1,1,74,0,0.0815531,"\int x^2 \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[x^2*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]","\frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9","\frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9",1,"(a*A*x^3)/3 + (a*B*x^4)/4 + ((A*b + a*C)*x^5)/5 + (b*B*x^6)/6 + ((A*c + b*C)*x^7)/7 + (B*c*x^8)/8 + (c*C*x^9)/9","A",2,1,26,0.03846,1,"{1628}"
2,1,74,0,0.0565914,"\int x \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[x*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]","\frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{6} x^6 (A c+b C)+\frac{1}{5} b B x^5+\frac{1}{7} B c x^7+\frac{1}{8} c C x^8","\frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{6} x^6 (A c+b C)+\frac{1}{5} b B x^5+\frac{1}{7} B c x^7+\frac{1}{8} c C x^8",1,"(a*A*x^2)/2 + (a*B*x^3)/3 + ((A*b + a*C)*x^4)/4 + (b*B*x^5)/5 + ((A*c + b*C)*x^6)/6 + (B*c*x^7)/7 + (c*C*x^8)/8","A",2,1,24,0.04167,1,"{1628}"
3,1,69,0,0.0355215,"\int \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]","\frac{1}{3} x^3 (a C+A b)+a A x+\frac{1}{2} a B x^2+\frac{1}{5} x^5 (A c+b C)+\frac{1}{4} b B x^4+\frac{1}{6} B c x^6+\frac{1}{7} c C x^7","\frac{1}{3} x^3 (a C+A b)+a A x+\frac{1}{2} a B x^2+\frac{1}{5} x^5 (A c+b C)+\frac{1}{4} b B x^4+\frac{1}{6} B c x^6+\frac{1}{7} c C x^7",1,"a*A*x + (a*B*x^2)/2 + ((A*b + a*C)*x^3)/3 + (b*B*x^4)/4 + ((A*c + b*C)*x^5)/5 + (B*c*x^6)/6 + (c*C*x^7)/7","A",2,1,23,0.04348,1,"{1657}"
4,1,65,0,0.0400262,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x,x]","\frac{1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac{1}{4} x^4 (A c+b C)+\frac{1}{3} b B x^3+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6","\frac{1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac{1}{4} x^4 (A c+b C)+\frac{1}{3} b B x^3+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6",1,"a*B*x + ((A*b + a*C)*x^2)/2 + (b*B*x^3)/3 + ((A*c + b*C)*x^4)/4 + (B*c*x^5)/5 + (c*C*x^6)/6 + a*A*Log[x]","A",2,1,26,0.03846,1,"{1628}"
5,1,63,0,0.0505412,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^2} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^2,x]","x (a C+A b)-\frac{a A}{x}+a B \log (x)+\frac{1}{3} x^3 (A c+b C)+\frac{1}{2} b B x^2+\frac{1}{4} B c x^4+\frac{1}{5} c C x^5","x (a C+A b)-\frac{a A}{x}+a B \log (x)+\frac{1}{3} x^3 (A c+b C)+\frac{1}{2} b B x^2+\frac{1}{4} B c x^4+\frac{1}{5} c C x^5",1,"-((a*A)/x) + (A*b + a*C)*x + (b*B*x^2)/2 + ((A*c + b*C)*x^3)/3 + (B*c*x^4)/4 + (c*C*x^5)/5 + a*B*Log[x]","A",2,1,26,0.03846,1,"{1628}"
6,1,63,0,0.048346,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^3} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^3,x]","\log (x) (a C+A b)-\frac{a A}{2 x^2}-\frac{a B}{x}+\frac{1}{2} x^2 (A c+b C)+b B x+\frac{1}{3} B c x^3+\frac{1}{4} c C x^4","\log (x) (a C+A b)-\frac{a A}{2 x^2}-\frac{a B}{x}+\frac{1}{2} x^2 (A c+b C)+b B x+\frac{1}{3} B c x^3+\frac{1}{4} c C x^4",1,"-(a*A)/(2*x^2) - (a*B)/x + b*B*x + ((A*c + b*C)*x^2)/2 + (B*c*x^3)/3 + (c*C*x^4)/4 + (A*b + a*C)*Log[x]","A",2,1,26,0.03846,1,"{1628}"
7,1,63,0,0.0509742,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^4} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^4,x]","-\frac{a C+A b}{x}-\frac{a A}{3 x^3}-\frac{a B}{2 x^2}+x (A c+b C)+b B \log (x)+\frac{1}{2} B c x^2+\frac{1}{3} c C x^3","-\frac{a C+A b}{x}-\frac{a A}{3 x^3}-\frac{a B}{2 x^2}+x (A c+b C)+b B \log (x)+\frac{1}{2} B c x^2+\frac{1}{3} c C x^3",1,"-(a*A)/(3*x^3) - (a*B)/(2*x^2) - (A*b + a*C)/x + (A*c + b*C)*x + (B*c*x^2)/2 + (c*C*x^3)/3 + b*B*Log[x]","A",2,1,26,0.03846,1,"{1628}"
8,1,63,0,0.0510479,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^5} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^5,x]","-\frac{a C+A b}{2 x^2}-\frac{a A}{4 x^4}-\frac{a B}{3 x^3}+\log (x) (A c+b C)-\frac{b B}{x}+B c x+\frac{1}{2} c C x^2","-\frac{a C+A b}{2 x^2}-\frac{a A}{4 x^4}-\frac{a B}{3 x^3}+\log (x) (A c+b C)-\frac{b B}{x}+B c x+\frac{1}{2} c C x^2",1,"-(a*A)/(4*x^4) - (a*B)/(3*x^3) - (A*b + a*C)/(2*x^2) - (b*B)/x + B*c*x + (c*C*x^2)/2 + (A*c + b*C)*Log[x]","A",2,1,26,0.03846,1,"{1628}"
9,1,63,0,0.0516926,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^6} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^6,x]","-\frac{a C+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{a B}{4 x^4}-\frac{A c+b C}{x}-\frac{b B}{2 x^2}+B c \log (x)+c C x","-\frac{a C+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{a B}{4 x^4}-\frac{A c+b C}{x}-\frac{b B}{2 x^2}+B c \log (x)+c C x",1,"-(a*A)/(5*x^5) - (a*B)/(4*x^4) - (A*b + a*C)/(3*x^3) - (b*B)/(2*x^2) - (A*c + b*C)/x + c*C*x + B*c*Log[x]","A",2,1,26,0.03846,1,"{1628}"
10,1,68,0,0.0482934,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)}{x^7} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^7,x]","-\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x)","-\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x)",1,"-(a*A)/(6*x^6) - (a*B)/(5*x^5) - (A*b + a*C)/(4*x^4) - (b*B)/(3*x^3) - (A*c + b*C)/(2*x^2) - (B*c)/x + c*C*Log[x]","A",2,1,26,0.03846,1,"{1628}"
11,1,159,0,0.2144703,"\int x^2 \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[x^2*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{1}{9} x^9 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{7} x^7 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{5} a x^5 (a C+2 A b)+\frac{1}{8} B x^8 \left(2 a c+b^2\right)+\frac{1}{3} a b B x^6+\frac{1}{11} c x^{11} (A c+2 b C)+\frac{1}{5} b B c x^{10}+\frac{1}{12} B c^2 x^{12}+\frac{1}{13} c^2 C x^{13}","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{1}{9} x^9 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{7} x^7 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{5} a x^5 (a C+2 A b)+\frac{1}{8} B x^8 \left(2 a c+b^2\right)+\frac{1}{3} a b B x^6+\frac{1}{11} c x^{11} (A c+2 b C)+\frac{1}{5} b B c x^{10}+\frac{1}{12} B c^2 x^{12}+\frac{1}{13} c^2 C x^{13}",1,"(a^2*A*x^3)/3 + (a^2*B*x^4)/4 + (a*(2*A*b + a*C)*x^5)/5 + (a*b*B*x^6)/3 + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^7)/7 + (B*(b^2 + 2*a*c)*x^8)/8 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^9)/9 + (b*B*c*x^10)/5 + (c*(A*c + 2*b*C)*x^11)/11 + (B*c^2*x^12)/12 + (c^2*C*x^13)/13","A",2,1,28,0.03571,1,"{1628}"
12,1,159,0,0.143461,"\int x \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[x*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]","\frac{1}{2} a^2 A x^2+\frac{1}{3} a^2 B x^3+\frac{1}{8} x^8 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{6} x^6 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{4} a x^4 (a C+2 A b)+\frac{1}{7} B x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b B x^5+\frac{1}{10} c x^{10} (A c+2 b C)+\frac{2}{9} b B c x^9+\frac{1}{11} B c^2 x^{11}+\frac{1}{12} c^2 C x^{12}","\frac{1}{2} a^2 A x^2+\frac{1}{3} a^2 B x^3+\frac{1}{8} x^8 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{6} x^6 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{4} a x^4 (a C+2 A b)+\frac{1}{7} B x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b B x^5+\frac{1}{10} c x^{10} (A c+2 b C)+\frac{2}{9} b B c x^9+\frac{1}{11} B c^2 x^{11}+\frac{1}{12} c^2 C x^{12}",1,"(a^2*A*x^2)/2 + (a^2*B*x^3)/3 + (a*(2*A*b + a*C)*x^4)/4 + (2*a*b*B*x^5)/5 + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^6)/6 + (B*(b^2 + 2*a*c)*x^7)/7 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^8)/8 + (2*b*B*c*x^9)/9 + (c*(A*c + 2*b*C)*x^10)/10 + (B*c^2*x^11)/11 + (c^2*C*x^12)/12","A",2,1,26,0.03846,1,"{1628}"
13,1,154,0,0.1109787,"\int \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]","a^2 A x+\frac{1}{2} a^2 B x^2+\frac{1}{7} x^7 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{5} x^5 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{3} a x^3 (a C+2 A b)+\frac{1}{6} B x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b B x^4+\frac{1}{9} c x^9 (A c+2 b C)+\frac{1}{4} b B c x^8+\frac{1}{10} B c^2 x^{10}+\frac{1}{11} c^2 C x^{11}","a^2 A x+\frac{1}{2} a^2 B x^2+\frac{1}{7} x^7 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{5} x^5 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{3} a x^3 (a C+2 A b)+\frac{1}{6} B x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b B x^4+\frac{1}{9} c x^9 (A c+2 b C)+\frac{1}{4} b B c x^8+\frac{1}{10} B c^2 x^{10}+\frac{1}{11} c^2 C x^{11}",1,"a^2*A*x + (a^2*B*x^2)/2 + (a*(2*A*b + a*C)*x^3)/3 + (a*b*B*x^4)/2 + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^5)/5 + (B*(b^2 + 2*a*c)*x^6)/6 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^7)/7 + (b*B*c*x^8)/4 + (c*(A*c + 2*b*C)*x^9)/9 + (B*c^2*x^10)/10 + (c^2*C*x^11)/11","A",2,1,25,0.04000,1,"{1657}"
14,1,150,0,0.1066121,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x,x]","a^2 A \log (x)+a^2 B x+\frac{1}{6} x^6 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{4} x^4 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{2} a x^2 (a C+2 A b)+\frac{1}{5} B x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b B x^3+\frac{1}{8} c x^8 (A c+2 b C)+\frac{2}{7} b B c x^7+\frac{1}{9} B c^2 x^9+\frac{1}{10} c^2 C x^{10}","a^2 A \log (x)+a^2 B x+\frac{1}{6} x^6 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{4} x^4 \left(A \left(2 a c+b^2\right)+2 a b C\right)+\frac{1}{2} a x^2 (a C+2 A b)+\frac{1}{5} B x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b B x^3+\frac{1}{8} c x^8 (A c+2 b C)+\frac{2}{7} b B c x^7+\frac{1}{9} B c^2 x^9+\frac{1}{10} c^2 C x^{10}",1,"a^2*B*x + (a*(2*A*b + a*C)*x^2)/2 + (2*a*b*B*x^3)/3 + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^4)/4 + (B*(b^2 + 2*a*c)*x^5)/5 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^6)/6 + (2*b*B*c*x^7)/7 + (c*(A*c + 2*b*C)*x^8)/8 + (B*c^2*x^9)/9 + (c^2*C*x^10)/10 + a^2*A*Log[x]","A",2,1,28,0.03571,1,"{1628}"
15,1,145,0,0.1211045,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^2} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^2,x]","-\frac{a^2 A}{x}+a^2 B \log (x)+\frac{1}{5} x^5 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b C\right)+a x (a C+2 A b)+\frac{1}{4} B x^4 \left(2 a c+b^2\right)+a b B x^2+\frac{1}{7} c x^7 (A c+2 b C)+\frac{1}{3} b B c x^6+\frac{1}{8} B c^2 x^8+\frac{1}{9} c^2 C x^9","-\frac{a^2 A}{x}+a^2 B \log (x)+\frac{1}{5} x^5 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b C\right)+a x (a C+2 A b)+\frac{1}{4} B x^4 \left(2 a c+b^2\right)+a b B x^2+\frac{1}{7} c x^7 (A c+2 b C)+\frac{1}{3} b B c x^6+\frac{1}{8} B c^2 x^8+\frac{1}{9} c^2 C x^9",1,"-((a^2*A)/x) + a*(2*A*b + a*C)*x + a*b*B*x^2 + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^3)/3 + (B*(b^2 + 2*a*c)*x^4)/4 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^5)/5 + (b*B*c*x^6)/3 + (c*(A*c + 2*b*C)*x^7)/7 + (B*c^2*x^8)/8 + (c^2*C*x^9)/9 + a^2*B*Log[x]","A",2,1,28,0.03571,1,"{1628}"
16,1,149,0,0.1225922,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^3} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^3,x]","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+\frac{1}{4} x^4 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{2} x^2 \left(A \left(2 a c+b^2\right)+2 a b C\right)+a \log (x) (a C+2 A b)+\frac{1}{3} B x^3 \left(2 a c+b^2\right)+2 a b B x+\frac{1}{6} c x^6 (A c+2 b C)+\frac{2}{5} b B c x^5+\frac{1}{7} B c^2 x^7+\frac{1}{8} c^2 C x^8","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+\frac{1}{4} x^4 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\frac{1}{2} x^2 \left(A \left(2 a c+b^2\right)+2 a b C\right)+a \log (x) (a C+2 A b)+\frac{1}{3} B x^3 \left(2 a c+b^2\right)+2 a b B x+\frac{1}{6} c x^6 (A c+2 b C)+\frac{2}{5} b B c x^5+\frac{1}{7} B c^2 x^7+\frac{1}{8} c^2 C x^8",1,"-(a^2*A)/(2*x^2) - (a^2*B)/x + 2*a*b*B*x + ((A*(b^2 + 2*a*c) + 2*a*b*C)*x^2)/2 + (B*(b^2 + 2*a*c)*x^3)/3 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^4)/4 + (2*b*B*c*x^5)/5 + (c*(A*c + 2*b*C)*x^6)/6 + (B*c^2*x^7)/7 + (c^2*C*x^8)/8 + a*(2*A*b + a*C)*Log[x]","A",2,1,28,0.03571,1,"{1628}"
17,1,149,0,0.1372913,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^4} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^4,x]","-\frac{a^2 A}{3 x^3}-\frac{a^2 B}{2 x^2}+\frac{1}{3} x^3 \left(C \left(2 a c+b^2\right)+2 A b c\right)+x \left(A \left(2 a c+b^2\right)+2 a b C\right)-\frac{a (a C+2 A b)}{x}+\frac{1}{2} B x^2 \left(2 a c+b^2\right)+2 a b B \log (x)+\frac{1}{5} c x^5 (A c+2 b C)+\frac{1}{2} b B c x^4+\frac{1}{6} B c^2 x^6+\frac{1}{7} c^2 C x^7","-\frac{a^2 A}{3 x^3}-\frac{a^2 B}{2 x^2}+\frac{1}{3} x^3 \left(C \left(2 a c+b^2\right)+2 A b c\right)+x \left(A \left(2 a c+b^2\right)+2 a b C\right)-\frac{a (a C+2 A b)}{x}+\frac{1}{2} B x^2 \left(2 a c+b^2\right)+2 a b B \log (x)+\frac{1}{5} c x^5 (A c+2 b C)+\frac{1}{2} b B c x^4+\frac{1}{6} B c^2 x^6+\frac{1}{7} c^2 C x^7",1,"-(a^2*A)/(3*x^3) - (a^2*B)/(2*x^2) - (a*(2*A*b + a*C))/x + (A*(b^2 + 2*a*c) + 2*a*b*C)*x + (B*(b^2 + 2*a*c)*x^2)/2 + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^3)/3 + (b*B*c*x^4)/2 + (c*(A*c + 2*b*C)*x^5)/5 + (B*c^2*x^6)/6 + (c^2*C*x^7)/7 + 2*a*b*B*Log[x]","A",2,1,28,0.03571,1,"{1628}"
18,1,148,0,0.1415684,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^5} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^5,x]","-\frac{a^2 A}{4 x^4}-\frac{a^2 B}{3 x^3}+\frac{1}{2} x^2 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\log (x) \left(A \left(2 a c+b^2\right)+2 a b C\right)-\frac{a (a C+2 A b)}{2 x^2}+B x \left(2 a c+b^2\right)-\frac{2 a b B}{x}+\frac{1}{4} c x^4 (A c+2 b C)+\frac{2}{3} b B c x^3+\frac{1}{5} B c^2 x^5+\frac{1}{6} c^2 C x^6","-\frac{a^2 A}{4 x^4}-\frac{a^2 B}{3 x^3}+\frac{1}{2} x^2 \left(C \left(2 a c+b^2\right)+2 A b c\right)+\log (x) \left(A \left(2 a c+b^2\right)+2 a b C\right)-\frac{a (a C+2 A b)}{2 x^2}+B x \left(2 a c+b^2\right)-\frac{2 a b B}{x}+\frac{1}{4} c x^4 (A c+2 b C)+\frac{2}{3} b B c x^3+\frac{1}{5} B c^2 x^5+\frac{1}{6} c^2 C x^6",1,"-(a^2*A)/(4*x^4) - (a^2*B)/(3*x^3) - (a*(2*A*b + a*C))/(2*x^2) - (2*a*b*B)/x + B*(b^2 + 2*a*c)*x + ((2*A*b*c + (b^2 + 2*a*c)*C)*x^2)/2 + (2*b*B*c*x^3)/3 + (c*(A*c + 2*b*C)*x^4)/4 + (B*c^2*x^5)/5 + (c^2*C*x^6)/6 + (A*(b^2 + 2*a*c) + 2*a*b*C)*Log[x]","A",2,1,28,0.03571,1,"{1628}"
19,1,143,0,0.1466622,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^6} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^6,x]","-\frac{a^2 A}{5 x^5}-\frac{a^2 B}{4 x^4}+x \left(C \left(2 a c+b^2\right)+2 A b c\right)-\frac{A \left(2 a c+b^2\right)+2 a b C}{x}-\frac{a (a C+2 A b)}{3 x^3}+B \log (x) \left(2 a c+b^2\right)-\frac{a b B}{x^2}+\frac{1}{3} c x^3 (A c+2 b C)+b B c x^2+\frac{1}{4} B c^2 x^4+\frac{1}{5} c^2 C x^5","-\frac{a^2 A}{5 x^5}-\frac{a^2 B}{4 x^4}+x \left(C \left(2 a c+b^2\right)+2 A b c\right)-\frac{A \left(2 a c+b^2\right)+2 a b C}{x}-\frac{a (a C+2 A b)}{3 x^3}+B \log (x) \left(2 a c+b^2\right)-\frac{a b B}{x^2}+\frac{1}{3} c x^3 (A c+2 b C)+b B c x^2+\frac{1}{4} B c^2 x^4+\frac{1}{5} c^2 C x^5",1,"-(a^2*A)/(5*x^5) - (a^2*B)/(4*x^4) - (a*(2*A*b + a*C))/(3*x^3) - (a*b*B)/x^2 - (A*(b^2 + 2*a*c) + 2*a*b*C)/x + (2*A*b*c + (b^2 + 2*a*c)*C)*x + b*B*c*x^2 + (c*(A*c + 2*b*C)*x^3)/3 + (B*c^2*x^4)/4 + (c^2*C*x^5)/5 + B*(b^2 + 2*a*c)*Log[x]","A",2,1,28,0.03571,1,"{1628}"
20,1,149,0,0.1431407,"\int \frac{\left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2}{x^7} \, dx","Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2)/x^7,x]","-\frac{a^2 A}{6 x^6}-\frac{a^2 B}{5 x^5}-\frac{A \left(2 a c+b^2\right)+2 a b C}{2 x^2}+\log (x) \left(C \left(2 a c+b^2\right)+2 A b c\right)-\frac{a (a C+2 A b)}{4 x^4}-\frac{B \left(2 a c+b^2\right)}{x}-\frac{2 a b B}{3 x^3}+\frac{1}{2} c x^2 (A c+2 b C)+2 b B c x+\frac{1}{3} B c^2 x^3+\frac{1}{4} c^2 C x^4","-\frac{a^2 A}{6 x^6}-\frac{a^2 B}{5 x^5}-\frac{A \left(2 a c+b^2\right)+2 a b C}{2 x^2}+\log (x) \left(C \left(2 a c+b^2\right)+2 A b c\right)-\frac{a (a C+2 A b)}{4 x^4}-\frac{B \left(2 a c+b^2\right)}{x}-\frac{2 a b B}{3 x^3}+\frac{1}{2} c x^2 (A c+2 b C)+2 b B c x+\frac{1}{3} B c^2 x^3+\frac{1}{4} c^2 C x^4",1,"-(a^2*A)/(6*x^6) - (a^2*B)/(5*x^5) - (a*(2*A*b + a*C))/(4*x^4) - (2*a*b*B)/(3*x^3) - (A*(b^2 + 2*a*c) + 2*a*b*C)/(2*x^2) - (B*(b^2 + 2*a*c))/x + 2*b*B*c*x + (c*(A*c + 2*b*C)*x^2)/2 + (B*c^2*x^3)/3 + (c^2*C*x^4)/4 + (2*A*b*c + (b^2 + 2*a*c)*C)*Log[x]","A",2,1,28,0.03571,1,"{1628}"
21,1,339,0,1.8559286,"\int \frac{x^4 \left(A+B x+C x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^4*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{A c \left(b^2-2 a c\right)-b C \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}+a c C+A b c+b^2 (-C)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{A c \left(b^2-2 a c\right)-b C \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}+a c C+A b c+b^2 (-C)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b B \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x (A c-b C)}{c^2}+\frac{B x^2}{2 c}+\frac{C x^3}{3 c}","-\frac{\left(-\frac{A c \left(b^2-2 a c\right)-b C \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}+a c C+A b c+b^2 (-C)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{A c \left(b^2-2 a c\right)-b C \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}+a c C+A b c+b^2 (-C)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b B \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x (A c-b C)}{c^2}+\frac{B x^2}{2 c}+\frac{C x^3}{3 c}",1,"((A*c - b*C)*x)/c^2 + (B*x^2)/(2*c) + (C*x^3)/(3*c) - ((A*b*c - b^2*C + a*c*C - (A*c*(b^2 - 2*a*c) - b*(b^2 - 3*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((A*b*c - b^2*C + a*c*C + (A*c*(b^2 - 2*a*c) - b*(b^2 - 3*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (B*(b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) - (b*B*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",13,11,28,0.3929,1,"{1662, 1279, 1166, 205, 12, 1114, 703, 634, 618, 206, 628}"
22,1,278,0,0.4659662,"\int \frac{x^3 \left(A+B x+C x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^3*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4),x]","\frac{\left(2 a c C+A b c+b^2 (-C)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(A c-b C) \log \left(a+b x^2+c x^4\right)}{4 c^2}-\frac{B \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B x}{c}+\frac{C x^2}{2 c}","\frac{\left(2 a c C+A b c+b^2 (-C)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(A c-b C) \log \left(a+b x^2+c x^4\right)}{4 c^2}-\frac{B \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B x}{c}+\frac{C x^2}{2 c}",1,"(B*x)/c + (C*x^2)/(2*c) - (B*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (B*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((A*b*c - b^2*C + 2*a*c*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) + ((A*c - b*C)*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",12,11,28,0.3929,1,"{1662, 1251, 773, 634, 618, 206, 628, 12, 1122, 1166, 205}"
23,1,270,0,0.834809,"\int \frac{x^2 \left(A+B x+C x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^2*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{A b c-C \left(b^2-2 a c\right)}{\sqrt{b^2-4 a c}}+A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a c C+A b c+b^2 (-C)}{\sqrt{b^2-4 a c}}+A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c}+\frac{C x}{c}","\frac{\left(-\frac{A b c-C \left(b^2-2 a c\right)}{\sqrt{b^2-4 a c}}+A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a c C+A b c+b^2 (-C)}{\sqrt{b^2-4 a c}}+A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c}+\frac{C x}{c}",1,"(C*x)/c + ((A*c - b*C - (A*b*c - (b^2 - 2*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((A*c - b*C + (A*b*c - b^2*C + 2*a*c*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + (B*Log[a + b*x^2 + c*x^4])/(4*c)","A",11,10,28,0.3571,1,"{1662, 1279, 1166, 205, 12, 1114, 634, 618, 206, 628}"
