 147344*x^10 - 30784*x^9 + 190124*x^8 + 197648*x^7 + 2645788*x^6 - 72044*x^5 + 129019*x^4 + 1580606*x^3 + 1452132*x^2 + 887031*x - 724437)/(x^4 + x + 3)^3","B",0