24,1,223,0,0.2128543,"\int \frac{x \left(A+B x+C x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4),x]","-\frac{(2 A c-b C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}-\frac{B \sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{B \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{C \log \left(a+b x^2+c x^4\right)}{4 c}","-\frac{(2 A c-b C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}-\frac{B \sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{B \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{C \log \left(a+b x^2+c x^4\right)}{4 c}",1,"-((B*Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (B*Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]) - ((2*A*c - b*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + (C*Log[a + b*x^2 + c*x^4])/(4*c)","A",10,9,26,0.3462,1,"{1662, 1247, 634, 618, 206, 628, 12, 1130, 205}"
25,1,211,0,0.2662542,"\int \frac{A+B x+C x^2}{a+b x^2+c x^4} \, dx","Int[(A + B*x + C*x^2)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 A c-b C}{\sqrt{b^2-4 a c}}+C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(C-\frac{2 A c-b C}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\left(\frac{2 A c-b C}{\sqrt{b^2-4 a c}}+C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(C-\frac{2 A c-b C}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"((C + (2*A*c - b*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((C - (2*A*c - b*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",8,7,25,0.2800,1,"{1673, 1166, 205, 12, 1107, 618, 206}"
26,1,229,0,0.2594778,"\int \frac{A+B x+C x^2}{x \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x + C*x^2)/(x*(a + b*x^2 + c*x^4)),x]","\frac{(A b-2 a C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{A \log (x)}{a}+\frac{\sqrt{2} B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{(A b-2 a C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{A \log (x)}{a}+\frac{\sqrt{2} B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2]*B*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*B*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((A*b - 2*a*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + (A*Log[x])/a - (A*Log[a + b*x^2 + c*x^4])/(4*a)","A",12,10,28,0.3571,1,"{1662, 1251, 800, 634, 618, 206, 628, 12, 1093, 205}"
27,1,260,0,0.4713521,"\int \frac{A+B x+C x^2}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x + C*x^2)/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\frac{A b-2 a C}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A-\frac{A b-2 a C}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{A}{a x}+\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{B \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{B \log (x)}{a}","-\frac{\sqrt{c} \left(\frac{A b-2 a C}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A-\frac{A b-2 a C}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{A}{a x}+\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{B \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{B \log (x)}{a}",1,"-(A/(a*x)) - (Sqrt[c]*(A + (A*b - 2*a*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(A - (A*b - 2*a*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + (B*Log[x])/a - (B*Log[a + b*x^2 + c*x^4])/(4*a)","A",13,12,28,0.4286,1,"{1662, 1281, 1166, 205, 12, 1114, 705, 29, 634, 618, 206, 628}"
28,1,288,0,0.4739217,"\int \frac{A+B x+C x^2}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x + C*x^2)/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\left(A \left(b^2-2 a c\right)-a b C\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(A b-a C) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (A b-a C)}{a^2}-\frac{A}{2 a x^2}-\frac{B \sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B}{a x}","-\frac{\left(A \left(b^2-2 a c\right)-a b C\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(A b-a C) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (A b-a C)}{a^2}-\frac{A}{2 a x^2}-\frac{B \sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B}{a x}",1,"-A/(2*a*x^2) - B/(a*x) - (B*Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (B*Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((A*(b^2 - 2*a*c) - a*b*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) - ((A*b - a*C)*Log[x])/a^2 + ((A*b - a*C)*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",13,11,28,0.3929,1,"{1662, 1251, 800, 634, 618, 206, 628, 12, 1123, 1166, 205}"
29,1,412,0,1.3337888,"\int \frac{x^4 \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^4*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(-\frac{A c \left(4 a c+b^2\right)+b C \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}+C \left(b^2-6 a c\right)+A b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{A c \left(4 a c+b^2\right)+b C \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}+C \left(b^2-6 a c\right)+A b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x (2 A c-b C)}{2 c \left(b^2-4 a c\right)}+\frac{B x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{\left(-\frac{A c \left(4 a c+b^2\right)+b C \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}+C \left(b^2-6 a c\right)+A b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{A c \left(4 a c+b^2\right)+b C \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}+C \left(b^2-6 a c\right)+A b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x (2 A c-b C)}{2 c \left(b^2-4 a c\right)}+\frac{B x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"((2*A*c - b*C)*x)/(2*c*(b^2 - 4*a*c)) + (B*x^2*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x^3*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((A*b*c + (b^2 - 6*a*c)*C - (A*c*(b^2 + 4*a*c) + b*(b^2 - 8*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((A*b*c + (b^2 - 6*a*c)*C + (A*c*(b^2 + 4*a*c) + b*(b^2 - 8*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (2*a*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,28,0.3571,1,"{1662, 1275, 1279, 1166, 205, 12, 1114, 722, 618, 206}"
30,1,347,0,0.6175032,"\int \frac{x^3 \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^3*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{x^2 \left(2 a c C+A b c+b^2 (-C)\right)+a (2 A c-b C)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(A b-2 a C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}+\frac{B x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x^2 \left(2 a c C+A b c+b^2 (-C)\right)+a (2 A c-b C)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(A b-2 a C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}+\frac{B x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(B*x*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (a*(2*A*c - b*C) + (A*b*c - b^2*C + 2*a*c*C)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (B*(b - (b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (B*(b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((A*b - 2*a*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,28,0.3214,1,"{1662, 1251, 777, 618, 206, 12, 1120, 1166, 205}"
31,1,356,0,0.9018465,"\int \frac{x^2 \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^2*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,28,0.3214,1,"{1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
32,1,317,0,0.4153495,"\int \frac{x \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{-2 a C+x^2 (2 A c-b C)+A b}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 A c-b C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{B x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{-2 a C+x^2 (2 A c-b C)+A b}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 A c-b C) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{B x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(B*x*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (A*b - 2*a*C + (2*A*c - b*C)*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (B*Sqrt[c]*(2*b - Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (B*Sqrt[c]*(2*b + Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((2*A*c - b*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,26,0.3462,1,"{1662, 1247, 638, 618, 206, 12, 1119, 1166, 205}"
33,1,368,0,0.8667416,"\int \frac{A+B x+C x^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x + C*x^2)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(c x^2 (A b-2 a C)-2 a A c-a b C+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{A \left(b^2-12 a c\right)+4 a b C}{\sqrt{b^2-4 a c}}-2 a C+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{-12 a A c+4 a b C+A b^2}{\sqrt{b^2-4 a c}}-2 a C+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 B c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x \left(c x^2 (A b-2 a C)-2 a A c-a b C+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{A \left(b^2-12 a c\right)+4 a b C}{\sqrt{b^2-4 a c}}-2 a C+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{-12 a A c+4 a b C+A b^2}{\sqrt{b^2-4 a c}}-2 a C+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{B \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 B c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"-(B*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (x*(A*b^2 - 2*a*A*c - a*b*C + c*(A*b - 2*a*C)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(A*b - 2*a*C + (A*(b^2 - 12*a*c) + 4*a*b*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(A*b - 2*a*C - (A*b^2 - 12*a*A*c + 4*a*b*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (2*B*c*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,25,0.3600,1,"{1673, 1178, 1166, 205, 12, 1107, 614, 618, 206}"
34,1,403,0,0.9319974,"\int \frac{A+B x+C x^2}{x \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x + C*x^2)/(x*(a + b*x^2 + c*x^4)^2),x]","\frac{\left(4 a^2 c C+A \left(b^3-6 a b c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{A \log (x)}{a^2}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\left(4 a^2 c C+A \left(b^3-6 a b c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{A \log (x)}{a^2}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{B \sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(B*x*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (A*(b^2 - 2*a*c) - a*b*C + c*(A*b - 2*a*C)*x^2)/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (B*Sqrt[c]*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (B*Sqrt[c]*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((A*(b^3 - 6*a*b*c) + 4*a^2*c*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + (A*Log[x])/a^2 - (A*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",14,12,28,0.4286,1,"{1662, 1251, 822, 800, 634, 618, 206, 628, 12, 1092, 1166, 205}"
35,1,514,0,1.4857082,"\int \frac{A+B x+C x^2}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x + C*x^2)/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{-10 a A c-a b C+3 A b^2}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-a C \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-\frac{A \left(3 b^3-16 a b c\right)-a C \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a A c-a b C+3 A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b B \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{B \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{B \log (x)}{a^2}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{-10 a A c-a b C+3 A b^2}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-a C \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-\frac{A \left(3 b^3-16 a b c\right)-a C \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a A c-a b C+3 A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b B \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{B \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{B \log (x)}{a^2}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(3*A*b^2 - 10*a*A*c - a*b*C)/(2*a^2*(b^2 - 4*a*c)*x) + (B*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (A*(b^2 - 2*a*c) - a*b*C + c*(A*b - 2*a*C)*x^2)/(2*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)) - (Sqrt[c]*(A*(3*b^3 - 16*a*b*c + 3*b^2*Sqrt[b^2 - 4*a*c] - 10*a*c*Sqrt[b^2 - 4*a*c]) - a*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*C)*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(3*A*b^2 - 10*a*A*c - a*b*C - (A*(3*b^3 - 16*a*b*c) - a*(b^2 - 12*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (b*B*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + (B*Log[x])/a^2 - (B*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",15,13,28,0.4643,1,"{1662, 1277, 1281, 1166, 205, 12, 1114, 740, 800, 634, 618, 206, 628}"
36,1,534,0,1.9923635,"\int \frac{A+B x+C x^2}{x^3 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x + C*x^2)/(x^3*(a + b*x^2 + c*x^4)^2),x]","-\frac{\left(2 A \left(6 a^2 c^2-6 a b^2 c+b^4\right)-a b C \left(b^2-6 a c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-6 a A c-a b C+2 A b^2}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{(2 A b-a C) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 A b-a C)}{a^3}-\frac{B \left(3 b^2-10 a c\right)}{2 a^2 x \left(b^2-4 a c\right)}-\frac{B \sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(-2 a c+b^2+b c x^2\right)}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{\left(2 A \left(6 a^2 c^2-6 a b^2 c+b^4\right)-a b C \left(b^2-6 a c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-6 a A c-a b C+2 A b^2}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{(2 A b-a C) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 A b-a C)}{a^3}-\frac{B \left(3 b^2-10 a c\right)}{2 a^2 x \left(b^2-4 a c\right)}-\frac{B \sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \left(-2 a c+b^2+b c x^2\right)}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(2*A*b^2 - 6*a*A*c - a*b*C)/(2*a^2*(b^2 - 4*a*c)*x^2) - (B*(3*b^2 - 10*a*c))/(2*a^2*(b^2 - 4*a*c)*x) + (B*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)) + (A*(b^2 - 2*a*c) - a*b*C + c*(A*b - 2*a*C)*x^2)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)) - (B*Sqrt[c]*(3*b^3 - 16*a*b*c + (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (B*Sqrt[c]*(3*b^3 - 16*a*b*c - (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((2*A*(b^4 - 6*a*b^2*c + 6*a^2*c^2) - a*b*(b^2 - 6*a*c)*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(3/2)) - ((2*A*b - a*C)*Log[x])/a^3 + ((2*A*b - a*C)*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",15,13,28,0.4643,1,"{1662, 1251, 822, 800, 634, 618, 206, 628, 12, 1121, 1281, 1166, 205}"
37,1,399,0,0.4249282,"\int (d x)^m \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[(d*x)^m*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{a^2 (d x)^{m+3} (a C+3 A b)}{d^3 (m+3)}+\frac{a^3 A (d x)^{m+1}}{d (m+1)}+\frac{3 a^2 b B (d x)^{m+4}}{d^4 (m+4)}+\frac{a^3 B (d x)^{m+2}}{d^2 (m+2)}+\frac{3 a (d x)^{m+5} \left(A \left(a c+b^2\right)+a b C\right)}{d^5 (m+5)}+\frac{(d x)^{m+7} \left(A \left(6 a b c+b^3\right)+3 a C \left(a c+b^2\right)\right)}{d^7 (m+7)}+\frac{(d x)^{m+9} \left(3 A c \left(a c+b^2\right)+b C \left(6 a c+b^2\right)\right)}{d^9 (m+9)}+\frac{3 c (d x)^{m+11} \left(C \left(a c+b^2\right)+A b c\right)}{d^{11} (m+11)}+\frac{3 a B \left(a c+b^2\right) (d x)^{m+6}}{d^6 (m+6)}+\frac{b B \left(6 a c+b^2\right) (d x)^{m+8}}{d^8 (m+8)}+\frac{3 B c \left(a c+b^2\right) (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 (d x)^{m+13} (A c+3 b C)}{d^{13} (m+13)}+\frac{3 b B c^2 (d x)^{m+12}}{d^{12} (m+12)}+\frac{B c^3 (d x)^{m+14}}{d^{14} (m+14)}+\frac{c^3 C (d x)^{m+15}}{d^{15} (m+15)}","\frac{a^2 (d x)^{m+3} (a C+3 A b)}{d^3 (m+3)}+\frac{a^3 A (d x)^{m+1}}{d (m+1)}+\frac{3 a^2 b B (d x)^{m+4}}{d^4 (m+4)}+\frac{a^3 B (d x)^{m+2}}{d^2 (m+2)}+\frac{3 a (d x)^{m+5} \left(A \left(a c+b^2\right)+a b C\right)}{d^5 (m+5)}+\frac{(d x)^{m+7} \left(A \left(6 a b c+b^3\right)+3 a C \left(a c+b^2\right)\right)}{d^7 (m+7)}+\frac{(d x)^{m+9} \left(3 A c \left(a c+b^2\right)+b C \left(6 a c+b^2\right)\right)}{d^9 (m+9)}+\frac{3 c (d x)^{m+11} \left(C \left(a c+b^2\right)+A b c\right)}{d^{11} (m+11)}+\frac{3 a B \left(a c+b^2\right) (d x)^{m+6}}{d^6 (m+6)}+\frac{b B \left(6 a c+b^2\right) (d x)^{m+8}}{d^8 (m+8)}+\frac{3 B c \left(a c+b^2\right) (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 (d x)^{m+13} (A c+3 b C)}{d^{13} (m+13)}+\frac{3 b B c^2 (d x)^{m+12}}{d^{12} (m+12)}+\frac{B c^3 (d x)^{m+14}}{d^{14} (m+14)}+\frac{c^3 C (d x)^{m+15}}{d^{15} (m+15)}",1,"(a^3*A*(d*x)^(1 + m))/(d*(1 + m)) + (a^3*B*(d*x)^(2 + m))/(d^2*(2 + m)) + (a^2*(3*A*b + a*C)*(d*x)^(3 + m))/(d^3*(3 + m)) + (3*a^2*b*B*(d*x)^(4 + m))/(d^4*(4 + m)) + (3*a*(A*(b^2 + a*c) + a*b*C)*(d*x)^(5 + m))/(d^5*(5 + m)) + (3*a*B*(b^2 + a*c)*(d*x)^(6 + m))/(d^6*(6 + m)) + ((A*(b^3 + 6*a*b*c) + 3*a*(b^2 + a*c)*C)*(d*x)^(7 + m))/(d^7*(7 + m)) + (b*B*(b^2 + 6*a*c)*(d*x)^(8 + m))/(d^8*(8 + m)) + ((3*A*c*(b^2 + a*c) + b*(b^2 + 6*a*c)*C)*(d*x)^(9 + m))/(d^9*(9 + m)) + (3*B*c*(b^2 + a*c)*(d*x)^(10 + m))/(d^10*(10 + m)) + (3*c*(A*b*c + (b^2 + a*c)*C)*(d*x)^(11 + m))/(d^11*(11 + m)) + (3*b*B*c^2*(d*x)^(12 + m))/(d^12*(12 + m)) + (c^2*(A*c + 3*b*C)*(d*x)^(13 + m))/(d^13*(13 + m)) + (B*c^3*(d*x)^(14 + m))/(d^14*(14 + m)) + (c^3*C*(d*x)^(15 + m))/(d^15*(15 + m))","A",2,1,30,0.03333,1,"{1628}"
38,1,260,0,0.2225007,"\int (d x)^m \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d*x)^m*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]","\frac{a^2 A (d x)^{m+1}}{d (m+1)}+\frac{a^2 B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+5} \left(A \left(2 a c+b^2\right)+2 a b C\right)}{d^5 (m+5)}+\frac{(d x)^{m+7} \left(C \left(2 a c+b^2\right)+2 A b c\right)}{d^7 (m+7)}+\frac{a (d x)^{m+3} (a C+2 A b)}{d^3 (m+3)}+\frac{B \left(2 a c+b^2\right) (d x)^{m+6}}{d^6 (m+6)}+\frac{2 a b B (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+9} (A c+2 b C)}{d^9 (m+9)}+\frac{2 b B c (d x)^{m+8}}{d^8 (m+8)}+\frac{B c^2 (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 C (d x)^{m+11}}{d^{11} (m+11)}","\frac{a^2 A (d x)^{m+1}}{d (m+1)}+\frac{a^2 B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+5} \left(A \left(2 a c+b^2\right)+2 a b C\right)}{d^5 (m+5)}+\frac{(d x)^{m+7} \left(C \left(2 a c+b^2\right)+2 A b c\right)}{d^7 (m+7)}+\frac{a (d x)^{m+3} (a C+2 A b)}{d^3 (m+3)}+\frac{B \left(2 a c+b^2\right) (d x)^{m+6}}{d^6 (m+6)}+\frac{2 a b B (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+9} (A c+2 b C)}{d^9 (m+9)}+\frac{2 b B c (d x)^{m+8}}{d^8 (m+8)}+\frac{B c^2 (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 C (d x)^{m+11}}{d^{11} (m+11)}",1,"(a^2*A*(d*x)^(1 + m))/(d*(1 + m)) + (a^2*B*(d*x)^(2 + m))/(d^2*(2 + m)) + (a*(2*A*b + a*C)*(d*x)^(3 + m))/(d^3*(3 + m)) + (2*a*b*B*(d*x)^(4 + m))/(d^4*(4 + m)) + ((A*(b^2 + 2*a*c) + 2*a*b*C)*(d*x)^(5 + m))/(d^5*(5 + m)) + (B*(b^2 + 2*a*c)*(d*x)^(6 + m))/(d^6*(6 + m)) + ((2*A*b*c + (b^2 + 2*a*c)*C)*(d*x)^(7 + m))/(d^7*(7 + m)) + (2*b*B*c*(d*x)^(8 + m))/(d^8*(8 + m)) + (c*(A*c + 2*b*C)*(d*x)^(9 + m))/(d^9*(9 + m)) + (B*c^2*(d*x)^(10 + m))/(d^10*(10 + m)) + (c^2*C*(d*x)^(11 + m))/(d^11*(11 + m))","A",2,1,30,0.03333,1,"{1628}"
39,1,137,0,0.0880793,"\int (d x)^m \left(A+B x+C x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[(d*x)^m*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]","\frac{(d x)^{m+3} (a C+A b)}{d^3 (m+3)}+\frac{a A (d x)^{m+1}}{d (m+1)}+\frac{a B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+5} (A c+b C)}{d^5 (m+5)}+\frac{b B (d x)^{m+4}}{d^4 (m+4)}+\frac{B c (d x)^{m+6}}{d^6 (m+6)}+\frac{c C (d x)^{m+7}}{d^7 (m+7)}","\frac{(d x)^{m+3} (a C+A b)}{d^3 (m+3)}+\frac{a A (d x)^{m+1}}{d (m+1)}+\frac{a B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+5} (A c+b C)}{d^5 (m+5)}+\frac{b B (d x)^{m+4}}{d^4 (m+4)}+\frac{B c (d x)^{m+6}}{d^6 (m+6)}+\frac{c C (d x)^{m+7}}{d^7 (m+7)}",1,"(a*A*(d*x)^(1 + m))/(d*(1 + m)) + (a*B*(d*x)^(2 + m))/(d^2*(2 + m)) + ((A*b + a*C)*(d*x)^(3 + m))/(d^3*(3 + m)) + (b*B*(d*x)^(4 + m))/(d^4*(4 + m)) + ((A*c + b*C)*(d*x)^(5 + m))/(d^5*(5 + m)) + (B*c*(d*x)^(6 + m))/(d^6*(6 + m)) + (c*C*(d*x)^(7 + m))/(d^7*(7 + m))","A",2,1,28,0.03571,1,"{1628}"
40,1,368,0,0.6216534,"\int \frac{(d x)^m \left(A+B x+C x^2\right)}{a+b x^2+c x^4} \, dx","Int[((d*x)^m*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4),x]","\frac{(d x)^{m+1} \left(\frac{2 A c-b C}{\sqrt{b^2-4 a c}}+C\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(d x)^{m+1} \left(C-\frac{2 A c-b C}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{2 B c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d^2 (m+2) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 B c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d^2 (m+2) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{(d x)^{m+1} \left(\frac{2 A c-b C}{\sqrt{b^2-4 a c}}+C\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(d x)^{m+1} \left(C-\frac{2 A c-b C}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{2 B c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d^2 (m+2) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 B c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d^2 (m+2) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"((C + (2*A*c - b*C)/Sqrt[b^2 - 4*a*c])*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) + ((C - (2*A*c - b*C)/Sqrt[b^2 - 4*a*c])*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*d*(1 + m)) + (2*B*c*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d^2*(2 + m)) - (2*B*c*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d^2*(2 + m))","A",8,5,30,0.1667,1,"{1662, 1285, 364, 12, 1131}"
41,1,670,0,2.3777946,"\int \frac{(d x)^m \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[((d*x)^m*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{c (d x)^{m+1} \left(A \left(b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right)+2 a C \left(2 b-(1-m) \sqrt{b^2-4 a c}\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(-(1-m) \sqrt{b^2-4 a c} (A b-2 a C)-4 a A c (3-m)+4 a b C+A b^2 (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C\right)}{2 a d \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{B c (d x)^{m+2} \left(b m \left(\sqrt{b^2-4 a c}+b\right)+4 a c (2-m)\right) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d^2 (m+2) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{B c (d x)^{m+2} \left(b m \left(b-\sqrt{b^2-4 a c}\right)+4 a c (2-m)\right) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d^2 (m+2) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{B (d x)^{m+2} \left(-2 a c+b^2+b c x^2\right)}{2 a d^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{c (d x)^{m+1} \left(A \left(b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right)+2 a C \left(2 b-(1-m) \sqrt{b^2-4 a c}\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(A \left(-b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right)+2 a C \left((1-m) \sqrt{b^2-4 a c}+2 b\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(A \left(b^2-2 a c\right)+c x^2 (A b-2 a C)-a b C\right)}{2 a d \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{B c (d x)^{m+2} \left(b m \left(\sqrt{b^2-4 a c}+b\right)+4 a c (2-m)\right) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d^2 (m+2) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{B c (d x)^{m+2} \left(b m \left(b-\sqrt{b^2-4 a c}\right)+4 a c (2-m)\right) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d^2 (m+2) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{B (d x)^{m+2} \left(-2 a c+b^2+b c x^2\right)}{2 a d^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(B*(d*x)^(2 + m)*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*d^2*(a + b*x^2 + c*x^4)) + ((d*x)^(1 + m)*(A*(b^2 - 2*a*c) - a*b*C + c*(A*b - 2*a*C)*x^2))/(2*a*(b^2 - 4*a*c)*d*(a + b*x^2 + c*x^4)) + (c*(2*a*C*(2*b - Sqrt[b^2 - 4*a*c]*(1 - m)) + A*(b^2*(1 - m) + b*Sqrt[b^2 - 4*a*c]*(1 - m) - 4*a*c*(3 - m)))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (c*(4*a*b*C + A*b^2*(1 - m) - Sqrt[b^2 - 4*a*c]*(A*b - 2*a*C)*(1 - m) - 4*a*A*c*(3 - m))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (B*c*(4*a*c*(2 - m) + b*(b + Sqrt[b^2 - 4*a*c])*m)*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*d^2*(2 + m)) + (B*c*(4*a*c*(2 - m) + b*(b - Sqrt[b^2 - 4*a*c])*m)*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*d^2*(2 + m))","A",10,6,30,0.2000,1,"{1662, 1277, 1285, 364, 12, 1121}"
42,1,356,0,0.9238222,"\int \frac{x^2 \left(A+B x+C x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^2*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,28,0.3214,1,"{1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
43,1,356,0,0.3709353,"\int \frac{x \left(A x+B x^2+C x^3\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x*(A*x + B*x^2 + C*x^3))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,30,0.3333,1,"{1585, 1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
44,1,356,0,0.3704767,"\int \frac{A x^2+B x^3+C x^4}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(A*x^2 + B*x^3 + C*x^4)/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,31,0.3226,1,"{1594, 1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
45,1,356,0,0.356423,"\int \frac{A x^3+B x^4+C x^5}{x \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A*x^3 + B*x^4 + C*x^5)/(x*(a + b*x^2 + c*x^4)^2),x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,34,0.2941,1,"{1585, 1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
46,1,356,0,0.358759,"\int \frac{A x^4+B x^5+C x^6}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A*x^4 + B*x^5 + C*x^6)/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x \left(-2 a C+x^2 (2 A c-b C)+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(-\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{4 A b c-C \left(4 a c+b^2\right)}{\sqrt{b^2-4 a c}}+2 A c-b C\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b B \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(B*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(A*b - 2*a*C + (2*A*c - b*C)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*A*c - b*C - (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*A*c - b*C + (4*A*b*c - (b^2 + 4*a*c)*C)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (b*B*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,34,0.2941,1,"{1585, 1662, 1275, 1166, 205, 12, 1114, 638, 618, 206}"
47,1,273,0,0.8541004,"\int \frac{x^7 \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x^7*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 c^3 e-4 a b^2 c^2 e-b^3 c (c d-5 a f)+a b c^2 (3 c d-5 a f)+b^4 c e+b^5 (-f)\right)}{2 c^5 \sqrt{b^2-4 a c}}+\frac{x^4 \left(-c (a f+b e)+b^2 f+c^2 d\right)}{4 c^3}+\frac{x^2 \left(-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{2 c^4}-\frac{\log \left(a+b x^2+c x^4\right) \left(-b^2 c (c d-3 a f)-2 a b c^2 e+a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)}{4 c^5}+\frac{x^6 (c e-b f)}{6 c^2}+\frac{f x^8}{8 c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 c^3 e-4 a b^2 c^2 e-b^3 c (c d-5 a f)+a b c^2 (3 c d-5 a f)+b^4 c e+b^5 (-f)\right)}{2 c^5 \sqrt{b^2-4 a c}}+\frac{x^4 \left(-c (a f+b e)+b^2 f+c^2 d\right)}{4 c^3}+\frac{x^2 \left(-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{2 c^4}-\frac{\log \left(a+b x^2+c x^4\right) \left(-b^2 c (c d-3 a f)-2 a b c^2 e+a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)}{4 c^5}+\frac{x^6 (c e-b f)}{6 c^2}+\frac{f x^8}{8 c}",1,"((b^2*c*e - a*c^2*e - b^3*f - b*c*(c*d - 2*a*f))*x^2)/(2*c^4) + ((c^2*d + b^2*f - c*(b*e + a*f))*x^4)/(4*c^3) + ((c*e - b*f)*x^6)/(6*c^2) + (f*x^8)/(8*c) - ((b^4*c*e - 4*a*b^2*c^2*e + 2*a^2*c^3*e - b^5*f - b^3*c*(c*d - 5*a*f) + a*b*c^2*(3*c*d - 5*a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^5*Sqrt[b^2 - 4*a*c]) - ((b^3*c*e - 2*a*b*c^2*e - b^4*f - b^2*c*(c*d - 3*a*f) + a*c^2*(c*d - a*f))*Log[a + b*x^2 + c*x^4])/(4*c^5)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
48,1,203,0,0.4236809,"\int \frac{x^5 \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x^5*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","\frac{x^2 \left(-c (a f+b e)+b^2 f+c^2 d\right)}{2 c^3}+\frac{\log \left(a+b x^2+c x^4\right) \left(-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{4 c^4}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)}{2 c^4 \sqrt{b^2-4 a c}}+\frac{x^4 (c e-b f)}{4 c^2}+\frac{f x^6}{6 c}","\frac{x^2 \left(-c (a f+b e)+b^2 f+c^2 d\right)}{2 c^3}+\frac{\log \left(a+b x^2+c x^4\right) \left(-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{4 c^4}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)}{2 c^4 \sqrt{b^2-4 a c}}+\frac{x^4 (c e-b f)}{4 c^2}+\frac{f x^6}{6 c}",1,"((c^2*d + b^2*f - c*(b*e + a*f))*x^2)/(2*c^3) + ((c*e - b*f)*x^4)/(4*c^2) + (f*x^6)/(6*c) + ((b^3*c*e - 3*a*b*c^2*e - b^4*f - b^2*c*(c*d - 4*a*f) + 2*a*c^2*(c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^4*Sqrt[b^2 - 4*a*c]) + ((b^2*c*e - a*c^2*e - b^3*f - b*c*(c*d - 2*a*f))*Log[a + b*x^2 + c*x^4])/(4*c^4)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
49,1,144,0,0.2716365,"\int \frac{x^3 \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x^3*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a f+b e)+b^2 f+c^2 d\right)}{4 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{x^2 (c e-b f)}{2 c^2}+\frac{f x^4}{4 c}","\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a f+b e)+b^2 f+c^2 d\right)}{4 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{x^2 (c e-b f)}{2 c^2}+\frac{f x^4}{4 c}",1,"((c*e - b*f)*x^2)/(2*c^2) + (f*x^4)/(4*c) - ((b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((c^2*d + b^2*f - c*(b*e + a*f))*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
50,1,103,0,0.1789579,"\int \frac{x \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(c e-b f) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{f x^2}{2 c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(c e-b f) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{f x^2}{2 c}",1,"(f*x^2)/(2*c) - ((2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) + ((c*e - b*f)*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",7,6,28,0.2143,1,"{1663, 1657, 634, 618, 206, 628}"
51,1,97,0,0.2004316,"\int \frac{d+e x^2+f x^4}{x \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x*(a + b*x^2 + c*x^4)),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (a b f-2 a c e+b c d)}{2 a c \sqrt{b^2-4 a c}}-\frac{(c d-a f) \log \left(a+b x^2+c x^4\right)}{4 a c}+\frac{d \log (x)}{a}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (a b f-2 a c e+b c d)}{2 a c \sqrt{b^2-4 a c}}-\frac{(c d-a f) \log \left(a+b x^2+c x^4\right)}{4 a c}+\frac{d \log (x)}{a}",1,"((b*c*d - 2*a*c*e + a*b*f)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*c*Sqrt[b^2 - 4*a*c]) + (d*Log[x])/a - ((c*d - a*f)*Log[a + b*x^2 + c*x^4])/(4*a*c)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
52,1,118,0,0.2853483,"\int \frac{d+e x^2+f x^4}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-a b e-2 a (c d-a f)+b^2 d\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{2 a x^2}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-a b e-2 a (c d-a f)+b^2 d\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{2 a x^2}",1,"-d/(2*a*x^2) - ((b^2*d - a*b*e - 2*a*(c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) - ((b*d - a*e)*Log[x])/a^2 + ((b*d - a*e)*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
53,1,174,0,0.4073402,"\int \frac{d+e x^2+f x^4}{x^5 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^5*(a + b*x^2 + c*x^4)),x]","-\frac{\log \left(a+b x^2+c x^4\right) \left(-a b e-a (c d-a f)+b^2 d\right)}{4 a^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)}{2 a^3 \sqrt{b^2-4 a c}}+\frac{\log (x) \left(-a b e-a (c d-a f)+b^2 d\right)}{a^3}+\frac{b d-a e}{2 a^2 x^2}-\frac{d}{4 a x^4}","-\frac{\log \left(a+b x^2+c x^4\right) \left(-a b e-a (c d-a f)+b^2 d\right)}{4 a^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)}{2 a^3 \sqrt{b^2-4 a c}}+\frac{\log (x) \left(-a b e-a (c d-a f)+b^2 d\right)}{a^3}+\frac{b d-a e}{2 a^2 x^2}-\frac{d}{4 a x^4}",1,"-d/(4*a*x^4) + (b*d - a*e)/(2*a^2*x^2) + ((b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*Sqrt[b^2 - 4*a*c]) + ((b^2*d - a*b*e - a*(c*d - a*f))*Log[x])/a^3 - ((b^2*d - a*b*e - a*(c*d - a*f))*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
54,1,244,0,0.5729023,"\int \frac{d+e x^2+f x^4}{x^7 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^7*(a + b*x^2 + c*x^4)),x]","-\frac{-a b e-a (c d-a f)+b^2 d}{2 a^3 x^2}+\frac{\log \left(a+b x^2+c x^4\right) \left(a^2 c e-a b^2 e-a b (2 c d-a f)+b^3 d\right)}{4 a^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(3 a^2 b c e+2 a^2 c (c d-a f)-a b^2 (4 c d-a f)-a b^3 e+b^4 d\right)}{2 a^4 \sqrt{b^2-4 a c}}-\frac{\log (x) \left(a^2 c e-a b^2 e-a b (2 c d-a f)+b^3 d\right)}{a^4}+\frac{b d-a e}{4 a^2 x^4}-\frac{d}{6 a x^6}","-\frac{-a b e-a (c d-a f)+b^2 d}{2 a^3 x^2}+\frac{\log \left(a+b x^2+c x^4\right) \left(a^2 c e-a b^2 e-a b (2 c d-a f)+b^3 d\right)}{4 a^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(3 a^2 b c e+2 a^2 c (c d-a f)-a b^2 (4 c d-a f)-a b^3 e+b^4 d\right)}{2 a^4 \sqrt{b^2-4 a c}}-\frac{\log (x) \left(a^2 c e-a b^2 e-a b (2 c d-a f)+b^3 d\right)}{a^4}+\frac{b d-a e}{4 a^2 x^4}-\frac{d}{6 a x^6}",1,"-d/(6*a*x^6) + (b*d - a*e)/(4*a^2*x^4) - (b^2*d - a*b*e - a*(c*d - a*f))/(2*a^3*x^2) - ((b^4*d - a*b^3*e + 3*a^2*b*c*e + 2*a^2*c*(c*d - a*f) - a*b^2*(4*c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*Sqrt[b^2 - 4*a*c]) - ((b^3*d - a*b^2*e + a^2*c*e - a*b*(2*c*d - a*f))*Log[x])/a^4 + ((b^3*d - a*b^2*e + a^2*c*e - a*b*(2*c*d - a*f))*Log[a + b*x^2 + c*x^4])/(4*a^4)","A",7,6,30,0.2000,1,"{1663, 1628, 634, 618, 206, 628}"
55,1,369,0,4.5773686,"\int \frac{x^4 \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x^4*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","\frac{x \left(-c (a f+b e)+b^2 f+c^2 d\right)}{c^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)}{\sqrt{b^2-4 a c}}-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)}{\sqrt{b^2-4 a c}}-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{\sqrt{2} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 (c e-b f)}{3 c^2}+\frac{f x^5}{5 c}","\frac{x \left(-c (a f+b e)+b^2 f+c^2 d\right)}{c^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)}{\sqrt{b^2-4 a c}}-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)}{\sqrt{b^2-4 a c}}-b c (c d-2 a f)-a c^2 e+b^2 c e+b^3 (-f)\right)}{\sqrt{2} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 (c e-b f)}{3 c^2}+\frac{f x^5}{5 c}",1,"((c^2*d + b^2*f - c*(b*e + a*f))*x)/c^3 + ((c*e - b*f)*x^3)/(3*c^2) + (f*x^5)/(5*c) + ((b^2*c*e - a*c^2*e - b^3*f - b*c*(c*d - 2*a*f) - (b^3*c*e - 3*a*b*c^2*e - b^4*f - b^2*c*(c*d - 4*a*f) + 2*a*c^2*(c*d - a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*c*e - a*c^2*e - b^3*f - b*c*(c*d - 2*a*f) + (b^3*c*e - 3*a*b*c^2*e - b^4*f - b^2*c*(c*d - 4*a*f) + 2*a*c^2*(c*d - a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,30,0.1000,1,"{1664, 1166, 205}"
56,1,282,0,3.5896878,"\int \frac{x^2 \left(d+e x^2+f x^4\right)}{a+b x^2+c x^4} \, dx","Int[(x^2*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)}{\sqrt{b^2-4 a c}}-a c f+b^2 f-b c e+c^2 d\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)}{\sqrt{b^2-4 a c}}-a c f+b^2 f-b c e+c^2 d\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x (c e-b f)}{c^2}+\frac{f x^3}{3 c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)}{\sqrt{b^2-4 a c}}-a c f+b^2 f-b c e+c^2 d\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)}{\sqrt{b^2-4 a c}}-a c f+b^2 f-b c e+c^2 d\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x (c e-b f)}{c^2}+\frac{f x^3}{3 c}",1,"((c*e - b*f)*x)/c^2 + (f*x^3)/(3*c) + ((c^2*d - b*c*e + b^2*f - a*c*f + (b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((c^2*d - b*c*e + b^2*f - a*c*f - (b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,30,0.1000,1,"{1664, 1166, 205}"
57,1,219,0,0.6372722,"\int \frac{d+e x^2+f x^4}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2 + f*x^4)/(a + b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a f+b e)+b^2 f+2 c^2 d}{\sqrt{b^2-4 a c}}-b f+c e\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c f+b^2 f-b c e+2 c^2 d}{\sqrt{b^2-4 a c}}-b f+c e\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f x}{c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a f+b e)+b^2 f+2 c^2 d}{\sqrt{b^2-4 a c}}-b f+c e\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c f+b^2 f-b c e+2 c^2 d}{\sqrt{b^2-4 a c}}-b f+c e\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f x}{c}",1,"(f*x)/c + ((c*e - b*f + (2*c^2*d + b^2*f - c*(b*e + 2*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((c*e - b*f - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,27,0.1111,1,"{1676, 1166, 205}"
58,1,213,0,0.8391724,"\int \frac{d+e x^2+f x^4}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{a b f-2 a c e+b c d}{\sqrt{b^2-4 a c}}-a f+c d\right)}{\sqrt{2} a \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{a b f-2 a c e+b c d}{\sqrt{b^2-4 a c}}-a f+c d\right)}{\sqrt{2} a \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a x}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{a b f-2 a c e+b c d}{\sqrt{b^2-4 a c}}-a f+c d\right)}{\sqrt{2} a \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{a b f-2 a c e+b c d}{\sqrt{b^2-4 a c}}-a f+c d\right)}{\sqrt{2} a \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a x}",1,"-(d/(a*x)) - ((c*d - a*f + (b*c*d - 2*a*c*e + a*b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((c*d - a*f - (b*c*d - 2*a*c*e + a*b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,30,0.1000,1,"{1664, 1166, 205}"
59,1,267,0,1.0651028,"\int \frac{d+e x^2+f x^4}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^4*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-a b e-2 a (c d-a f)+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{\sqrt{2} a^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-a \left(-e \sqrt{b^2-4 a c}-2 a f+2 c d\right)-b \left(d \sqrt{b^2-4 a c}+a e\right)+b^2 d\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b d-a e}{a^2 x}-\frac{d}{3 a x^3}","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-a b e-2 a (c d-a f)+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{\sqrt{2} a^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-a \left(-e \sqrt{b^2-4 a c}-2 a f+2 c d\right)-b \left(d \sqrt{b^2-4 a c}+a e\right)+b^2 d\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b d-a e}{a^2 x}-\frac{d}{3 a x^3}",1,"-d/(3*a*x^3) + (b*d - a*e)/(a^2*x) + (Sqrt[c]*(b*d - a*e + (b^2*d - a*b*e - 2*a*(c*d - a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(b^2*d - b*(Sqrt[b^2 - 4*a*c]*d + a*e) - a*(2*c*d - Sqrt[b^2 - 4*a*c]*e - 2*a*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,30,0.1000,1,"{1664, 1166, 205}"
60,1,329,0,1.9419715,"\int \frac{d+e x^2+f x^4}{x^6 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2 + f*x^4)/(x^6*(a + b*x^2 + c*x^4)),x]","-\frac{-a b e-a (c d-a f)+b^2 d}{a^3 x}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a (c d-a f)+b^2 d\right)}{\sqrt{2} a^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a (c d-a f)+b^2 d\right)}{\sqrt{2} a^3 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b d-a e}{3 a^2 x^3}-\frac{d}{5 a x^5}","-\frac{-a b e-a (c d-a f)+b^2 d}{a^3 x}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a (c d-a f)+b^2 d\right)}{\sqrt{2} a^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a (c d-a f)+b^2 d\right)}{\sqrt{2} a^3 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b d-a e}{3 a^2 x^3}-\frac{d}{5 a x^5}",1,"-d/(5*a*x^5) + (b*d - a*e)/(3*a^2*x^3) - (b^2*d - a*b*e - a*(c*d - a*f))/(a^3*x) - (Sqrt[c]*(b^2*d - a*b*e - a*(c*d - a*f) + (b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(b^2*d - a*b*e - a*(c*d - a*f) - (b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,30,0.1000,1,"{1664, 1166, 205}"
61,1,320,0,1.2325323,"\int \frac{x^7 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^7*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 c^3 e-12 a b^2 c^2 e-b^3 c (c d-20 a f)+6 a b c^2 (c d-5 a f)+2 b^4 c e-3 b^5 f\right)}{2 c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{x^6 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x^4 \left(-2 c (4 a f+b e)+3 b^2 f+4 c^2 d\right)}{4 c^2 \left(b^2-4 a c\right)}+\frac{x^2 \left(-b c (c d-11 a f)-6 a c^2 e+2 b^2 c e-3 b^3 f\right)}{2 c^3 \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right) \left(-2 c (a f+b e)+3 b^2 f+c^2 d\right)}{4 c^4}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 c^3 e-12 a b^2 c^2 e-b^3 c (c d-20 a f)+6 a b c^2 (c d-5 a f)+2 b^4 c e-3 b^5 f\right)}{2 c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{x^6 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x^4 \left(-2 c (4 a f+b e)+3 b^2 f+4 c^2 d\right)}{4 c^2 \left(b^2-4 a c\right)}+\frac{x^2 \left(-b c (c d-11 a f)-6 a c^2 e+2 b^2 c e-3 b^3 f\right)}{2 c^3 \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right) \left(-2 c (a f+b e)+3 b^2 f+c^2 d\right)}{4 c^4}",1,"((2*b^2*c*e - 6*a*c^2*e - 3*b^3*f - b*c*(c*d - 11*a*f))*x^2)/(2*c^3*(b^2 - 4*a*c)) + ((4*c^2*d + 3*b^2*f - 2*c*(b*e + 4*a*f))*x^4)/(4*c^2*(b^2 - 4*a*c)) + (x^6*(2*a*c*e - b*(c*d + a*f) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*b^4*c*e - 12*a*b^2*c^2*e + 12*a^2*c^3*e - 3*b^5*f - b^3*c*(c*d - 20*a*f) + 6*a*b*c^2*(c*d - 5*a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^4*(b^2 - 4*a*c)^(3/2)) + ((c^2*d + 3*b^2*f - 2*c*(b*e + a*f))*Log[a + b*x^2 + c*x^4])/(4*c^4)","A",8,7,30,0.2333,1,"{1663, 1644, 800, 634, 618, 206, 628}"
62,1,236,0,0.4402257,"\int \frac{x^5 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^5*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 c^2 f-2 a c \left(6 b^2 f-3 b c e+2 c^2 d\right)+b^3 (-(c e-2 b f))\right)}{2 c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x^2 \left(-c (6 a f+b e)+2 b^2 f+2 c^2 d\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{(c e-2 b f) \log \left(a+b x^2+c x^4\right)}{4 c^3}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 c^2 f-2 a c \left(6 b^2 f-3 b c e+2 c^2 d\right)+b^3 (-(c e-2 b f))\right)}{2 c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x^2 \left(-c (6 a f+b e)+2 b^2 f+2 c^2 d\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{(c e-2 b f) \log \left(a+b x^2+c x^4\right)}{4 c^3}",1,"((2*c^2*d + 2*b^2*f - c*(b*e + 6*a*f))*x^2)/(2*c^2*(b^2 - 4*a*c)) + (x^4*(2*a*c*e - b*(c*d + a*f) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((12*a^2*c^2*f - b^3*(c*e - 2*b*f) - 2*a*c*(2*c^2*d - 3*b*c*e + 6*b^2*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*(b^2 - 4*a*c)^(3/2)) + ((c*e - 2*b*f)*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,7,30,0.2333,1,"{1663, 1644, 773, 634, 618, 206, 628}"
63,1,165,0,0.2869013,"\int \frac{x^3 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^3*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","\frac{x^2 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 b c (3 a f+c d)+4 a c^2 e+b^3 f\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{f \log \left(a+b x^2+c x^4\right)}{4 c^2}","\frac{x^2 \left(x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 b c (3 a f+c d)+4 a c^2 e+b^3 f\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{f \log \left(a+b x^2+c x^4\right)}{4 c^2}",1,"(x^2*(2*a*c*e - b*(c*d + a*f) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((4*a*c^2*e + b^3*f - 2*b*c*(c*d + 3*a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + (f*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",6,6,30,0.2000,1,"{1663, 1644, 634, 618, 206, 628}"
64,1,123,0,0.1837951,"\int \frac{x \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","\frac{x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (2 a f-b e+2 c d)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x^2 \left(-\left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)-b (a f+c d)+2 a c e}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (2 a f-b e+2 c d)}{\left(b^2-4 a c\right)^{3/2}}",1,"(2*a*c*e - b*(c*d + a*f) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((2*c*d - b*e + 2*a*f)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",5,5,28,0.1786,1,"{1663, 1660, 12, 618, 206}"
65,1,166,0,0.3936985,"\int \frac{d+e x^2+f x^4}{x \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(x*(a + b*x^2 + c*x^4)^2),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(4 a^2 c e-2 a b (a f+3 c d)+b^3 d\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{d \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{d \log (x)}{a^2}+\frac{x^2 (a b f-2 a c e+b c d)-a b e-2 a (c d-a f)+b^2 d}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(4 a^2 c e-2 a b (a f+3 c d)+b^3 d\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{d \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{d \log (x)}{a^2}+\frac{x^2 (a b f-2 a c e+b c d)-a b e-2 a (c d-a f)+b^2 d}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(b^2*d - a*b*e - 2*a*(c*d - a*f) + (b*c*d - 2*a*c*e + a*b*f)*x^2)/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^3*d + 4*a^2*c*e - 2*a*b*(3*c*d + a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + (d*Log[x])/a^2 - (d*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",8,7,30,0.2333,1,"{1663, 1646, 800, 634, 618, 206, 628}"
66,1,234,0,0.7250959,"\int \frac{d+e x^2+f x^4}{x^3 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(x^3*(a + b*x^2 + c*x^4)^2),x]","-\frac{2 a^2 c e+c x^2 \left(-a b e-2 a (c d-a f)+b^2 d\right)-a b^2 e-a b (3 c d-a f)+b^3 d}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(6 a^2 b c e+4 a^2 c (3 c d-a f)-12 a b^2 c d-a b^3 e+2 b^4 d\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}+\frac{(2 b d-a e) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 b d-a e)}{a^3}-\frac{d}{2 a^2 x^2}","-\frac{2 a^2 c e+c x^2 \left(-a b e-2 a (c d-a f)+b^2 d\right)-a b^2 e-a b (3 c d-a f)+b^3 d}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(6 a^2 b c e+4 a^2 c (3 c d-a f)-12 a b^2 c d-a b^3 e+2 b^4 d\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}+\frac{(2 b d-a e) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 b d-a e)}{a^3}-\frac{d}{2 a^2 x^2}",1,"-d/(2*a^2*x^2) - (b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f) + c*(b^2*d - a*b*e - 2*a*(c*d - a*f))*x^2)/(2*a^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*b^4*d - 12*a*b^2*c*d - a*b^3*e + 6*a^2*b*c*e + 4*a^2*c*(3*c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(3/2)) - ((2*b*d - a*e)*Log[x])/a^3 + ((2*b*d - a*e)*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",8,7,30,0.2333,1,"{1663, 1646, 1628, 634, 618, 206, 628}"
67,1,329,0,1.1573109,"\int \frac{d+e x^2+f x^4}{x^5 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(x^5*(a + b*x^2 + c*x^4)^2),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 b^2 c e+6 a^2 b c (5 c d-a f)-12 a^3 c^2 e-a b^3 (20 c d-a f)-2 a b^4 e+3 b^5 d\right)}{2 a^4 \left(b^2-4 a c\right)^{3/2}}+\frac{c x^2 \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)+3 a^2 b c e+2 a^2 c (c d-a f)-a b^2 (4 c d-a f)-a b^3 e+b^4 d}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\log \left(a+b x^2+c x^4\right) \left(-2 a b e-a (2 c d-a f)+3 b^2 d\right)}{4 a^4}+\frac{\log (x) \left(-2 a b e-a (2 c d-a f)+3 b^2 d\right)}{a^4}+\frac{2 b d-a e}{2 a^3 x^2}-\frac{d}{4 a^2 x^4}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(12 a^2 b^2 c e+6 a^2 b c (5 c d-a f)-12 a^3 c^2 e-a b^3 (20 c d-a f)-2 a b^4 e+3 b^5 d\right)}{2 a^4 \left(b^2-4 a c\right)^{3/2}}+\frac{c x^2 \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)+3 a^2 b c e+2 a^2 c (c d-a f)-a b^2 (4 c d-a f)-a b^3 e+b^4 d}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\log \left(a+b x^2+c x^4\right) \left(-2 a b e-a (2 c d-a f)+3 b^2 d\right)}{4 a^4}+\frac{\log (x) \left(-2 a b e-a (2 c d-a f)+3 b^2 d\right)}{a^4}+\frac{2 b d-a e}{2 a^3 x^2}-\frac{d}{4 a^2 x^4}",1,"-d/(4*a^2*x^4) + (2*b*d - a*e)/(2*a^3*x^2) + (b^4*d - a*b^3*e + 3*a^2*b*c*e + 2*a^2*c*(c*d - a*f) - a*b^2*(4*c*d - a*f) + c*(b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f))*x^2)/(2*a^3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((3*b^5*d - 2*a*b^4*e + 12*a^2*b^2*c*e - 12*a^3*c^2*e + 6*a^2*b*c*(5*c*d - a*f) - a*b^3*(20*c*d - a*f))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2*d - 2*a*b*e - a*(2*c*d - a*f))*Log[x])/a^4 - ((3*b^2*d - 2*a*b*e - a*(2*c*d - a*f))*Log[a + b*x^2 + c*x^4])/(4*a^4)","A",8,7,30,0.2333,1,"{1663, 1646, 1628, 634, 618, 206, 628}"
68,1,550,0,13.2271952,"\int \frac{x^6 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^6*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{20 a^2 c^3 e-19 a b^2 c^2 e-b^3 c (c d-34 a f)+4 a b c^2 (2 c d-13 a f)+3 b^4 c e-5 b^5 f}{\sqrt{b^2-4 a c}}-b^2 c (c d-24 a f)-13 a b c^2 e+2 a c^2 (3 c d-7 a f)+3 b^3 c e-5 b^4 f\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{20 a^2 c^3 e-19 a b^2 c^2 e-b^3 c (c d-34 a f)+4 a b c^2 (2 c d-13 a f)+3 b^4 c e-5 b^5 f}{\sqrt{b^2-4 a c}}-b^2 c (c d-24 a f)-13 a b c^2 e+2 a c^2 (3 c d-7 a f)+3 b^3 c e-5 b^4 f\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(x^2 \left(-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)+a \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)\right)}{2 c^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x (c e-2 b f)}{c^3}+\frac{f x^3}{3 c^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{20 a^2 c^3 e-19 a b^2 c^2 e-b^3 c (c d-34 a f)+4 a b c^2 (2 c d-13 a f)+3 b^4 c e-5 b^5 f}{\sqrt{b^2-4 a c}}-b^2 c (c d-24 a f)-13 a b c^2 e+2 a c^2 (3 c d-7 a f)+3 b^3 c e-5 b^4 f\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{20 a^2 c^3 e-19 a b^2 c^2 e-b^3 c (c d-34 a f)+4 a b c^2 (2 c d-13 a f)+3 b^4 c e-5 b^5 f}{\sqrt{b^2-4 a c}}-b^2 c (c d-24 a f)-13 a b c^2 e+2 a c^2 (3 c d-7 a f)+3 b^3 c e-5 b^4 f\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(x^2 \left(-b^2 c (c d-4 a f)-3 a b c^2 e+2 a c^2 (c d-a f)+b^3 c e+b^4 (-f)\right)+a \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)\right)}{2 c^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x (c e-2 b f)}{c^3}+\frac{f x^3}{3 c^2}",1,"((c*e - 2*b*f)*x)/c^3 + (f*x^3)/(3*c^2) + (x*(a*(b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f)) + (b^3*c*e - 3*a*b*c^2*e - b^4*f - b^2*c*(c*d - 4*a*f) + 2*a*c^2*(c*d - a*f))*x^2))/(2*c^3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^3*c*e - 13*a*b*c^2*e - 5*b^4*f - b^2*c*(c*d - 24*a*f) + 2*a*c^2*(3*c*d - 7*a*f) - (3*b^4*c*e - 19*a*b^2*c^2*e + 20*a^2*c^3*e - 5*b^5*f - b^3*c*(c*d - 34*a*f) + 4*a*b*c^2*(2*c*d - 13*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(7/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3*c*e - 13*a*b*c^2*e - 5*b^4*f - b^2*c*(c*d - 24*a*f) + 2*a*c^2*(3*c*d - 7*a*f) + (3*b^4*c*e - 19*a*b^2*c^2*e + 20*a^2*c^3*e - 5*b^5*f - b^3*c*(c*d - 34*a*f) + 4*a*b*c^2*(2*c*d - 13*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(7/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,30,0.1333,1,"{1668, 1676, 1166, 205}"
69,1,436,0,5.5411763,"\int \frac{x^4 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^4*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(a \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)-x^2 \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)\right)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{b^2 c (19 a f+c d)-8 a b c^2 e+4 a c^2 (c d-5 a f)+b^3 c e-3 b^4 f}{\sqrt{b^2-4 a c}}+b c (13 a f+c d)-6 a c^2 e+b^2 c e-3 b^3 f\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{b^2 c (19 a f+c d)-8 a b c^2 e+4 a c^2 (c d-5 a f)+b^3 c e-3 b^4 f}{\sqrt{b^2-4 a c}}+b c (13 a f+c d)-6 a c^2 e+b^2 c e-3 b^3 f\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f x}{c^2}","\frac{x \left(a \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)-x^2 \left(-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)\right)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{b^2 c (19 a f+c d)-8 a b c^2 e+4 a c^2 (c d-5 a f)+b^3 c e-3 b^4 f}{\sqrt{b^2-4 a c}}+b c (13 a f+c d)-6 a c^2 e+b^2 c e-3 b^3 f\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{b^2 c (19 a f+c d)-8 a b c^2 e+4 a c^2 (c d-5 a f)+b^3 c e-3 b^4 f}{\sqrt{b^2-4 a c}}+b c (13 a f+c d)-6 a c^2 e+b^2 c e-3 b^3 f\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f x}{c^2}",1,"(f*x)/c^2 + (x*(a*(2*c^2*d - b*c*e + b^2*f - 2*a*c*f) - (b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))*x^2))/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^2*c*e - 6*a*c^2*e - 3*b^3*f + b*c*(c*d + 13*a*f) - (b^3*c*e - 8*a*b*c^2*e - 3*b^4*f + 4*a*c^2*(c*d - 5*a*f) + b^2*c*(c*d + 19*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*c*e - 6*a*c^2*e - 3*b^3*f + b*c*(c*d + 13*a*f) + (b^3*c*e - 8*a*b*c^2*e - 3*b^4*f + 4*a*c^2*(c*d - 5*a*f) + b^2*c*(c*d + 19*a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,30,0.1333,1,"{1668, 1676, 1166, 205}"
70,1,362,0,2.4975128,"\int \frac{x^2 \left(d+e x^2+f x^4\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^2*(d + e*x^2 + f*x^4))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(x^2 \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)+a b f-2 a c e+b c d\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-4 b c (2 a f+c d)+4 a c^2 e+b^2 c e+b^3 f}{c \sqrt{b^2-4 a c}}+6 a f-\frac{b^2 f}{c}-b e+2 c d\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-4 b c (2 a f+c d)+4 a c^2 e+b^2 c e+b^3 f}{c \sqrt{b^2-4 a c}}+6 a f-\frac{b^2 f}{c}-b e+2 c d\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(x^2 \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)+a b f-2 a c e+b c d\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-4 b c (2 a f+c d)+4 a c^2 e+b^2 c e+b^3 f}{c \sqrt{b^2-4 a c}}+6 a f-\frac{b^2 f}{c}-b e+2 c d\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-4 b c (2 a f+c d)+4 a c^2 e+b^2 c e+b^3 f}{c \sqrt{b^2-4 a c}}+6 a f-\frac{b^2 f}{c}-b e+2 c d\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(b*c*d - 2*a*c*e + a*b*f + (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*c*d - b*e + 6*a*f - (b^2*f)/c + (b^2*c*e + 4*a*c^2*e + b^3*f - 4*b*c*(c*d + 2*a*f))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*c*d - b*e + 6*a*f - (b^2*f)/c - (b^2*c*e + 4*a*c^2*e + b^3*f - 4*b*c*(c*d + 2*a*f))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,30,0.1000,1,"{1668, 1166, 205}"
71,1,346,0,1.8964856,"\int \frac{d+e x^2+f x^4}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(x^2 (a b f-2 a c e+b c d)-a b e-2 a (c d-a f)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a f)+4 a b c e-4 a c (a f+3 c d)}{\sqrt{b^2-4 a c}}+a b f-2 a c e+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a f)+4 a b c e-4 a c (a f+3 c d)}{\sqrt{b^2-4 a c}}+a b f-2 a c e+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(x^2 (a b f-2 a c e+b c d)-a b e-2 a (c d-a f)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a f)+4 a b c e-4 a c (a f+3 c d)}{\sqrt{b^2-4 a c}}+a b f-2 a c e+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a f)+4 a b c e-4 a c (a f+3 c d)}{\sqrt{b^2-4 a c}}+a b f-2 a c e+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(b^2*d - a*b*e - 2*a*(c*d - a*f) + (b*c*d - 2*a*c*e + a*b*f)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*c*d - 2*a*c*e + a*b*f + (4*a*b*c*e + b^2*(c*d - a*f) - 4*a*c*(3*c*d + a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*c*d - 2*a*c*e + a*b*f - (4*a*b*c*e + b^2*(c*d - a*f) - 4*a*c*(3*c*d + a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,27,0.1111,1,"{1678, 1166, 205}"
72,1,399,0,2.2029287,"\int \frac{d+e x^2+f x^4}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{x \left(c x^2 \left(-a b e-2 a (c d-a f)+b^2 d\right)+a \left(\frac{b^3 d}{a}+a (b f+2 c e)-b (b e+3 c d)\right)\right)}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{12 a^2 c e-a b^2 e-4 a b (a f+4 c d)+3 b^3 d}{\sqrt{b^2-4 a c}}-a b e-2 a (5 c d-a f)+3 b^2 d\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{12 a^2 c e-a b^2 e-4 a b (a f+4 c d)+3 b^3 d}{\sqrt{b^2-4 a c}}-a b e-2 a (5 c d-a f)+3 b^2 d\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a^2 x}","-\frac{x \left(c x^2 \left(-a b e-2 a (c d-a f)+b^2 d\right)+a \left(\frac{b^3 d}{a}+a (b f+2 c e)-b (b e+3 c d)\right)\right)}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{12 a^2 c e-a b^2 e-4 a b (a f+4 c d)+3 b^3 d}{\sqrt{b^2-4 a c}}-a b e-2 a (5 c d-a f)+3 b^2 d\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{12 a^2 c e-a b^2 e-4 a b (a f+4 c d)+3 b^3 d}{\sqrt{b^2-4 a c}}-a b e-2 a (5 c d-a f)+3 b^2 d\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a^2 x}",1,"-(d/(a^2*x)) - (x*(a*((b^3*d)/a - b*(3*c*d + b*e) + a*(2*c*e + b*f)) + c*(b^2*d - a*b*e - 2*a*(c*d - a*f))*x^2))/(2*a^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (Sqrt[c]*(3*b^2*d - a*b*e - 2*a*(5*c*d - a*f) + (3*b^3*d - a*b^2*e + 12*a^2*c*e - 4*a*b*(4*c*d + a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(3*b^2*d - a*b*e - 2*a*(5*c*d - a*f) - (3*b^3*d - a*b^2*e + 12*a^2*c*e - 4*a*b*(4*c*d + a*f))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,30,0.1333,1,"{1669, 1664, 1166, 205}"
73,1,575,0,9.905648,"\int \frac{d+e x^2+f x^4}{x^4 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4)/(x^4*(a + b*x^2 + c*x^4)^2),x]","\frac{x \left(a^2 \left(\frac{b^4 d}{a^2}-\frac{b^2 (b e+4 c d)}{a}-2 a c f+b^2 f+3 b c e+2 c^2 d\right)+c x^2 \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)\right)}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(2 a^2 c \left(5 e \sqrt{b^2-4 a c}-6 a f+14 c d\right)-a b^2 \left(3 e \sqrt{b^2-4 a c}-a f+29 c d\right)-a b \left(19 c d \sqrt{b^2-4 a c}-a f \sqrt{b^2-4 a c}-16 a c e\right)+b^3 \left(5 d \sqrt{b^2-4 a c}-3 a e\right)+5 b^4 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(2 a^2 c \left(-5 e \sqrt{b^2-4 a c}-6 a f+14 c d\right)-a b^2 \left(-3 e \sqrt{b^2-4 a c}-a f+29 c d\right)+a b \left(19 c d \sqrt{b^2-4 a c}-a f \sqrt{b^2-4 a c}+16 a c e\right)-b^3 \left(5 d \sqrt{b^2-4 a c}+3 a e\right)+5 b^4 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 b d-a e}{a^3 x}-\frac{d}{3 a^2 x^3}","\frac{x \left(a^2 \left(\frac{b^4 d}{a^2}-\frac{b^2 (b e+4 c d)}{a}-2 a c f+b^2 f+3 b c e+2 c^2 d\right)+c x^2 \left(2 a^2 c e-a b^2 e-a b (3 c d-a f)+b^3 d\right)\right)}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(2 a^2 c \left(5 e \sqrt{b^2-4 a c}-6 a f+14 c d\right)-a b^2 \left(3 e \sqrt{b^2-4 a c}-a f+29 c d\right)-a b \left(19 c d \sqrt{b^2-4 a c}-a f \sqrt{b^2-4 a c}-16 a c e\right)+b^3 \left(5 d \sqrt{b^2-4 a c}-3 a e\right)+5 b^4 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(2 a^2 c \left(-5 e \sqrt{b^2-4 a c}-6 a f+14 c d\right)-a b^2 \left(-3 e \sqrt{b^2-4 a c}-a f+29 c d\right)+a b \left(19 c d \sqrt{b^2-4 a c}-a f \sqrt{b^2-4 a c}+16 a c e\right)-b^3 \left(5 d \sqrt{b^2-4 a c}+3 a e\right)+5 b^4 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 b d-a e}{a^3 x}-\frac{d}{3 a^2 x^3}",1,"-d/(3*a^2*x^3) + (2*b*d - a*e)/(a^3*x) + (x*(a^2*((b^4*d)/a^2 + 2*c^2*d + 3*b*c*e - (b^2*(4*c*d + b*e))/a + b^2*f - 2*a*c*f) + c*(b^3*d - a*b^2*e + 2*a^2*c*e - a*b*(3*c*d - a*f))*x^2))/(2*a^3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(5*b^4*d + b^3*(5*Sqrt[b^2 - 4*a*c]*d - 3*a*e) + 2*a^2*c*(14*c*d + 5*Sqrt[b^2 - 4*a*c]*e - 6*a*f) - a*b^2*(29*c*d + 3*Sqrt[b^2 - 4*a*c]*e - a*f) - a*b*(19*c*Sqrt[b^2 - 4*a*c]*d - 16*a*c*e - a*Sqrt[b^2 - 4*a*c]*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(5*b^4*d - b^3*(5*Sqrt[b^2 - 4*a*c]*d + 3*a*e) + 2*a^2*c*(14*c*d - 5*Sqrt[b^2 - 4*a*c]*e - 6*a*f) - a*b^2*(29*c*d - 3*Sqrt[b^2 - 4*a*c]*e - a*f) + a*b*(19*c*Sqrt[b^2 - 4*a*c]*d + 16*a*c*e - a*Sqrt[b^2 - 4*a*c]*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,30,0.1333,1,"{1669, 1664, 1166, 205}"
74,1,68,0,0.1260488,"\int \frac{x^9 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^9*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^8}{8}-\frac{9 x^6}{2}+\frac{49 x^4}{2}-\frac{293 x^2}{2}+\frac{415 x^2+414}{2 \left(x^4+3 x^2+2\right)}+2 \log \left(x^2+1\right)+392 \log \left(x^2+2\right)","\frac{5 x^8}{8}-\frac{9 x^6}{2}+\frac{49 x^4}{2}-\frac{293 x^2}{2}+\frac{415 x^2+414}{2 \left(x^4+3 x^2+2\right)}+2 \log \left(x^2+1\right)+392 \log \left(x^2+2\right)",1,"(-293*x^2)/2 + (49*x^4)/2 - (9*x^6)/2 + (5*x^8)/8 + (414 + 415*x^2)/(2*(2 + 3*x^2 + x^4)) + 2*Log[1 + x^2] + 392*Log[2 + x^2]","A",7,5,31,0.1613,1,"{1663, 1660, 1657, 632, 31}"
75,1,61,0,0.1175392,"\int \frac{x^7 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^7*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^6}{6}-\frac{27 x^4}{4}+49 x^2-\frac{207 x^2+206}{2 \left(x^4+3 x^2+2\right)}-\frac{5}{2} \log \left(x^2+1\right)-144 \log \left(x^2+2\right)","\frac{5 x^6}{6}-\frac{27 x^4}{4}+49 x^2-\frac{207 x^2+206}{2 \left(x^4+3 x^2+2\right)}-\frac{5}{2} \log \left(x^2+1\right)-144 \log \left(x^2+2\right)",1,"49*x^2 - (27*x^4)/4 + (5*x^6)/6 - (206 + 207*x^2)/(2*(2 + 3*x^2 + x^4)) - (5*Log[1 + x^2])/2 - 144*Log[2 + x^2]","A",7,5,31,0.1613,1,"{1663, 1660, 1657, 632, 31}"
76,1,54,0,0.1083654,"\int \frac{x^5 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^5*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^4}{4}-\frac{27 x^2}{2}+\frac{103 x^2+102}{2 \left(x^4+3 x^2+2\right)}+3 \log \left(x^2+1\right)+46 \log \left(x^2+2\right)","\frac{5 x^4}{4}-\frac{27 x^2}{2}+\frac{103 x^2+102}{2 \left(x^4+3 x^2+2\right)}+3 \log \left(x^2+1\right)+46 \log \left(x^2+2\right)",1,"(-27*x^2)/2 + (5*x^4)/4 + (102 + 103*x^2)/(2*(2 + 3*x^2 + x^4)) + 3*Log[1 + x^2] + 46*Log[2 + x^2]","A",7,5,31,0.1613,1,"{1663, 1660, 1657, 632, 31}"
77,1,49,0,0.0856682,"\int \frac{x^3 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^3*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^2}{2}-\frac{51 x^2+50}{2 \left(x^4+3 x^2+2\right)}-\frac{7}{2} \log \left(x^2+1\right)-10 \log \left(x^2+2\right)","\frac{5 x^2}{2}-\frac{51 x^2+50}{2 \left(x^4+3 x^2+2\right)}-\frac{7}{2} \log \left(x^2+1\right)-10 \log \left(x^2+2\right)",1,"(5*x^2)/2 - (50 + 51*x^2)/(2*(2 + 3*x^2 + x^4)) - (7*Log[1 + x^2])/2 - 10*Log[2 + x^2]","A",7,5,31,0.1613,1,"{1663, 1660, 1657, 632, 31}"
78,1,42,0,0.0491766,"\int \frac{x \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{25 x^2+24}{2 \left(x^4+3 x^2+2\right)}+4 \log \left(x^2+1\right)-\frac{3}{2} \log \left(x^2+2\right)","\frac{25 x^2+24}{2 \left(x^4+3 x^2+2\right)}+4 \log \left(x^2+1\right)-\frac{3}{2} \log \left(x^2+2\right)",1,"(24 + 25*x^2)/(2*(2 + 3*x^2 + x^4)) + 4*Log[1 + x^2] - (3*Log[2 + x^2])/2","A",5,4,29,0.1379,1,"{1663, 1660, 632, 31}"
79,1,44,0,0.0766938,"\int \frac{4+x^2+3 x^4+5 x^6}{x \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x*(2 + 3*x^2 + x^4)^2),x]","-\frac{12 x^2+11}{2 \left(x^4+3 x^2+2\right)}-\frac{9}{2} \log \left(x^2+1\right)+4 \log \left(x^2+2\right)+\log (x)","-\frac{12 x^2+11}{2 \left(x^4+3 x^2+2\right)}-\frac{9}{2} \log \left(x^2+1\right)+4 \log \left(x^2+2\right)+\log (x)",1,"-(11 + 12*x^2)/(2*(2 + 3*x^2 + x^4)) + Log[x] - (9*Log[1 + x^2])/2 + 4*Log[2 + x^2]","A",4,3,31,0.09677,1,"{1663, 1646, 800}"
80,1,55,0,0.1043227,"\int \frac{4+x^2+3 x^4+5 x^6}{x^3 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^3*(2 + 3*x^2 + x^4)^2),x]","\frac{11 x^2+9}{4 \left(x^4+3 x^2+2\right)}-\frac{1}{2 x^2}+5 \log \left(x^2+1\right)-\frac{29}{8} \log \left(x^2+2\right)-\frac{11 \log (x)}{4}","\frac{11 x^2+9}{4 \left(x^4+3 x^2+2\right)}-\frac{1}{2 x^2}+5 \log \left(x^2+1\right)-\frac{29}{8} \log \left(x^2+2\right)-\frac{11 \log (x)}{4}",1,"-1/(2*x^2) + (9 + 11*x^2)/(4*(2 + 3*x^2 + x^4)) - (11*Log[x])/4 + 5*Log[1 + x^2] - (29*Log[2 + x^2])/8","A",4,3,31,0.09677,1,"{1663, 1646, 1628}"
81,1,64,0,0.110765,"\int \frac{4+x^2+3 x^4+5 x^6}{x^5 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^5*(2 + 3*x^2 + x^4)^2),x]","-\frac{9 x^2+5}{8 \left(x^4+3 x^2+2\right)}+\frac{11}{8 x^2}-\frac{1}{4 x^4}-\frac{11}{2} \log \left(x^2+1\right)+\frac{21}{8} \log \left(x^2+2\right)+\frac{23 \log (x)}{4}","-\frac{9 x^2+5}{8 \left(x^4+3 x^2+2\right)}+\frac{11}{8 x^2}-\frac{1}{4 x^4}-\frac{11}{2} \log \left(x^2+1\right)+\frac{21}{8} \log \left(x^2+2\right)+\frac{23 \log (x)}{4}",1,"-1/(4*x^4) + 11/(8*x^2) - (5 + 9*x^2)/(8*(2 + 3*x^2 + x^4)) + (23*Log[x])/4 - (11*Log[1 + x^2])/2 + (21*Log[2 + x^2])/8","A",4,3,31,0.09677,1,"{1663, 1646, 1628}"
82,1,70,0,0.0845314,"\int \frac{x^8 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^8*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^7}{7}-\frac{27 x^5}{5}+\frac{98 x^3}{3}-\frac{\left(207 x^2+206\right) x}{2 \left(x^4+3 x^2+2\right)}-293 x+\frac{9}{2} \tan ^{-1}(x)+340 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{5 x^7}{7}-\frac{27 x^5}{5}+\frac{98 x^3}{3}-\frac{\left(207 x^2+206\right) x}{2 \left(x^4+3 x^2+2\right)}-293 x+\frac{9}{2} \tan ^{-1}(x)+340 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"-293*x + (98*x^3)/3 - (27*x^5)/5 + (5*x^7)/7 - (x*(206 + 207*x^2))/(2*(2 + 3*x^2 + x^4)) + (9*ArcTan[x])/2 + 340*Sqrt[2]*ArcTan[x/Sqrt[2]]","A",6,4,31,0.1290,1,"{1668, 1676, 1166, 203}"
83,1,57,0,0.0821456,"\int \frac{x^6 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^6*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","x^5-9 x^3+\frac{\left(103 x^2+102\right) x}{2 \left(x^4+3 x^2+2\right)}+98 x-\frac{11}{2} \tan ^{-1}(x)-118 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","x^5-9 x^3+\frac{\left(103 x^2+102\right) x}{2 \left(x^4+3 x^2+2\right)}+98 x-\frac{11}{2} \tan ^{-1}(x)-118 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"98*x - 9*x^3 + x^5 + (x*(102 + 103*x^2))/(2*(2 + 3*x^2 + x^4)) - (11*ArcTan[x])/2 - 118*Sqrt[2]*ArcTan[x/Sqrt[2]]","A",6,4,31,0.1290,1,"{1668, 1676, 1166, 203}"
84,1,56,0,0.0727921,"\int \frac{x^4 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^4*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{5 x^3}{3}-\frac{\left(51 x^2+50\right) x}{2 \left(x^4+3 x^2+2\right)}-27 x+\frac{13}{2} \tan ^{-1}(x)+33 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{5 x^3}{3}-\frac{\left(51 x^2+50\right) x}{2 \left(x^4+3 x^2+2\right)}-27 x+\frac{13}{2} \tan ^{-1}(x)+33 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"-27*x + (5*x^3)/3 - (x*(50 + 51*x^2))/(2*(2 + 3*x^2 + x^4)) + (13*ArcTan[x])/2 + 33*Sqrt[2]*ArcTan[x/Sqrt[2]]","A",6,4,31,0.1290,1,"{1668, 1676, 1166, 203}"
85,1,49,0,0.0663581,"\int \frac{x^2 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(x^2*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^2,x]","\frac{\left(25 x^2+24\right) x}{2 \left(x^4+3 x^2+2\right)}+5 x-\frac{15}{2} \tan ^{-1}(x)-\frac{7 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\left(25 x^2+24\right) x}{2 \left(x^4+3 x^2+2\right)}+5 x-\frac{15}{2} \tan ^{-1}(x)-\frac{7 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"5*x + (x*(24 + 25*x^2))/(2*(2 + 3*x^2 + x^4)) - (15*ArcTan[x])/2 - (7*ArcTan[x/Sqrt[2]])/Sqrt[2]","A",6,4,31,0.1290,1,"{1668, 1676, 1166, 203}"
86,1,48,0,0.0280516,"\int \frac{4+x^2+3 x^4+5 x^6}{\left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(2 + 3*x^2 + x^4)^2,x]","-\frac{x \left(12 x^2+11\right)}{2 \left(x^4+3 x^2+2\right)}+\frac{17}{2} \tan ^{-1}(x)-\frac{19 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}","-\frac{x \left(12 x^2+11\right)}{2 \left(x^4+3 x^2+2\right)}+\frac{17}{2} \tan ^{-1}(x)-\frac{19 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"-(x*(11 + 12*x^2))/(2*(2 + 3*x^2 + x^4)) + (17*ArcTan[x])/2 - (19*ArcTan[x/Sqrt[2]])/(2*Sqrt[2])","A",4,3,28,0.1071,1,"{1678, 1166, 203}"
87,1,53,0,0.0729781,"\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^2*(2 + 3*x^2 + x^4)^2),x]","\frac{x \left(11 x^2+9\right)}{4 \left(x^4+3 x^2+2\right)}-\frac{1}{x}-\frac{19}{2} \tan ^{-1}(x)+\frac{45 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{x \left(11 x^2+9\right)}{4 \left(x^4+3 x^2+2\right)}-\frac{1}{x}-\frac{19}{2} \tan ^{-1}(x)+\frac{45 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"-x^(-1) + (x*(9 + 11*x^2))/(4*(2 + 3*x^2 + x^4)) - (19*ArcTan[x])/2 + (45*ArcTan[x/Sqrt[2]])/(4*Sqrt[2])","A",5,3,31,0.09677,1,"{1669, 1664, 203}"
88,1,62,0,0.0842406,"\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^4*(2 + 3*x^2 + x^4)^2),x]","-\frac{x \left(9 x^2+5\right)}{8 \left(x^4+3 x^2+2\right)}-\frac{1}{3 x^3}+\frac{11}{4 x}+\frac{21}{2} \tan ^{-1}(x)-\frac{71 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{8 \sqrt{2}}","-\frac{x \left(9 x^2+5\right)}{8 \left(x^4+3 x^2+2\right)}-\frac{1}{3 x^3}+\frac{11}{4 x}+\frac{21}{2} \tan ^{-1}(x)-\frac{71 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"-1/(3*x^3) + 11/(4*x) - (x*(5 + 9*x^2))/(8*(2 + 3*x^2 + x^4)) + (21*ArcTan[x])/2 - (71*ArcTan[x/Sqrt[2]])/(8*Sqrt[2])","A",5,3,31,0.09677,1,"{1669, 1664, 203}"
89,1,69,0,0.0904842,"\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^6*(2 + 3*x^2 + x^4)^2),x]","-\frac{x \left(3-5 x^2\right)}{16 \left(x^4+3 x^2+2\right)}+\frac{11}{12 x^3}-\frac{1}{5 x^5}-\frac{23}{4 x}-\frac{23}{2} \tan ^{-1}(x)+\frac{97 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{16 \sqrt{2}}","-\frac{x \left(3-5 x^2\right)}{16 \left(x^4+3 x^2+2\right)}+\frac{11}{12 x^3}-\frac{1}{5 x^5}-\frac{23}{4 x}-\frac{23}{2} \tan ^{-1}(x)+\frac{97 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{16 \sqrt{2}}",1,"-1/(5*x^5) + 11/(12*x^3) - 23/(4*x) - (x*(3 - 5*x^2))/(16*(2 + 3*x^2 + x^4)) - (23*ArcTan[x])/2 + (97*ArcTan[x/Sqrt[2]])/(16*Sqrt[2])","A",5,3,31,0.09677,1,"{1669, 1664, 203}"
90,1,76,0,0.0999244,"\int \frac{4+x^2+3 x^4+5 x^6}{x^8 \left(2+3 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^8*(2 + 3*x^2 + x^4)^2),x]","\frac{x \left(3 x^2+19\right)}{32 \left(x^4+3 x^2+2\right)}-\frac{23}{12 x^3}+\frac{11}{20 x^5}-\frac{1}{7 x^7}+\frac{137}{16 x}+\frac{25}{2} \tan ^{-1}(x)-\frac{123 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{32 \sqrt{2}}","\frac{x \left(3 x^2+19\right)}{32 \left(x^4+3 x^2+2\right)}-\frac{23}{12 x^3}+\frac{11}{20 x^5}-\frac{1}{7 x^7}+\frac{137}{16 x}+\frac{25}{2} \tan ^{-1}(x)-\frac{123 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{32 \sqrt{2}}",1,"-1/(7*x^7) + 11/(20*x^5) - 23/(12*x^3) + 137/(16*x) + (x*(19 + 3*x^2))/(32*(2 + 3*x^2 + x^4)) + (25*ArcTan[x])/2 - (123*ArcTan[x/Sqrt[2]])/(32*Sqrt[2])","A",5,3,31,0.09677,1,"{1669, 1664, 203}"
91,1,81,0,0.1124916,"\int \frac{x^{10} \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(x^10*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^3,x]","x^5-14 x^3+\frac{\left(1669 x^2+824\right) x}{8 \left(x^4+3 x^2+2\right)}+\frac{\left(415 x^2+414\right) x}{4 \left(x^4+3 x^2+2\right)^2}+214 x+\frac{477}{8} \tan ^{-1}(x)-351 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","x^5-14 x^3+\frac{\left(1669 x^2+824\right) x}{8 \left(x^4+3 x^2+2\right)}+\frac{\left(415 x^2+414\right) x}{4 \left(x^4+3 x^2+2\right)^2}+214 x+\frac{477}{8} \tan ^{-1}(x)-351 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"214*x - 14*x^3 + x^5 + (x*(414 + 415*x^2))/(4*(2 + 3*x^2 + x^4)^2) + (x*(824 + 1669*x^2))/(8*(2 + 3*x^2 + x^4)) + (477*ArcTan[x])/8 - 351*Sqrt[2]*ArcTan[x/Sqrt[2]]","A",7,5,31,0.1613,1,"{1668, 1678, 1676, 1166, 203}"
92,1,80,0,0.1004812,"\int \frac{x^8 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(x^8*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^3,x]","\frac{5 x^3}{3}+\frac{\left(24-409 x^2\right) x}{8 \left(x^4+3 x^2+2\right)}-\frac{\left(207 x^2+206\right) x}{4 \left(x^4+3 x^2+2\right)^2}-42 x-\frac{449}{8} \tan ^{-1}(x)+\frac{219 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{5 x^3}{3}+\frac{\left(24-409 x^2\right) x}{8 \left(x^4+3 x^2+2\right)}-\frac{\left(207 x^2+206\right) x}{4 \left(x^4+3 x^2+2\right)^2}-42 x-\frac{449}{8} \tan ^{-1}(x)+\frac{219 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-42*x + (5*x^3)/3 - (x*(206 + 207*x^2))/(4*(2 + 3*x^2 + x^4)^2) + (x*(24 - 409*x^2))/(8*(2 + 3*x^2 + x^4)) - (449*ArcTan[x])/8 + (219*ArcTan[x/Sqrt[2]])/Sqrt[2]","A",7,5,31,0.1613,1,"{1668, 1678, 1676, 1166, 203}"
93,1,75,0,0.0913924,"\int \frac{x^6 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(x^6*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^3,x]","-\frac{\left(15 x^2+244\right) x}{8 \left(x^4+3 x^2+2\right)}+\frac{\left(103 x^2+102\right) x}{4 \left(x^4+3 x^2+2\right)^2}+5 x+\frac{413}{8} \tan ^{-1}(x)-\frac{191 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}","-\frac{\left(15 x^2+244\right) x}{8 \left(x^4+3 x^2+2\right)}+\frac{\left(103 x^2+102\right) x}{4 \left(x^4+3 x^2+2\right)^2}+5 x+\frac{413}{8} \tan ^{-1}(x)-\frac{191 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"5*x + (x*(102 + 103*x^2))/(4*(2 + 3*x^2 + x^4)^2) - (x*(244 + 15*x^2))/(8*(2 + 3*x^2 + x^4)) + (413*ArcTan[x])/8 - (191*ArcTan[x/Sqrt[2]])/(2*Sqrt[2])","A",7,5,31,0.1613,1,"{1668, 1678, 1676, 1166, 203}"
94,1,72,0,0.0678667,"\int \frac{x^4 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(x^4*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^3,x]","-\frac{x \left(51 x^2+50\right)}{4 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(125 x^2+254\right)}{8 \left(x^4+3 x^2+2\right)}-\frac{369}{8} \tan ^{-1}(x)+\frac{267 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}","-\frac{x \left(51 x^2+50\right)}{4 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(125 x^2+254\right)}{8 \left(x^4+3 x^2+2\right)}-\frac{369}{8} \tan ^{-1}(x)+\frac{267 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"-(x*(50 + 51*x^2))/(4*(2 + 3*x^2 + x^4)^2) + (x*(254 + 125*x^2))/(8*(2 + 3*x^2 + x^4)) - (369*ArcTan[x])/8 + (267*ArcTan[x/Sqrt[2]])/(4*Sqrt[2])","A",5,4,31,0.1290,1,"{1668, 1678, 1166, 203}"
95,1,72,0,0.0655951,"\int \frac{x^2 \left(4+x^2+3 x^4+5 x^6\right)}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(x^2*(4 + x^2 + 3*x^4 + 5*x^6))/(2 + 3*x^2 + x^4)^3,x]","\frac{x \left(25 x^2+24\right)}{4 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(130 x^2+211\right)}{8 \left(x^4+3 x^2+2\right)}+\frac{317}{8} \tan ^{-1}(x)-\frac{447 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{x \left(25 x^2+24\right)}{4 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(130 x^2+211\right)}{8 \left(x^4+3 x^2+2\right)}+\frac{317}{8} \tan ^{-1}(x)-\frac{447 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(x*(24 + 25*x^2))/(4*(2 + 3*x^2 + x^4)^2) - (x*(211 + 130*x^2))/(8*(2 + 3*x^2 + x^4)) + (317*ArcTan[x])/8 - (447*ArcTan[x/Sqrt[2]])/(8*Sqrt[2])","A",5,4,31,0.1290,1,"{1668, 1678, 1166, 203}"
96,1,72,0,0.037454,"\int \frac{4+x^2+3 x^4+5 x^6}{\left(2+3 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(2 + 3*x^2 + x^4)^3,x]","-\frac{x \left(12 x^2+11\right)}{4 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(217 x^2+335\right)}{16 \left(x^4+3 x^2+2\right)}-\frac{257}{8} \tan ^{-1}(x)+\frac{731 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{16 \sqrt{2}}","-\frac{x \left(12 x^2+11\right)}{4 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(217 x^2+335\right)}{16 \left(x^4+3 x^2+2\right)}-\frac{257}{8} \tan ^{-1}(x)+\frac{731 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{16 \sqrt{2}}",1,"-(x*(11 + 12*x^2))/(4*(2 + 3*x^2 + x^4)^2) + (x*(335 + 217*x^2))/(16*(2 + 3*x^2 + x^4)) - (257*ArcTan[x])/8 + (731*ArcTan[x/Sqrt[2]])/(16*Sqrt[2])","A",5,4,28,0.1429,1,"{1678, 1178, 1166, 203}"
97,1,79,0,0.1031809,"\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left(2+3 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^2*(2 + 3*x^2 + x^4)^3),x]","\frac{x \left(11 x^2+9\right)}{8 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(347 x^2+547\right)}{32 \left(x^4+3 x^2+2\right)}-\frac{1}{2 x}+\frac{189}{8} \tan ^{-1}(x)-\frac{1119 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{32 \sqrt{2}}","\frac{x \left(11 x^2+9\right)}{8 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(347 x^2+547\right)}{32 \left(x^4+3 x^2+2\right)}-\frac{1}{2 x}+\frac{189}{8} \tan ^{-1}(x)-\frac{1119 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{32 \sqrt{2}}",1,"-1/(2*x) + (x*(9 + 11*x^2))/(8*(2 + 3*x^2 + x^4)^2) - (x*(547 + 347*x^2))/(32*(2 + 3*x^2 + x^4)) + (189*ArcTan[x])/8 - (1119*ArcTan[x/Sqrt[2]])/(32*Sqrt[2])","A",6,3,31,0.09677,1,"{1669, 1664, 203}"
98,1,86,0,0.1188853,"\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left(2+3 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^4*(2 + 3*x^2 + x^4)^3),x]","-\frac{x \left(9 x^2+5\right)}{16 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(571 x^2+951\right)}{64 \left(x^4+3 x^2+2\right)}-\frac{1}{6 x^3}+\frac{17}{8 x}-\frac{113}{8} \tan ^{-1}(x)+\frac{1611 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{64 \sqrt{2}}","-\frac{x \left(9 x^2+5\right)}{16 \left(x^4+3 x^2+2\right)^2}+\frac{x \left(571 x^2+951\right)}{64 \left(x^4+3 x^2+2\right)}-\frac{1}{6 x^3}+\frac{17}{8 x}-\frac{113}{8} \tan ^{-1}(x)+\frac{1611 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{64 \sqrt{2}}",1,"-1/(6*x^3) + 17/(8*x) - (x*(5 + 9*x^2))/(16*(2 + 3*x^2 + x^4)^2) + (x*(951 + 571*x^2))/(64*(2 + 3*x^2 + x^4)) - (113*ArcTan[x])/8 + (1611*ArcTan[x/Sqrt[2]])/(64*Sqrt[2])","A",6,3,31,0.09677,1,"{1669, 1664, 203}"
99,1,93,0,0.1342057,"\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left(2+3 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^6*(2 + 3*x^2 + x^4)^3),x]","-\frac{x \left(3-5 x^2\right)}{32 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(999 x^2+1771\right)}{128 \left(x^4+3 x^2+2\right)}+\frac{17}{24 x^3}-\frac{1}{10 x^5}-\frac{93}{16 x}+\frac{29}{8} \tan ^{-1}(x)-\frac{2207 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{128 \sqrt{2}}","-\frac{x \left(3-5 x^2\right)}{32 \left(x^4+3 x^2+2\right)^2}-\frac{x \left(999 x^2+1771\right)}{128 \left(x^4+3 x^2+2\right)}+\frac{17}{24 x^3}-\frac{1}{10 x^5}-\frac{93}{16 x}+\frac{29}{8} \tan ^{-1}(x)-\frac{2207 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{128 \sqrt{2}}",1,"-1/(10*x^5) + 17/(24*x^3) - 93/(16*x) - (x*(3 - 5*x^2))/(32*(2 + 3*x^2 + x^4)^2) - (x*(1771 + 999*x^2))/(128*(2 + 3*x^2 + x^4)) + (29*ArcTan[x])/8 - (2207*ArcTan[x/Sqrt[2]])/(128*Sqrt[2])","A",6,3,31,0.09677,1,"{1669, 1664, 203}"
100,1,86,0,0.135313,"\int \frac{x^9 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^9*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^8}{8}-\frac{17 x^6}{6}+\frac{19 x^4}{4}+19 x^2-\frac{25 \left(7 x^2+15\right)}{8 \left(x^4+2 x^2+3\right)}-\frac{183}{4} \log \left(x^4+2 x^2+3\right)+\frac{201 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{5 x^8}{8}-\frac{17 x^6}{6}+\frac{19 x^4}{4}+19 x^2-\frac{25 \left(7 x^2+15\right)}{8 \left(x^4+2 x^2+3\right)}-\frac{183}{4} \log \left(x^4+2 x^2+3\right)+\frac{201 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"19*x^2 + (19*x^4)/4 - (17*x^6)/6 + (5*x^8)/8 - (25*(15 + 7*x^2))/(8*(3 + 2*x^2 + x^4)) + (201*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2]) - (183*Log[3 + 2*x^2 + x^4])/4","A",8,7,31,0.2258,1,"{1663, 1660, 1657, 634, 618, 204, 628}"
101,1,81,0,0.1273605,"\int \frac{x^7 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^7*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^6}{6}-\frac{17 x^4}{4}+\frac{19 x^2}{2}+\frac{25 \left(5 x^2+3\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{19}{2} \log \left(x^4+2 x^2+3\right)-\frac{455 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{5 x^6}{6}-\frac{17 x^4}{4}+\frac{19 x^2}{2}+\frac{25 \left(5 x^2+3\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{19}{2} \log \left(x^4+2 x^2+3\right)-\frac{455 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(19*x^2)/2 - (17*x^4)/4 + (5*x^6)/6 + (25*(3 + 5*x^2))/(8*(3 + 2*x^2 + x^4)) - (455*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2]) + (19*Log[3 + 2*x^2 + x^4])/2","A",8,7,31,0.2258,1,"{1663, 1660, 1657, 634, 618, 204, 628}"
102,1,74,0,0.1208685,"\int \frac{x^5 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^5*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^4}{4}-\frac{17 x^2}{2}+\frac{25 \left(3-x^2\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{19}{4} \log \left(x^4+2 x^2+3\right)+\frac{203 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{5 x^4}{4}-\frac{17 x^2}{2}+\frac{25 \left(3-x^2\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{19}{4} \log \left(x^4+2 x^2+3\right)+\frac{203 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(-17*x^2)/2 + (5*x^4)/4 + (25*(3 - x^2))/(8*(3 + 2*x^2 + x^4)) + (203*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2]) + (19*Log[3 + 2*x^2 + x^4])/4","A",8,7,31,0.2258,1,"{1663, 1660, 1657, 634, 618, 204, 628}"
103,1,65,0,0.105306,"\int \frac{x^3 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^3*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^2}{2}-\frac{25 \left(x^2+3\right)}{8 \left(x^4+2 x^2+3\right)}-\frac{17}{4} \log \left(x^4+2 x^2+3\right)-\frac{17 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{5 x^2}{2}-\frac{25 \left(x^2+3\right)}{8 \left(x^4+2 x^2+3\right)}-\frac{17}{4} \log \left(x^4+2 x^2+3\right)-\frac{17 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(5*x^2)/2 - (25*(3 + x^2))/(8*(3 + 2*x^2 + x^4)) - (17*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2]) - (17*Log[3 + 2*x^2 + x^4])/4","A",8,7,31,0.2258,1,"{1663, 1660, 1657, 634, 618, 204, 628}"
104,1,58,0,0.0669888,"\int \frac{x \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{25 \left(x^2+1\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{5}{4} \log \left(x^4+2 x^2+3\right)-\frac{23 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{25 \left(x^2+1\right)}{8 \left(x^4+2 x^2+3\right)}+\frac{5}{4} \log \left(x^4+2 x^2+3\right)-\frac{23 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(25*(1 + x^2))/(8*(3 + 2*x^2 + x^4)) - (23*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2]) + (5*Log[3 + 2*x^2 + x^4])/4","A",6,6,29,0.2069,1,"{1663, 1660, 634, 618, 204, 628}"
105,1,66,0,0.1080789,"\int \frac{4+x^2+3 x^4+5 x^6}{x \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x*(3 + 2*x^2 + x^4)^2),x]","\frac{25 \left(1-x^2\right)}{24 \left(x^4+2 x^2+3\right)}-\frac{1}{9} \log \left(x^4+2 x^2+3\right)+\frac{89 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{72 \sqrt{2}}+\frac{4 \log (x)}{9}","\frac{25 \left(1-x^2\right)}{24 \left(x^4+2 x^2+3\right)}-\frac{1}{9} \log \left(x^4+2 x^2+3\right)+\frac{89 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{72 \sqrt{2}}+\frac{4 \log (x)}{9}",1,"(25*(1 - x^2))/(24*(3 + 2*x^2 + x^4)) + (89*ArcTan[(1 + x^2)/Sqrt[2]])/(72*Sqrt[2]) + (4*Log[x])/9 - Log[3 + 2*x^2 + x^4]/9","A",8,7,31,0.2258,1,"{1663, 1646, 800, 634, 618, 204, 628}"
106,1,71,0,0.1338111,"\int \frac{4+x^2+3 x^4+5 x^6}{x^3 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^3*(3 + 2*x^2 + x^4)^2),x]","-\frac{25 \left(x^2+5\right)}{72 \left(x^4+2 x^2+3\right)}-\frac{2}{9 x^2}+\frac{13}{108} \log \left(x^4+2 x^2+3\right)-\frac{71 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{216 \sqrt{2}}-\frac{13 \log (x)}{27}","-\frac{25 \left(x^2+5\right)}{72 \left(x^4+2 x^2+3\right)}-\frac{2}{9 x^2}+\frac{13}{108} \log \left(x^4+2 x^2+3\right)-\frac{71 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{216 \sqrt{2}}-\frac{13 \log (x)}{27}",1,"-2/(9*x^2) - (25*(5 + x^2))/(72*(3 + 2*x^2 + x^4)) - (71*ArcTan[(1 + x^2)/Sqrt[2]])/(216*Sqrt[2]) - (13*Log[x])/27 + (13*Log[3 + 2*x^2 + x^4])/108","A",8,7,31,0.2258,1,"{1663, 1646, 1628, 634, 618, 204, 628}"
107,1,80,0,0.1367484,"\int \frac{4+x^2+3 x^4+5 x^6}{x^5 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^5*(3 + 2*x^2 + x^4)^2),x]","\frac{25 \left(5 x^2+7\right)}{216 \left(x^4+2 x^2+3\right)}+\frac{13}{54 x^2}-\frac{1}{9 x^4}-\frac{13}{108} \log \left(x^4+2 x^2+3\right)+\frac{125 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{216 \sqrt{2}}+\frac{13 \log (x)}{27}","\frac{25 \left(5 x^2+7\right)}{216 \left(x^4+2 x^2+3\right)}+\frac{13}{54 x^2}-\frac{1}{9 x^4}-\frac{13}{108} \log \left(x^4+2 x^2+3\right)+\frac{125 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{216 \sqrt{2}}+\frac{13 \log (x)}{27}",1,"-1/(9*x^4) + 13/(54*x^2) + (25*(7 + 5*x^2))/(216*(3 + 2*x^2 + x^4)) + (125*ArcTan[(1 + x^2)/Sqrt[2]])/(216*Sqrt[2]) + (13*Log[x])/27 - (13*Log[3 + 2*x^2 + x^4])/108","A",8,7,31,0.2258,1,"{1663, 1646, 1628, 634, 618, 204, 628}"
108,1,87,0,0.1489858,"\int \frac{4+x^2+3 x^4+5 x^6}{x^7 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^7*(3 + 2*x^2 + x^4)^2),x]","\frac{25 \left(1-7 x^2\right)}{648 \left(x^4+2 x^2+3\right)}-\frac{13}{54 x^2}+\frac{13}{108 x^4}-\frac{2}{27 x^6}-\frac{61}{972} \log \left(x^4+2 x^2+3\right)-\frac{1237 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{1944 \sqrt{2}}+\frac{61 \log (x)}{243}","\frac{25 \left(1-7 x^2\right)}{648 \left(x^4+2 x^2+3\right)}-\frac{13}{54 x^2}+\frac{13}{108 x^4}-\frac{2}{27 x^6}-\frac{61}{972} \log \left(x^4+2 x^2+3\right)-\frac{1237 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{1944 \sqrt{2}}+\frac{61 \log (x)}{243}",1,"-2/(27*x^6) + 13/(108*x^4) - 13/(54*x^2) + (25*(1 - 7*x^2))/(648*(3 + 2*x^2 + x^4)) - (1237*ArcTan[(1 + x^2)/Sqrt[2]])/(1944*Sqrt[2]) + (61*Log[x])/243 - (61*Log[3 + 2*x^2 + x^4])/972","A",8,7,31,0.2258,1,"{1663, 1646, 1628, 634, 618, 204, 628}"
109,1,248,0,0.3449041,"\int \frac{x^8 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^8*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^7}{7}-\frac{17 x^5}{5}+\frac{19 x^3}{3}+\frac{25 \left(5 x^2+3\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{2} \left(618291 \sqrt{3}-262771\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{2} \left(618291 \sqrt{3}-262771\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+38 x+\frac{1}{16} \sqrt{\frac{1}{2} \left(262771+618291 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{16} \sqrt{\frac{1}{2} \left(262771+618291 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{5 x^7}{7}-\frac{17 x^5}{5}+\frac{19 x^3}{3}+\frac{25 \left(5 x^2+3\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{2} \left(618291 \sqrt{3}-262771\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{2} \left(618291 \sqrt{3}-262771\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+38 x+\frac{1}{16} \sqrt{\frac{1}{2} \left(262771+618291 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{16} \sqrt{\frac{1}{2} \left(262771+618291 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"38*x + (19*x^3)/3 - (17*x^5)/5 + (5*x^7)/7 + (25*x*(3 + 5*x^2))/(8*(3 + 2*x^2 + x^4)) + (Sqrt[(262771 + 618291*Sqrt[3])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (Sqrt[(262771 + 618291*Sqrt[3])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (Sqrt[(-262771 + 618291*Sqrt[3])/2]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32 + (Sqrt[(-262771 + 618291*Sqrt[3])/2]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32","A",12,7,31,0.2258,1,"{1668, 1676, 1169, 634, 618, 204, 628}"
110,1,237,0,0.2930247,"\int \frac{x^6 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^6*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","x^5-\frac{17 x^3}{3}+\frac{25 \left(3-x^2\right) x}{8 \left(x^4+2 x^2+3\right)}+\frac{3}{32} \sqrt{\frac{3}{2} \left(8669+5011 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{3}{32} \sqrt{\frac{3}{2} \left(8669+5011 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+19 x+\frac{3}{16} \sqrt{\frac{3}{2} \left(5011 \sqrt{3}-8669\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{3}{16} \sqrt{\frac{3}{2} \left(5011 \sqrt{3}-8669\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","x^5-\frac{17 x^3}{3}+\frac{25 \left(3-x^2\right) x}{8 \left(x^4+2 x^2+3\right)}+\frac{3}{32} \sqrt{\frac{3}{2} \left(8669+5011 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{3}{32} \sqrt{\frac{3}{2} \left(8669+5011 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+19 x+\frac{3}{16} \sqrt{\frac{3}{2} \left(5011 \sqrt{3}-8669\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{3}{16} \sqrt{\frac{3}{2} \left(5011 \sqrt{3}-8669\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"19*x - (17*x^3)/3 + x^5 + (25*x*(3 - x^2))/(8*(3 + 2*x^2 + x^4)) + (3*Sqrt[(3*(-8669 + 5011*Sqrt[3]))/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (3*Sqrt[(3*(-8669 + 5011*Sqrt[3]))/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 + (3*Sqrt[(3*(8669 + 5011*Sqrt[3]))/2]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32 - (3*Sqrt[(3*(8669 + 5011*Sqrt[3]))/2]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32","A",12,7,31,0.2258,1,"{1668, 1676, 1169, 634, 618, 204, 628}"
111,1,232,0,0.2923915,"\int \frac{x^4 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^4*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{5 x^3}{3}-\frac{25 \left(x^2+3\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{2} \left(26499 \sqrt{3}-14395\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{2} \left(26499 \sqrt{3}-14395\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-17 x-\frac{1}{16} \sqrt{\frac{1}{2} \left(14395+26499 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{16} \sqrt{\frac{1}{2} \left(14395+26499 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{5 x^3}{3}-\frac{25 \left(x^2+3\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{2} \left(26499 \sqrt{3}-14395\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{2} \left(26499 \sqrt{3}-14395\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-17 x-\frac{1}{16} \sqrt{\frac{1}{2} \left(14395+26499 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{16} \sqrt{\frac{1}{2} \left(14395+26499 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"-17*x + (5*x^3)/3 - (25*x*(3 + x^2))/(8*(3 + 2*x^2 + x^4)) - (Sqrt[(14395 + 26499*Sqrt[3])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 + (Sqrt[(14395 + 26499*Sqrt[3])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (Sqrt[(-14395 + 26499*Sqrt[3])/2]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32 + (Sqrt[(-14395 + 26499*Sqrt[3])/2]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32","A",12,7,31,0.2258,1,"{1668, 1676, 1169, 634, 618, 204, 628}"
112,1,225,0,0.2971397,"\int \frac{x^2 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(x^2*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^2,x]","\frac{25 \left(x^2+1\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{6} \left(12899 \sqrt{3}-19291\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{6} \left(12899 \sqrt{3}-19291\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+5 x+\frac{1}{16} \sqrt{\frac{1}{6} \left(19291+12899 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{16} \sqrt{\frac{1}{6} \left(19291+12899 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{25 \left(x^2+1\right) x}{8 \left(x^4+2 x^2+3\right)}-\frac{1}{32} \sqrt{\frac{1}{6} \left(12899 \sqrt{3}-19291\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{32} \sqrt{\frac{1}{6} \left(12899 \sqrt{3}-19291\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+5 x+\frac{1}{16} \sqrt{\frac{1}{6} \left(19291+12899 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{16} \sqrt{\frac{1}{6} \left(19291+12899 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"5*x + (25*x*(1 + x^2))/(8*(3 + 2*x^2 + x^4)) + (Sqrt[(19291 + 12899*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (Sqrt[(19291 + 12899*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/16 - (Sqrt[(-19291 + 12899*Sqrt[3])/6]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32 + (Sqrt[(-19291 + 12899*Sqrt[3])/6]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/32","A",12,7,31,0.2258,1,"{1668, 1676, 1169, 634, 618, 204, 628}"
113,1,224,0,0.215101,"\int \frac{4+x^2+3 x^4+5 x^6}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(3 + 2*x^2 + x^4)^2,x]","\frac{25 x \left(1-x^2\right)}{24 \left(x^4+2 x^2+3\right)}+\frac{1}{96} \sqrt{\frac{1}{6} \left(11567+12897 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{96} \sqrt{\frac{1}{6} \left(11567+12897 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{48} \sqrt{\frac{1}{6} \left(12897 \sqrt{3}-11567\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{48} \sqrt{\frac{1}{6} \left(12897 \sqrt{3}-11567\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{25 x \left(1-x^2\right)}{24 \left(x^4+2 x^2+3\right)}+\frac{1}{96} \sqrt{\frac{1}{6} \left(11567+12897 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{96} \sqrt{\frac{1}{6} \left(11567+12897 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{48} \sqrt{\frac{1}{6} \left(12897 \sqrt{3}-11567\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{48} \sqrt{\frac{1}{6} \left(12897 \sqrt{3}-11567\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"(25*x*(1 - x^2))/(24*(3 + 2*x^2 + x^4)) - (Sqrt[(-11567 + 12897*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/48 + (Sqrt[(-11567 + 12897*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/48 + (Sqrt[(11567 + 12897*Sqrt[3])/6]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/96 - (Sqrt[(11567 + 12897*Sqrt[3])/6]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/96","A",10,6,28,0.2143,1,"{1678, 1169, 634, 618, 204, 628}"
114,1,229,0,0.3100325,"\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^2*(3 + 2*x^2 + x^4)^2),x]","-\frac{25 x \left(x^2+5\right)}{72 \left(x^4+2 x^2+3\right)}-\frac{1}{96} \sqrt{\frac{1}{6} \left(965+699 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{96} \sqrt{\frac{1}{6} \left(965+699 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{4}{9 x}+\frac{1}{48} \sqrt{\frac{1}{6} \left(699 \sqrt{3}-965\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{48} \sqrt{\frac{1}{6} \left(699 \sqrt{3}-965\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","-\frac{25 x \left(x^2+5\right)}{72 \left(x^4+2 x^2+3\right)}-\frac{1}{96} \sqrt{\frac{1}{6} \left(965+699 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{96} \sqrt{\frac{1}{6} \left(965+699 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{4}{9 x}+\frac{1}{48} \sqrt{\frac{1}{6} \left(699 \sqrt{3}-965\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{48} \sqrt{\frac{1}{6} \left(699 \sqrt{3}-965\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"-4/(9*x) - (25*x*(5 + x^2))/(72*(3 + 2*x^2 + x^4)) + (Sqrt[(-965 + 699*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/48 - (Sqrt[(-965 + 699*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/48 - (Sqrt[(965 + 699*Sqrt[3])/6]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/96 + (Sqrt[(965 + 699*Sqrt[3])/6]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/96","A",12,7,31,0.2258,1,"{1669, 1664, 1169, 634, 618, 204, 628}"
115,1,238,0,0.3353612,"\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^4*(3 + 2*x^2 + x^4)^2),x]","\frac{25 x \left(5 x^2+7\right)}{216 \left(x^4+2 x^2+3\right)}-\frac{4}{27 x^3}+\frac{1}{864} \sqrt{\frac{1}{6} \left(56673 \sqrt{3}-6073\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{864} \sqrt{\frac{1}{6} \left(56673 \sqrt{3}-6073\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{13}{27 x}-\frac{1}{432} \sqrt{\frac{1}{6} \left(6073+56673 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{432} \sqrt{\frac{1}{6} \left(6073+56673 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{25 x \left(5 x^2+7\right)}{216 \left(x^4+2 x^2+3\right)}-\frac{4}{27 x^3}+\frac{1}{864} \sqrt{\frac{1}{6} \left(56673 \sqrt{3}-6073\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{864} \sqrt{\frac{1}{6} \left(56673 \sqrt{3}-6073\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{13}{27 x}-\frac{1}{432} \sqrt{\frac{1}{6} \left(6073+56673 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{432} \sqrt{\frac{1}{6} \left(6073+56673 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"-4/(27*x^3) + 13/(27*x) + (25*x*(7 + 5*x^2))/(216*(3 + 2*x^2 + x^4)) - (Sqrt[(6073 + 56673*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/432 + (Sqrt[(6073 + 56673*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/432 + (Sqrt[(-6073 + 56673*Sqrt[3])/6]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/864 - (Sqrt[(-6073 + 56673*Sqrt[3])/6]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/864","A",12,7,31,0.2258,1,"{1669, 1664, 1169, 634, 618, 204, 628}"
116,1,245,0,0.3289805,"\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left(3+2 x^2+x^4\right)^2} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^6*(3 + 2*x^2 + x^4)^2),x]","\frac{25 x \left(1-7 x^2\right)}{648 \left(x^4+2 x^2+3\right)}+\frac{13}{81 x^3}-\frac{4}{45 x^5}-\frac{\sqrt{\frac{1}{6} \left(1139381+688419 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{2592}+\frac{\sqrt{\frac{1}{6} \left(1139381+688419 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{2592}-\frac{13}{27 x}+\frac{\sqrt{\frac{1}{6} \left(688419 \sqrt{3}-1139381\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{1296}-\frac{\sqrt{\frac{1}{6} \left(688419 \sqrt{3}-1139381\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{1296}","\frac{25 x \left(1-7 x^2\right)}{648 \left(x^4+2 x^2+3\right)}+\frac{13}{81 x^3}-\frac{4}{45 x^5}-\frac{\sqrt{\frac{1}{6} \left(1139381+688419 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{2592}+\frac{\sqrt{\frac{1}{6} \left(1139381+688419 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{2592}-\frac{13}{27 x}+\frac{\sqrt{\frac{1}{6} \left(688419 \sqrt{3}-1139381\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{1296}-\frac{\sqrt{\frac{1}{6} \left(688419 \sqrt{3}-1139381\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{1296}",1,"-4/(45*x^5) + 13/(81*x^3) - 13/(27*x) + (25*x*(1 - 7*x^2))/(648*(3 + 2*x^2 + x^4)) + (Sqrt[(-1139381 + 688419*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/1296 - (Sqrt[(-1139381 + 688419*Sqrt[3])/6]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/1296 - (Sqrt[(1139381 + 688419*Sqrt[3])/6]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/2592 + (Sqrt[(1139381 + 688419*Sqrt[3])/6]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/2592","A",12,7,31,0.2258,1,"{1669, 1664, 1169, 634, 618, 204, 628}"
117,1,243,0,0.3598974,"\int \frac{x^{10} \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(x^10*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^3,x]","x^5-9 x^3+\frac{\left(252 x^2+3305\right) x}{64 \left(x^4+2 x^2+3\right)}-\frac{25 \left(7 x^2+15\right) x}{16 \left(x^4+2 x^2+3\right)^2}+\frac{3}{512} \sqrt{8595619+7678611 \sqrt{3}} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{3}{512} \sqrt{8595619+7678611 \sqrt{3}} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+58 x+\frac{3}{256} \sqrt{7678611 \sqrt{3}-8595619} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{3}{256} \sqrt{7678611 \sqrt{3}-8595619} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","x^5-9 x^3+\frac{\left(252 x^2+3305\right) x}{64 \left(x^4+2 x^2+3\right)}-\frac{25 \left(7 x^2+15\right) x}{16 \left(x^4+2 x^2+3\right)^2}+\frac{3}{512} \sqrt{8595619+7678611 \sqrt{3}} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{3}{512} \sqrt{8595619+7678611 \sqrt{3}} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+58 x+\frac{3}{256} \sqrt{7678611 \sqrt{3}-8595619} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{3}{256} \sqrt{7678611 \sqrt{3}-8595619} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"58*x - 9*x^3 + x^5 - (25*x*(15 + 7*x^2))/(16*(3 + 2*x^2 + x^4)^2) + (x*(3305 + 252*x^2))/(64*(3 + 2*x^2 + x^4)) + (3*Sqrt[-8595619 + 7678611*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 - (3*Sqrt[-8595619 + 7678611*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (3*Sqrt[8595619 + 7678611*Sqrt[3]]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512 - (3*Sqrt[8595619 + 7678611*Sqrt[3]]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512","A",13,8,31,0.2581,1,"{1668, 1678, 1676, 1169, 634, 618, 204, 628}"
118,1,242,0,0.309967,"\int \frac{x^8 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(x^8*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^3,x]","\frac{5 x^3}{3}-\frac{\left(835 x^2+1468\right) x}{64 \left(x^4+2 x^2+3\right)}+\frac{25 \left(5 x^2+3\right) x}{16 \left(x^4+2 x^2+3\right)^2}-\frac{21}{512} \sqrt{22721 \sqrt{3}-34271} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{21}{512} \sqrt{22721 \sqrt{3}-34271} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-27 x-\frac{21}{256} \sqrt{34271+22721 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{21}{256} \sqrt{34271+22721 \sqrt{3}} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{5 x^3}{3}-\frac{\left(835 x^2+1468\right) x}{64 \left(x^4+2 x^2+3\right)}+\frac{25 \left(5 x^2+3\right) x}{16 \left(x^4+2 x^2+3\right)^2}-\frac{21}{512} \sqrt{22721 \sqrt{3}-34271} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{21}{512} \sqrt{22721 \sqrt{3}-34271} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-27 x-\frac{21}{256} \sqrt{34271+22721 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{21}{256} \sqrt{34271+22721 \sqrt{3}} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"-27*x + (5*x^3)/3 + (25*x*(3 + 5*x^2))/(16*(3 + 2*x^2 + x^4)^2) - (x*(1468 + 835*x^2))/(64*(3 + 2*x^2 + x^4)) - (21*Sqrt[34271 + 22721*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (21*Sqrt[34271 + 22721*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 - (21*Sqrt[-34271 + 22721*Sqrt[3]]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512 + (21*Sqrt[-34271 + 22721*Sqrt[3]]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512","A",13,8,31,0.2581,1,"{1668, 1678, 1676, 1169, 634, 618, 204, 628}"
119,1,235,0,0.3004974,"\int \frac{x^6 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(x^6*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^3,x]","\frac{7 \left(58 x^2+11\right) x}{64 \left(x^4+2 x^2+3\right)}+\frac{25 \left(3-x^2\right) x}{16 \left(x^4+2 x^2+3\right)^2}-\frac{1}{512} \sqrt{1176531 \sqrt{3}-827621} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{512} \sqrt{1176531 \sqrt{3}-827621} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+5 x+\frac{1}{256} \sqrt{827621+1176531 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{256} \sqrt{827621+1176531 \sqrt{3}} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{7 \left(58 x^2+11\right) x}{64 \left(x^4+2 x^2+3\right)}+\frac{25 \left(3-x^2\right) x}{16 \left(x^4+2 x^2+3\right)^2}-\frac{1}{512} \sqrt{1176531 \sqrt{3}-827621} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+\frac{1}{512} \sqrt{1176531 \sqrt{3}-827621} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)+5 x+\frac{1}{256} \sqrt{827621+1176531 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)-\frac{1}{256} \sqrt{827621+1176531 \sqrt{3}} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"5*x + (25*x*(3 - x^2))/(16*(3 + 2*x^2 + x^4)^2) + (7*x*(11 + 58*x^2))/(64*(3 + 2*x^2 + x^4)) + (Sqrt[827621 + 1176531*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 - (Sqrt[827621 + 1176531*Sqrt[3]]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 - (Sqrt[-827621 + 1176531*Sqrt[3]]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512 + (Sqrt[-827621 + 1176531*Sqrt[3]]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512","A",13,8,31,0.2581,1,"{1668, 1678, 1676, 1169, 634, 618, 204, 628}"
120,1,238,0,0.2900929,"\int \frac{x^4 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(x^4*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^3,x]","\frac{x \left(238-59 x^2\right)}{64 \left(x^4+2 x^2+3\right)}-\frac{25 x \left(x^2+3\right)}{16 \left(x^4+2 x^2+3\right)^2}+\frac{1}{512} \sqrt{3 \left(48835+32827 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{512} \sqrt{3 \left(48835+32827 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{256} \sqrt{3 \left(32827 \sqrt{3}-48835\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{256} \sqrt{3 \left(32827 \sqrt{3}-48835\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{x \left(238-59 x^2\right)}{64 \left(x^4+2 x^2+3\right)}-\frac{25 x \left(x^2+3\right)}{16 \left(x^4+2 x^2+3\right)^2}+\frac{1}{512} \sqrt{3 \left(48835+32827 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{512} \sqrt{3 \left(48835+32827 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{256} \sqrt{3 \left(32827 \sqrt{3}-48835\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{256} \sqrt{3 \left(32827 \sqrt{3}-48835\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"(-25*x*(3 + x^2))/(16*(3 + 2*x^2 + x^4)^2) + (x*(238 - 59*x^2))/(64*(3 + 2*x^2 + x^4)) - (Sqrt[3*(-48835 + 32827*Sqrt[3])]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (Sqrt[3*(-48835 + 32827*Sqrt[3])]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (Sqrt[3*(48835 + 32827*Sqrt[3])]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512 - (Sqrt[3*(48835 + 32827*Sqrt[3])]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512","A",11,7,31,0.2258,1,"{1668, 1678, 1169, 634, 618, 204, 628}"
121,1,246,0,0.2843632,"\int \frac{x^2 \left(4+x^2+3 x^4+5 x^6\right)}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(x^2*(4 + x^2 + 3*x^4 + 5*x^6))/(3 + 2*x^2 + x^4)^3,x]","\frac{25 x \left(x^2+1\right)}{16 \left(x^4+2 x^2+3\right)^2}-\frac{x \left(88 x^2+353\right)}{192 \left(x^4+2 x^2+3\right)}-\frac{11 \sqrt{\frac{1}{3} \left(1825+1089 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{1536}+\frac{11 \sqrt{\frac{1}{3} \left(1825+1089 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{1536}-\frac{11}{768} \sqrt{\frac{1}{3} \left(1089 \sqrt{3}-1825\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{11}{768} \sqrt{\frac{1}{3} \left(1089 \sqrt{3}-1825\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{25 x \left(x^2+1\right)}{16 \left(x^4+2 x^2+3\right)^2}-\frac{x \left(88 x^2+353\right)}{192 \left(x^4+2 x^2+3\right)}-\frac{11 \sqrt{\frac{1}{3} \left(1825+1089 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{1536}+\frac{11 \sqrt{\frac{1}{3} \left(1825+1089 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{1536}-\frac{11}{768} \sqrt{\frac{1}{3} \left(1089 \sqrt{3}-1825\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{11}{768} \sqrt{\frac{1}{3} \left(1089 \sqrt{3}-1825\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"(25*x*(1 + x^2))/(16*(3 + 2*x^2 + x^4)^2) - (x*(353 + 88*x^2))/(192*(3 + 2*x^2 + x^4)) - (11*Sqrt[(-1825 + 1089*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/768 + (11*Sqrt[(-1825 + 1089*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/768 - (11*Sqrt[(1825 + 1089*Sqrt[3])/3]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/1536 + (11*Sqrt[(1825 + 1089*Sqrt[3])/3]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/1536","A",11,7,31,0.2258,1,"{1668, 1678, 1169, 634, 618, 204, 628}"
122,1,248,0,0.2543416,"\int \frac{4+x^2+3 x^4+5 x^6}{\left(3+2 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(3 + 2*x^2 + x^4)^3,x]","\frac{25 x \left(1-x^2\right)}{48 \left(x^4+2 x^2+3\right)^2}+\frac{x \left(51 x^2+64\right)}{192 \left(x^4+2 x^2+3\right)}+\frac{1}{512} \sqrt{\frac{1}{3} \left(1291+1019 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{512} \sqrt{\frac{1}{3} \left(1291+1019 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{256} \sqrt{\frac{1}{3} \left(1019 \sqrt{3}-1291\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{256} \sqrt{\frac{1}{3} \left(1019 \sqrt{3}-1291\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)","\frac{25 x \left(1-x^2\right)}{48 \left(x^4+2 x^2+3\right)^2}+\frac{x \left(51 x^2+64\right)}{192 \left(x^4+2 x^2+3\right)}+\frac{1}{512} \sqrt{\frac{1}{3} \left(1291+1019 \sqrt{3}\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{512} \sqrt{\frac{1}{3} \left(1291+1019 \sqrt{3}\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)-\frac{1}{256} \sqrt{\frac{1}{3} \left(1019 \sqrt{3}-1291\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)+\frac{1}{256} \sqrt{\frac{1}{3} \left(1019 \sqrt{3}-1291\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)",1,"(25*x*(1 - x^2))/(48*(3 + 2*x^2 + x^4)^2) + (x*(64 + 51*x^2))/(192*(3 + 2*x^2 + x^4)) - (Sqrt[(-1291 + 1019*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (Sqrt[(-1291 + 1019*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/256 + (Sqrt[(1291 + 1019*Sqrt[3])/3]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512 - (Sqrt[(1291 + 1019*Sqrt[3])/3]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/512","A",11,7,28,0.2500,1,"{1678, 1178, 1169, 634, 618, 204, 628}"
123,1,253,0,0.342795,"\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left(3+2 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^2*(3 + 2*x^2 + x^4)^3),x]","-\frac{25 x \left(x^2+5\right)}{144 \left(x^4+2 x^2+3\right)^2}-\frac{x \left(242 x^2+325\right)}{1728 \left(x^4+2 x^2+3\right)}-\frac{\sqrt{\frac{1}{3} \left(55161 \sqrt{3}-59711\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{4608}+\frac{\sqrt{\frac{1}{3} \left(55161 \sqrt{3}-59711\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{4608}-\frac{4}{27 x}+\frac{\sqrt{\frac{1}{3} \left(59711+55161 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{2304}-\frac{\sqrt{\frac{1}{3} \left(59711+55161 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{2304}","-\frac{25 x \left(x^2+5\right)}{144 \left(x^4+2 x^2+3\right)^2}-\frac{x \left(242 x^2+325\right)}{1728 \left(x^4+2 x^2+3\right)}-\frac{\sqrt{\frac{1}{3} \left(55161 \sqrt{3}-59711\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{4608}+\frac{\sqrt{\frac{1}{3} \left(55161 \sqrt{3}-59711\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{4608}-\frac{4}{27 x}+\frac{\sqrt{\frac{1}{3} \left(59711+55161 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{2304}-\frac{\sqrt{\frac{1}{3} \left(59711+55161 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{2304}",1,"-4/(27*x) - (25*x*(5 + x^2))/(144*(3 + 2*x^2 + x^4)^2) - (x*(325 + 242*x^2))/(1728*(3 + 2*x^2 + x^4)) + (Sqrt[(59711 + 55161*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/2304 - (Sqrt[(59711 + 55161*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/2304 - (Sqrt[(-59711 + 55161*Sqrt[3])/3]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/4608 + (Sqrt[(-59711 + 55161*Sqrt[3])/3]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/4608","A",13,7,31,0.2258,1,"{1669, 1664, 1169, 634, 618, 204, 628}"
124,1,262,0,0.3658875,"\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left(3+2 x^2+x^4\right)^3} \, dx","Int[(4 + x^2 + 3*x^4 + 5*x^6)/(x^4*(3 + 2*x^2 + x^4)^3),x]","\frac{25 x \left(5 x^2+7\right)}{432 \left(x^4+2 x^2+3\right)^2}+\frac{x \left(1025 x^2+1474\right)}{5184 \left(x^4+2 x^2+3\right)}-\frac{4}{81 x^3}+\frac{\sqrt{\frac{1}{3} \left(11240451 \sqrt{3}-10004741\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{41472}-\frac{\sqrt{\frac{1}{3} \left(11240451 \sqrt{3}-10004741\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{41472}+\frac{7}{27 x}-\frac{\sqrt{\frac{1}{3} \left(10004741+11240451 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{20736}+\frac{\sqrt{\frac{1}{3} \left(10004741+11240451 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{20736}","\frac{25 x \left(5 x^2+7\right)}{432 \left(x^4+2 x^2+3\right)^2}+\frac{x \left(1025 x^2+1474\right)}{5184 \left(x^4+2 x^2+3\right)}-\frac{4}{81 x^3}+\frac{\sqrt{\frac{1}{3} \left(11240451 \sqrt{3}-10004741\right)} \log \left(x^2-\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{41472}-\frac{\sqrt{\frac{1}{3} \left(11240451 \sqrt{3}-10004741\right)} \log \left(x^2+\sqrt{2 \left(\sqrt{3}-1\right)} x+\sqrt{3}\right)}{41472}+\frac{7}{27 x}-\frac{\sqrt{\frac{1}{3} \left(10004741+11240451 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{3}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{20736}+\frac{\sqrt{\frac{1}{3} \left(10004741+11240451 \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{3}-1\right)}}{\sqrt{2 \left(1+\sqrt{3}\right)}}\right)}{20736}",1,"-4/(81*x^3) + 7/(27*x) + (25*x*(7 + 5*x^2))/(432*(3 + 2*x^2 + x^4)^2) + (x*(1474 + 1025*x^2))/(5184*(3 + 2*x^2 + x^4)) - (Sqrt[(10004741 + 11240451*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] - 2*x)/Sqrt[2*(1 + Sqrt[3])]])/20736 + (Sqrt[(10004741 + 11240451*Sqrt[3])/3]*ArcTan[(Sqrt[2*(-1 + Sqrt[3])] + 2*x)/Sqrt[2*(1 + Sqrt[3])]])/20736 + (Sqrt[(-10004741 + 11240451*Sqrt[3])/3]*Log[Sqrt[3] - Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/41472 - (Sqrt[(-10004741 + 11240451*Sqrt[3])/3]*Log[Sqrt[3] + Sqrt[2*(-1 + Sqrt[3])]*x + x^2])/41472","A",13,7,31,0.2258,1,"{1669, 1664, 1169, 634, 618, 204, 628}"
125,1,149,0,0.2948406,"\int \frac{x \left(d+e x^2+f x^4+g x^6\right)}{a+b x^2+c x^4} \, dx","Int[(x*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a g+b f)+b^2 g+c^2 e\right)}{4 c^3}+\frac{x^2 (c f-b g)}{2 c^2}+\frac{g x^4}{4 c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a g+b f)+b^2 g+c^2 e\right)}{4 c^3}+\frac{x^2 (c f-b g)}{2 c^2}+\frac{g x^4}{4 c}",1,"((c*f - b*g)*x^2)/(2*c^2) + (g*x^4)/(4*c) - ((2*c^3*d - c^2*(b*e + 2*a*f) - b^3*g + b*c*(b*f + 3*a*g))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((c^2*e + b^2*g - c*(b*f + a*g))*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,6,33,0.1818,1,"{1663, 1657, 634, 618, 206, 628}"
126,1,594,0,14.1128896,"\int \frac{x^4 \left(d+e x^2+f x^4+g x^6\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^4*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(x^2 \left(-b^2 c (c e-4 a g)+b c^2 (c d-3 a f)+2 a c^2 (c e-a g)+b^3 c f+b^4 (-g)\right)+a \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)\right)}{2 c^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt{b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt{b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x (c f-2 b g)}{c^3}+\frac{g x^3}{3 c^2}","\frac{x \left(x^2 \left(-b^2 c (c e-4 a g)+b c^2 (c d-3 a f)+2 a c^2 (c e-a g)+b^3 c f+b^4 (-g)\right)+a \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)\right)}{2 c^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt{b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt{b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right)}{2 \sqrt{2} c^{7/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x (c f-2 b g)}{c^3}+\frac{g x^3}{3 c^2}",1,"((c*f - 2*b*g)*x)/c^3 + (g*x^3)/(3*c^2) + (x*(a*(2*c^3*d - c^2*(b*e + 2*a*f) - b^3*g + b*c*(b*f + 3*a*g)) + (b^3*c*f + b*c^2*(c*d - 3*a*f) - b^4*g - b^2*c*(c*e - 4*a*g) + 2*a*c^2*(c*e - a*g))*x^2))/(2*c^3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^3*c*f - b*c^2*(c*d + 13*a*f) - 5*b^4*g - b^2*c*(c*e - 24*a*g) + 2*a*c^2*(3*c*e - 7*a*g) - (3*b^4*c*f - 4*a*c^3*(c*d - 5*a*f) - b^2*c^2*(c*d + 19*a*f) - 5*b^5*g - b^3*c*(c*e - 34*a*g) + 4*a*b*c^2*(2*c*e - 13*a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(7/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3*c*f - b*c^2*(c*d + 13*a*f) - 5*b^4*g - b^2*c*(c*e - 24*a*g) + 2*a*c^2*(3*c*e - 7*a*g) + (3*b^4*c*f - 4*a*c^3*(c*d - 5*a*f) - b^2*c^2*(c*d + 19*a*f) - 5*b^5*g - b^3*c*(c*e - 34*a*g) + 4*a*b*c^2*(2*c*e - 13*a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(7/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,35,0.1143,1,"{1668, 1676, 1166, 205}"
127,1,471,0,6.661827,"\int \frac{x^2 \left(d+e x^2+f x^4+g x^6\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^2*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(x^2 \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt{b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt{b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{g x}{c^2}","-\frac{x \left(x^2 \left(-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right)-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt{b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt{b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{g x}{c^2}",1,"(g*x)/c^2 - (x*(b*c*(c*d + a*f) - a*b^2*g - 2*a*c*(c*e - a*g) + (2*c^3*d - c^2*(b*e + 2*a*f) - b^3*g + b*c*(b*f + 3*a*g))*x^2))/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*c^3*d - c^2*(b*e - 6*a*f) + 3*b^3*g - b*c*(b*f + 13*a*g) + (b^3*c*f - 4*b*c^2*(c*d + 2*a*f) - 3*b^4*g + 4*a*c^2*(c*e - 5*a*g) + b^2*c*(c*e + 19*a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*c^3*d - c^2*(b*e - 6*a*f) + 3*b^3*g - b*c*(b*f + 13*a*g) - (b^3*c*f - 4*b*c^2*(c*d + 2*a*f) - 3*b^4*g + 4*a*c^2*(c*e - 5*a*g) + b^2*c*(c*e + 19*a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,35,0.1143,1,"{1668, 1676, 1166, 205}"
128,1,449,0,2.8669479,"\int \frac{d+e x^2+f x^4+g x^6}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4 + g*x^6)/(a + b*x^2 + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (c d-a f)-a b^3 g+4 a b c (2 a g+c e)-4 a c^2 (a f+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 g}{c}+b (a f+c d)-2 a (3 a g+c e)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (c d-a f)-a b^3 g+4 a b c (2 a g+c e)-4 a c^2 (a f+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 g}{c}+b (a f+c d)-2 a (3 a g+c e)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(x^2 \left(-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right)+c \left(-\frac{a b (a g+c e)}{c}-2 a (c d-a f)+b^2 d\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (c d-a f)-a b^3 g+4 a b c (2 a g+c e)-4 a c^2 (a f+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 g}{c}+b (a f+c d)-2 a (3 a g+c e)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (c d-a f)-a b^3 g+4 a b c (2 a g+c e)-4 a c^2 (a f+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 g}{c}+b (a f+c d)-2 a (3 a g+c e)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(x^2 \left(-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right)+c \left(-\frac{a b (a g+c e)}{c}-2 a (c d-a f)+b^2 d\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(x*(c*(b^2*d - 2*a*(c*d - a*f) - (a*b*(c*e + a*g))/c) + (b*c*(c*d + a*f) - a*b^2*g - 2*a*c*(c*e - a*g))*x^2))/(2*a*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*(c*d + a*f) + (a*b^2*g)/c - 2*a*(c*e + 3*a*g) + (b^2*c*(c*d - a*f) - 4*a*c^2*(3*c*d + a*f) - a*b^3*g + 4*a*b*c*(c*e + 2*a*g))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*(c*d + a*f) + (a*b^2*g)/c - 2*a*(c*e + 3*a*g) - (b^2*c*(c*d - a*f) - 4*a*c^2*(3*c*d + a*f) - a*b^3*g + 4*a*b*c*(c*e + 2*a*g))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,32,0.09375,1,"{1678, 1166, 205}"
129,1,460,0,2.7910477,"\int \frac{d+e x^2+f x^4+g x^6}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4 + g*x^6)/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{x \left(a \left(-2 a^2 g+\frac{b^3 d}{a}+a (b f+2 c e)-b (b e+3 c d)\right)+x^2 \left(-a b (a g+c e)-2 a c (c d-a f)+b^2 c d\right)\right)}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{4 a^2 c (a g+3 c e)-a b^2 (c e-a g)-4 a b c (a f+4 c d)+3 b^3 c d}{\sqrt{b^2-4 a c}}-a b (a g+c e)-2 a c (5 c d-a f)+3 b^2 c d\right)}{2 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{4 a^2 c (a g+3 c e)-a b^2 (c e-a g)-4 a b c (a f+4 c d)+3 b^3 c d}{\sqrt{b^2-4 a c}}-a b (a g+c e)-2 a c (5 c d-a f)+3 b^2 c d\right)}{2 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a^2 x}","-\frac{x \left(a \left(-2 a^2 g+\frac{b^3 d}{a}+a (b f+2 c e)-b (b e+3 c d)\right)+x^2 \left(-a b (a g+c e)-2 a c (c d-a f)+b^2 c d\right)\right)}{2 a^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{4 a^2 c (a g+3 c e)-a b^2 (c e-a g)-4 a b c (a f+4 c d)+3 b^3 c d}{\sqrt{b^2-4 a c}}-a b (a g+c e)-2 a c (5 c d-a f)+3 b^2 c d\right)}{2 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{4 a^2 c (a g+3 c e)-a b^2 (c e-a g)-4 a b c (a f+4 c d)+3 b^3 c d}{\sqrt{b^2-4 a c}}-a b (a g+c e)-2 a c (5 c d-a f)+3 b^2 c d\right)}{2 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{a^2 x}",1,"-(d/(a^2*x)) - (x*(a*((b^3*d)/a - b*(3*c*d + b*e) + a*(2*c*e + b*f) - 2*a^2*g) + (b^2*c*d - 2*a*c*(c*d - a*f) - a*b*(c*e + a*g))*x^2))/(2*a^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^2*c*d - 2*a*c*(5*c*d - a*f) - a*b*(c*e + a*g) + (3*b^3*c*d - 4*a*b*c*(4*c*d + a*f) - a*b^2*(c*e - a*g) + 4*a^2*c*(3*c*e + a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^2*c*d - 2*a*c*(5*c*d - a*f) - a*b*(c*e + a*g) - (3*b^3*c*d - 4*a*b*c*(4*c*d + a*f) - a*b^2*(c*e - a*g) + 4*a^2*c*(3*c*e + a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,35,0.1143,1,"{1669, 1664, 1166, 205}"
130,1,542,0,7.2649599,"\int \frac{d+e x^2+f x^4+g x^6}{x^4 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2 + f*x^4 + g*x^6)/(x^4*(a + b*x^2 + c*x^4)^2),x]","\frac{x \left(a^2 \left(\frac{b^4 d}{a^2}-\frac{b^2 (b e+4 c d)}{a}-a (b g+2 c f)+b^2 f+3 b c e+2 c^2 d\right)+c x^2 \left(2 a^2 (c e-a g)-a b^2 e-a b (3 c d-a f)+b^3 d\right)\right)}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt{b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt{b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 b d-a e}{a^3 x}-\frac{d}{3 a^2 x^3}","\frac{x \left(a^2 \left(\frac{b^4 d}{a^2}-\frac{b^2 (b e+4 c d)}{a}-a (b g+2 c f)+b^2 f+3 b c e+2 c^2 d\right)+c x^2 \left(2 a^2 (c e-a g)-a b^2 e-a b (3 c d-a f)+b^3 d\right)\right)}{2 a^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt{b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt{b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 b d-a e}{a^3 x}-\frac{d}{3 a^2 x^3}",1,"-d/(3*a^2*x^3) + (2*b*d - a*e)/(a^3*x) + (x*(a^2*((b^4*d)/a^2 + 2*c^2*d + 3*b*c*e - (b^2*(4*c*d + b*e))/a + b^2*f - a*(2*c*f + b*g)) + c*(b^3*d - a*b^2*e - a*b*(3*c*d - a*f) + 2*a^2*(c*e - a*g))*x^2))/(2*a^3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(5*b^3*d - 3*a*b^2*e - a*b*(19*c*d - a*f) + 2*a^2*(5*c*e - a*g) + (5*b^4*d - 3*a*b^3*e + 4*a^2*c*(7*c*d - 3*a*f) - a*b^2*(29*c*d - a*f) + 4*a^2*b*(4*c*e + a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(5*b^3*d - 3*a*b^2*e - a*b*(19*c*d - a*f) + 2*a^2*(5*c*e - a*g) - (5*b^4*d - 3*a*b^3*e + 4*a^2*c*(7*c*d - 3*a*f) - a*b^2*(29*c*d - a*f) + 4*a^2*b*(4*c*e + a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,35,0.1143,1,"{1669, 1664, 1166, 205}"
131,1,20,0,0.0363838,"\int x^2 \left(a+b x^2+c x^4\right)^p \left(3 a+b (5+2 p) x^2+c (7+4 p) x^4\right) \, dx","Int[x^2*(a + b*x^2 + c*x^4)^p*(3*a + b*(5 + 2*p)*x^2 + c*(7 + 4*p)*x^4),x]","x^3 \left(a+b x^2+c x^4\right)^{p+1}","x^3 \left(a+b x^2+c x^4\right)^{p+1}",1,"x^3*(a + b*x^2 + c*x^4)^(1 + p)","A",1,1,42,0.02381,1,"{1588}"
132,1,278,0,0.3145316,"\int \frac{x^5 \left(a+b x^2+c x^4\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x^5*(a + b*x^2 + c*x^4))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\left(d^2-e^2 x^2\right)^3 \left(a e^4+3 b d^2 e^2+6 c d^4\right)}{5 e^{10} \sqrt{d-e x} \sqrt{d+e x}}+\frac{d^2 \left(d^2-e^2 x^2\right)^2 \left(2 a e^4+3 b d^2 e^2+4 c d^4\right)}{3 e^{10} \sqrt{d-e x} \sqrt{d+e x}}-\frac{d^4 \left(d^2-e^2 x^2\right) \left(a e^4+b d^2 e^2+c d^4\right)}{e^{10} \sqrt{d-e x} \sqrt{d+e x}}+\frac{\left(d^2-e^2 x^2\right)^4 \left(b e^2+4 c d^2\right)}{7 e^{10} \sqrt{d-e x} \sqrt{d+e x}}-\frac{c \left(d^2-e^2 x^2\right)^5}{9 e^{10} \sqrt{d-e x} \sqrt{d+e x}}","-\frac{(d-e x)^{5/2} (d+e x)^{5/2} \left(a e^4+3 b d^2 e^2+6 c d^4\right)}{5 e^{10}}+\frac{d^2 (d-e x)^{3/2} (d+e x)^{3/2} \left(2 a e^4+3 b d^2 e^2+4 c d^4\right)}{3 e^{10}}-\frac{d^4 \sqrt{d-e x} \sqrt{d+e x} \left(a e^4+b d^2 e^2+c d^4\right)}{e^{10}}+\frac{(d-e x)^{7/2} (d+e x)^{7/2} \left(b e^2+4 c d^2\right)}{7 e^{10}}-\frac{c (d-e x)^{9/2} (d+e x)^{9/2}}{9 e^{10}}",1,"-((d^4*(c*d^4 + b*d^2*e^2 + a*e^4)*(d^2 - e^2*x^2))/(e^10*Sqrt[d - e*x]*Sqrt[d + e*x])) + (d^2*(4*c*d^4 + 3*b*d^2*e^2 + 2*a*e^4)*(d^2 - e^2*x^2)^2)/(3*e^10*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((6*c*d^4 + 3*b*d^2*e^2 + a*e^4)*(d^2 - e^2*x^2)^3)/(5*e^10*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((4*c*d^2 + b*e^2)*(d^2 - e^2*x^2)^4)/(7*e^10*Sqrt[d - e*x]*Sqrt[d + e*x]) - (c*(d^2 - e^2*x^2)^5)/(9*e^10*Sqrt[d - e*x]*Sqrt[d + e*x])","A",5,4,35,0.1143,1,"{520, 1251, 897, 1153}"
133,1,213,0,0.1894421,"\int \frac{x^3 \left(a+b x^2+c x^4\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x^3*(a + b*x^2 + c*x^4))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{\left(d^2-e^2 x^2\right)^2 \left(a e^4+2 b d^2 e^2+3 c d^4\right)}{3 e^8 \sqrt{d-e x} \sqrt{d+e x}}-\frac{d^2 \left(d^2-e^2 x^2\right) \left(a e^4+b d^2 e^2+c d^4\right)}{e^8 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right)^3 \left(b e^2+3 c d^2\right)}{5 e^8 \sqrt{d-e x} \sqrt{d+e x}}+\frac{c \left(d^2-e^2 x^2\right)^4}{7 e^8 \sqrt{d-e x} \sqrt{d+e x}}","\frac{(d-e x)^{3/2} (d+e x)^{3/2} \left(a e^4+2 b d^2 e^2+3 c d^4\right)}{3 e^8}-\frac{d^2 \sqrt{d-e x} \sqrt{d+e x} \left(a e^4+b d^2 e^2+c d^4\right)}{e^8}-\frac{(d-e x)^{5/2} (d+e x)^{5/2} \left(b e^2+3 c d^2\right)}{5 e^8}+\frac{c (d-e x)^{7/2} (d+e x)^{7/2}}{7 e^8}",1,"-((d^2*(c*d^4 + b*d^2*e^2 + a*e^4)*(d^2 - e^2*x^2))/(e^8*Sqrt[d - e*x]*Sqrt[d + e*x])) + ((3*c*d^4 + 2*b*d^2*e^2 + a*e^4)*(d^2 - e^2*x^2)^2)/(3*e^8*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((3*c*d^2 + b*e^2)*(d^2 - e^2*x^2)^3)/(5*e^8*Sqrt[d - e*x]*Sqrt[d + e*x]) + (c*(d^2 - e^2*x^2)^4)/(7*e^8*Sqrt[d - e*x]*Sqrt[d + e*x])","A",4,3,35,0.08571,1,"{520, 1251, 771}"
134,1,149,0,0.1220999,"\int \frac{x \left(a+b x^2+c x^4\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x*(a + b*x^2 + c*x^4))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\left(d^2-e^2 x^2\right) \left(a e^4+b d^2 e^2+c d^4\right)}{e^6 \sqrt{d-e x} \sqrt{d+e x}}+\frac{\left(d^2-e^2 x^2\right)^2 \left(b e^2+2 c d^2\right)}{3 e^6 \sqrt{d-e x} \sqrt{d+e x}}-\frac{c \left(d^2-e^2 x^2\right)^3}{5 e^6 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(a e^4+b d^2 e^2+c d^4\right)}{e^6}+\frac{(d-e x)^{3/2} (d+e x)^{3/2} \left(b e^2+2 c d^2\right)}{3 e^6}-\frac{c (d-e x)^{5/2} (d+e x)^{5/2}}{5 e^6}",1,"-(((c*d^4 + b*d^2*e^2 + a*e^4)*(d^2 - e^2*x^2))/(e^6*Sqrt[d - e*x]*Sqrt[d + e*x])) + ((2*c*d^2 + b*e^2)*(d^2 - e^2*x^2)^2)/(3*e^6*Sqrt[d - e*x]*Sqrt[d + e*x]) - (c*(d^2 - e^2*x^2)^3)/(5*e^6*Sqrt[d - e*x]*Sqrt[d + e*x])","A",4,3,33,0.09091,1,"{520, 1247, 698}"
135,1,151,0,0.1646065,"\int \frac{a+b x^2+c x^4}{x \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{a \sqrt{d^2-e^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(b e^2+c d^2\right)}{e^4 \sqrt{d-e x} \sqrt{d+e x}}+\frac{c \left(d^2-e^2 x^2\right)^2}{3 e^4 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{a \tanh ^{-1}\left(\frac{\sqrt{d-e x} \sqrt{d+e x}}{d}\right)}{d}-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(b e^2+c d^2\right)}{e^4}+\frac{c (d-e x)^{3/2} (d+e x)^{3/2}}{3 e^4}",1,"-(((c*d^2 + b*e^2)*(d^2 - e^2*x^2))/(e^4*Sqrt[d - e*x]*Sqrt[d + e*x])) + (c*(d^2 - e^2*x^2)^2)/(3*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (a*Sqrt[d^2 - e^2*x^2]*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(d*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,5,35,0.1429,1,"{520, 1251, 897, 1153, 208}"
136,1,155,0,0.2519052,"\int \frac{a+b x^2+c x^4}{x^3 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^3*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d^2-e^2 x^2} \left(a e^2+2 b d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{2 d^2 x^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{c \left(d^2-e^2 x^2\right)}{e^2 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\left(a e^2+2 b d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d-e x} \sqrt{d+e x}}{d}\right)}{2 d^3}-\frac{a \sqrt{d-e x} \sqrt{d+e x}}{2 d^2 x^2}-\frac{c \sqrt{d-e x} \sqrt{d+e x}}{e^2}",1,"-((c*(d^2 - e^2*x^2))/(e^2*Sqrt[d - e*x]*Sqrt[d + e*x])) - (a*(d^2 - e^2*x^2))/(2*d^2*x^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((2*b*d^2 + a*e^2)*Sqrt[d^2 - e^2*x^2]*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^3*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,6,35,0.1714,1,"{520, 1251, 897, 1157, 388, 208}"
137,1,182,0,0.2768392,"\int \frac{a+b x^2+c x^4}{x^5 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^5*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{d^2-e^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right) \left(3 a e^4+4 b d^2 e^2+8 c d^4\right)}{8 d^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(3 a e^2+4 b d^2\right)}{8 d^4 x^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{4 d^2 x^4 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d-e x} \sqrt{d+e x}}{d}\right) \left(3 a e^4+4 b d^2 e^2+8 c d^4\right)}{8 d^5}-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(3 a e^2+4 b d^2\right)}{8 d^4 x^2}-\frac{a \sqrt{d-e x} \sqrt{d+e x}}{4 d^2 x^4}",1,"-(a*(d^2 - e^2*x^2))/(4*d^2*x^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((4*b*d^2 + 3*a*e^2)*(d^2 - e^2*x^2))/(8*d^4*x^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((8*c*d^4 + 4*b*d^2*e^2 + 3*a*e^4)*Sqrt[d^2 - e^2*x^2]*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d^5*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,6,35,0.1714,1,"{520, 1251, 897, 1157, 385, 208}"
138,1,248,0,0.3726652,"\int \frac{a+b x^2+c x^4}{x^7 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^7*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\left(d^2-e^2 x^2\right) \left(5 a e^4+6 b d^2 e^2+8 c d^4\right)}{16 d^6 x^2 \sqrt{d-e x} \sqrt{d+e x}}-\frac{e^2 \sqrt{d^2-e^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right) \left(5 a e^4+6 b d^2 e^2+8 c d^4\right)}{16 d^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(5 a e^2+6 b d^2\right)}{24 d^4 x^4 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{6 d^2 x^6 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(5 a e^4+6 b d^2 e^2+8 c d^4\right)}{16 d^6 x^2}-\frac{e^2 \sqrt{d^2-e^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right) \left(5 a e^4+6 b d^2 e^2+8 c d^4\right)}{16 d^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\sqrt{d-e x} \sqrt{d+e x} \left(5 a e^2+6 b d^2\right)}{24 d^4 x^4}-\frac{a \sqrt{d-e x} \sqrt{d+e x}}{6 d^2 x^6}",1,"-(a*(d^2 - e^2*x^2))/(6*d^2*x^6*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((6*b*d^2 + 5*a*e^2)*(d^2 - e^2*x^2))/(24*d^4*x^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((8*c*d^4 + 6*b*d^2*e^2 + 5*a*e^4)*(d^2 - e^2*x^2))/(16*d^6*x^2*Sqrt[d - e*x]*Sqrt[d + e*x]) - (e^2*(8*c*d^4 + 6*b*d^2*e^2 + 5*a*e^4)*Sqrt[d^2 - e^2*x^2]*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^7*Sqrt[d - e*x]*Sqrt[d + e*x])","A",7,7,35,0.2000,1,"{520, 1251, 897, 1157, 385, 199, 208}"
139,1,245,0,0.2050811,"\int \frac{x^2 \left(a+b x^2+c x^4\right)}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(x^2*(a + b*x^2 + c*x^4))/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{x \left(d^2-e^2 x^2\right) \left(8 a e^4+6 b d^2 e^2+5 c d^4\right)}{16 e^6 \sqrt{d-e x} \sqrt{d+e x}}+\frac{d^2 \sqrt{d^2-e^2 x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(8 a e^4+6 b d^2 e^2+5 c d^4\right)}{16 e^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{x^3 \left(d^2-e^2 x^2\right) \left(6 b e^2+5 c d^2\right)}{24 e^4 \sqrt{d-e x} \sqrt{d+e x}}-\frac{c x^5 \left(d^2-e^2 x^2\right)}{6 e^2 \sqrt{d-e x} \sqrt{d+e x}}","\frac{d^2 \sqrt{d^2-e^2 x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(8 a e^4+6 b d^2 e^2+5 c d^4\right)}{16 e^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{x \sqrt{d-e x} \sqrt{d+e x} \left(8 a e^4+6 b d^2 e^2+5 c d^4\right)}{16 e^6}-\frac{x^3 \sqrt{d-e x} \sqrt{d+e x} \left(6 b e^2+5 c d^2\right)}{24 e^4}+\frac{c x^5 (e x-d) \sqrt{d+e x}}{6 e^2 \sqrt{d-e x}}",1,"-((5*c*d^4 + 6*b*d^2*e^2 + 8*a*e^4)*x*(d^2 - e^2*x^2))/(16*e^6*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((5*c*d^2 + 6*b*e^2)*x^3*(d^2 - e^2*x^2))/(24*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (c*x^5*(d^2 - e^2*x^2))/(6*e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + (d^2*(5*c*d^4 + 6*b*d^2*e^2 + 8*a*e^4)*Sqrt[d^2 - e^2*x^2]*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^7*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,6,35,0.1714,1,"{520, 1267, 459, 321, 217, 203}"
140,1,179,0,0.0911319,"\int \frac{a+b x^2+c x^4}{\sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(Sqrt[d - e*x]*Sqrt[d + e*x]),x]","\frac{\sqrt{d^2-e^2 x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(8 a e^4+4 b d^2 e^2+3 c d^4\right)}{8 e^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{x \left(d^2-e^2 x^2\right) \left(4 b e^2+3 c d^2\right)}{8 e^4 \sqrt{d-e x} \sqrt{d+e x}}-\frac{c x^3 \left(d^2-e^2 x^2\right)}{4 e^2 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{d-e x}}{\sqrt{d+e x}}\right) \left(8 a e^4+4 b d^2 e^2+3 c d^4\right)}{4 e^5}-\frac{x \sqrt{d-e x} \sqrt{d+e x} \left(4 b e^2+3 c d^2\right)}{8 e^4}+\frac{c x^3 (e x-d) \sqrt{d+e x}}{4 e^2 \sqrt{d-e x}}",1,"-((3*c*d^2 + 4*b*e^2)*x*(d^2 - e^2*x^2))/(8*e^4*Sqrt[d - e*x]*Sqrt[d + e*x]) - (c*x^3*(d^2 - e^2*x^2))/(4*e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((3*c*d^4 + 4*b*d^2*e^2 + 8*a*e^4)*Sqrt[d^2 - e^2*x^2]*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^5*Sqrt[d - e*x]*Sqrt[d + e*x])","A",5,5,32,0.1562,1,"{520, 1159, 388, 217, 203}"
141,1,155,0,0.1218313,"\int \frac{a+b x^2+c x^4}{x^2 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^2*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{a \left(d^2-e^2 x^2\right)}{d^2 x \sqrt{d-e x} \sqrt{d+e x}}+\frac{\sqrt{d^2-e^2 x^2} \left(2 b e^2+c d^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{c x \left(d^2-e^2 x^2\right)}{2 e^2 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{a \sqrt{d-e x} \sqrt{d+e x}}{d^2 x}-\frac{\left(2 b e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{d-e x}}{\sqrt{d+e x}}\right)}{e^3}+\frac{c x (e x-d) \sqrt{d+e x}}{2 e^2 \sqrt{d-e x}}",1,"-((a*(d^2 - e^2*x^2))/(d^2*x*Sqrt[d - e*x]*Sqrt[d + e*x])) - (c*x*(d^2 - e^2*x^2))/(2*e^2*Sqrt[d - e*x]*Sqrt[d + e*x]) + ((c*d^2 + 2*b*e^2)*Sqrt[d^2 - e^2*x^2]*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3*Sqrt[d - e*x]*Sqrt[d + e*x])","A",5,5,35,0.1429,1,"{520, 1265, 388, 217, 203}"
142,1,157,0,0.1245135,"\int \frac{a+b x^2+c x^4}{x^4 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^4*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\left(d^2-e^2 x^2\right) \left(2 a e^2+3 b d^2\right)}{3 d^4 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{3 d^2 x^3 \sqrt{d-e x} \sqrt{d+e x}}+\frac{c \sqrt{d^2-e^2 x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\left(d^2-e^2 x^2\right) \left(2 a e^2+3 b d^2\right)}{3 d^4 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{3 d^2 x^3 \sqrt{d-e x} \sqrt{d+e x}}+\frac{c \sqrt{d^2-e^2 x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e \sqrt{d-e x} \sqrt{d+e x}}",1,"-(a*(d^2 - e^2*x^2))/(3*d^2*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((3*b*d^2 + 2*a*e^2)*(d^2 - e^2*x^2))/(3*d^4*x*Sqrt[d - e*x]*Sqrt[d + e*x]) + (c*Sqrt[d^2 - e^2*x^2]*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(e*Sqrt[d - e*x]*Sqrt[d + e*x])","A",5,5,35,0.1429,1,"{520, 1265, 451, 217, 203}"
143,1,160,0,0.1450749,"\int \frac{a+b x^2+c x^4}{x^6 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^6*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{\left(d^2-e^2 x^2\right) \left(8 a e^4+10 b d^2 e^2+15 c d^4\right)}{15 d^6 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(4 a e^2+5 b d^2\right)}{15 d^4 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{5 d^2 x^5 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{\left(d^2-e^2 x^2\right) \left(8 a e^4+10 b d^2 e^2+15 c d^4\right)}{15 d^6 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(4 a e^2+5 b d^2\right)}{15 d^4 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{5 d^2 x^5 \sqrt{d-e x} \sqrt{d+e x}}",1,"-(a*(d^2 - e^2*x^2))/(5*d^2*x^5*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((5*b*d^2 + 4*a*e^2)*(d^2 - e^2*x^2))/(15*d^4*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((15*c*d^4 + 10*b*d^2*e^2 + 8*a*e^4)*(d^2 - e^2*x^2))/(15*d^6*x*Sqrt[d - e*x]*Sqrt[d + e*x])","A",4,4,35,0.1143,1,"{520, 1265, 453, 264}"
144,1,226,0,0.1783864,"\int \frac{a+b x^2+c x^4}{x^8 \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^8*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{2 e^2 \left(d^2-e^2 x^2\right) \left(24 a e^4+28 b d^2 e^2+35 c d^4\right)}{105 d^8 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(24 a e^4+28 b d^2 e^2+35 c d^4\right)}{105 d^6 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(6 a e^2+7 b d^2\right)}{35 d^4 x^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{7 d^2 x^7 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{2 e^2 \left(d^2-e^2 x^2\right) \left(24 a e^4+28 b d^2 e^2+35 c d^4\right)}{105 d^8 x \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(24 a e^4+28 b d^2 e^2+35 c d^4\right)}{105 d^6 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(6 a e^2+7 b d^2\right)}{35 d^4 x^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{7 d^2 x^7 \sqrt{d-e x} \sqrt{d+e x}}",1,"-(a*(d^2 - e^2*x^2))/(7*d^2*x^7*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((7*b*d^2 + 6*a*e^2)*(d^2 - e^2*x^2))/(35*d^4*x^5*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((35*c*d^4 + 28*b*d^2*e^2 + 24*a*e^4)*(d^2 - e^2*x^2))/(105*d^6*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (2*e^2*(35*c*d^4 + 28*b*d^2*e^2 + 24*a*e^4)*(d^2 - e^2*x^2))/(105*d^8*x*Sqrt[d - e*x]*Sqrt[d + e*x])","A",5,5,35,0.1429,1,"{520, 1265, 453, 271, 264}"
145,1,292,0,0.2415326,"\int \frac{a+b x^2+c x^4}{x^{10} \sqrt{d-e x} \sqrt{d+e x}} \, dx","Int[(a + b*x^2 + c*x^4)/(x^10*Sqrt[d - e*x]*Sqrt[d + e*x]),x]","-\frac{8 e^4 \left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{315 d^{10} x \sqrt{d-e x} \sqrt{d+e x}}-\frac{4 e^2 \left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{315 d^8 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{105 d^6 x^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(8 a e^2+9 b d^2\right)}{63 d^4 x^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{9 d^2 x^9 \sqrt{d-e x} \sqrt{d+e x}}","-\frac{8 e^4 \left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{315 d^{10} x \sqrt{d-e x} \sqrt{d+e x}}-\frac{4 e^2 \left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{315 d^8 x^3 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(16 a e^4+18 b d^2 e^2+21 c d^4\right)}{105 d^6 x^5 \sqrt{d-e x} \sqrt{d+e x}}-\frac{\left(d^2-e^2 x^2\right) \left(8 a e^2+9 b d^2\right)}{63 d^4 x^7 \sqrt{d-e x} \sqrt{d+e x}}-\frac{a \left(d^2-e^2 x^2\right)}{9 d^2 x^9 \sqrt{d-e x} \sqrt{d+e x}}",1,"-(a*(d^2 - e^2*x^2))/(9*d^2*x^9*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((9*b*d^2 + 8*a*e^2)*(d^2 - e^2*x^2))/(63*d^4*x^7*Sqrt[d - e*x]*Sqrt[d + e*x]) - ((21*c*d^4 + 18*b*d^2*e^2 + 16*a*e^4)*(d^2 - e^2*x^2))/(105*d^6*x^5*Sqrt[d - e*x]*Sqrt[d + e*x]) - (4*e^2*(21*c*d^4 + 18*b*d^2*e^2 + 16*a*e^4)*(d^2 - e^2*x^2))/(315*d^8*x^3*Sqrt[d - e*x]*Sqrt[d + e*x]) - (8*e^4*(21*c*d^4 + 18*b*d^2*e^2 + 16*a*e^4)*(d^2 - e^2*x^2))/(315*d^10*x*Sqrt[d - e*x]*Sqrt[d + e*x])","A",6,5,35,0.1429,1,"{520, 1265, 453, 271, 264}"