1,1,911,0,0.983776," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{3} d m^{5} + 25 \, B b^{3} d m^{4} + 230 \, B b^{3} d m^{3} + 950 \, B b^{3} d m^{2} + 1689 \, B b^{3} d m + 945 \, B b^{3} d\right)} x^{11} + {\left({\left(B b^{3} c + {\left(3 \, B a b^{2} + A b^{3}\right)} d\right)} m^{5} + 1155 \, B b^{3} c + 27 \, {\left(B b^{3} c + {\left(3 \, B a b^{2} + A b^{3}\right)} d\right)} m^{4} + 262 \, {\left(B b^{3} c + {\left(3 \, B a b^{2} + A b^{3}\right)} d\right)} m^{3} + 1122 \, {\left(B b^{3} c + {\left(3 \, B a b^{2} + A b^{3}\right)} d\right)} m^{2} + 1155 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d + 2041 \, {\left(B b^{3} c + {\left(3 \, B a b^{2} + A b^{3}\right)} d\right)} m\right)} x^{9} + {\left({\left({\left(3 \, B a b^{2} + A b^{3}\right)} c + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d\right)} m^{5} + 29 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d\right)} m^{4} + 302 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d\right)} m^{3} + 1366 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d\right)} m^{2} + 1485 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c + 4455 \, {\left(B a^{2} b + A a b^{2}\right)} d + 2577 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d\right)} m\right)} x^{7} + {\left({\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} c + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} m^{5} + 31 \, {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} c + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} m^{4} + 350 \, {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} c + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} m^{3} + 1730 \, {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} c + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} m^{2} + 6237 \, {\left(B a^{2} b + A a b^{2}\right)} c + 2079 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d + 3489 \, {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} c + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} m\right)} x^{5} + {\left({\left(A a^{3} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c\right)} m^{5} + 3465 \, A a^{3} d + 33 \, {\left(A a^{3} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c\right)} m^{4} + 406 \, {\left(A a^{3} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c\right)} m^{3} + 2262 \, {\left(A a^{3} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c\right)} m^{2} + 3465 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c + 5353 \, {\left(A a^{3} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c\right)} m\right)} x^{3} + {\left(A a^{3} c m^{5} + 35 \, A a^{3} c m^{4} + 470 \, A a^{3} c m^{3} + 3010 \, A a^{3} c m^{2} + 9129 \, A a^{3} c m + 10395 \, A a^{3} c\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((B*b^3*d*m^5 + 25*B*b^3*d*m^4 + 230*B*b^3*d*m^3 + 950*B*b^3*d*m^2 + 1689*B*b^3*d*m + 945*B*b^3*d)*x^11 + ((B*b^3*c + (3*B*a*b^2 + A*b^3)*d)*m^5 + 1155*B*b^3*c + 27*(B*b^3*c + (3*B*a*b^2 + A*b^3)*d)*m^4 + 262*(B*b^3*c + (3*B*a*b^2 + A*b^3)*d)*m^3 + 1122*(B*b^3*c + (3*B*a*b^2 + A*b^3)*d)*m^2 + 1155*(3*B*a*b^2 + A*b^3)*d + 2041*(B*b^3*c + (3*B*a*b^2 + A*b^3)*d)*m)*x^9 + (((3*B*a*b^2 + A*b^3)*c + 3*(B*a^2*b + A*a*b^2)*d)*m^5 + 29*((3*B*a*b^2 + A*b^3)*c + 3*(B*a^2*b + A*a*b^2)*d)*m^4 + 302*((3*B*a*b^2 + A*b^3)*c + 3*(B*a^2*b + A*a*b^2)*d)*m^3 + 1366*((3*B*a*b^2 + A*b^3)*c + 3*(B*a^2*b + A*a*b^2)*d)*m^2 + 1485*(3*B*a*b^2 + A*b^3)*c + 4455*(B*a^2*b + A*a*b^2)*d + 2577*((3*B*a*b^2 + A*b^3)*c + 3*(B*a^2*b + A*a*b^2)*d)*m)*x^7 + ((3*(B*a^2*b + A*a*b^2)*c + (B*a^3 + 3*A*a^2*b)*d)*m^5 + 31*(3*(B*a^2*b + A*a*b^2)*c + (B*a^3 + 3*A*a^2*b)*d)*m^4 + 350*(3*(B*a^2*b + A*a*b^2)*c + (B*a^3 + 3*A*a^2*b)*d)*m^3 + 1730*(3*(B*a^2*b + A*a*b^2)*c + (B*a^3 + 3*A*a^2*b)*d)*m^2 + 6237*(B*a^2*b + A*a*b^2)*c + 2079*(B*a^3 + 3*A*a^2*b)*d + 3489*(3*(B*a^2*b + A*a*b^2)*c + (B*a^3 + 3*A*a^2*b)*d)*m)*x^5 + ((A*a^3*d + (B*a^3 + 3*A*a^2*b)*c)*m^5 + 3465*A*a^3*d + 33*(A*a^3*d + (B*a^3 + 3*A*a^2*b)*c)*m^4 + 406*(A*a^3*d + (B*a^3 + 3*A*a^2*b)*c)*m^3 + 2262*(A*a^3*d + (B*a^3 + 3*A*a^2*b)*c)*m^2 + 3465*(B*a^3 + 3*A*a^2*b)*c + 5353*(A*a^3*d + (B*a^3 + 3*A*a^2*b)*c)*m)*x^3 + (A*a^3*c*m^5 + 35*A*a^3*c*m^4 + 470*A*a^3*c*m^3 + 3010*A*a^3*c*m^2 + 9129*A*a^3*c*m + 10395*A*a^3*c)*x)*(e*x)^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
2,1,532,0,1.086837," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} d m^{4} + 16 \, B b^{2} d m^{3} + 86 \, B b^{2} d m^{2} + 176 \, B b^{2} d m + 105 \, B b^{2} d\right)} x^{9} + {\left({\left(B b^{2} c + {\left(2 \, B a b + A b^{2}\right)} d\right)} m^{4} + 135 \, B b^{2} c + 18 \, {\left(B b^{2} c + {\left(2 \, B a b + A b^{2}\right)} d\right)} m^{3} + 104 \, {\left(B b^{2} c + {\left(2 \, B a b + A b^{2}\right)} d\right)} m^{2} + 135 \, {\left(2 \, B a b + A b^{2}\right)} d + 222 \, {\left(B b^{2} c + {\left(2 \, B a b + A b^{2}\right)} d\right)} m\right)} x^{7} + {\left({\left({\left(2 \, B a b + A b^{2}\right)} c + {\left(B a^{2} + 2 \, A a b\right)} d\right)} m^{4} + 20 \, {\left({\left(2 \, B a b + A b^{2}\right)} c + {\left(B a^{2} + 2 \, A a b\right)} d\right)} m^{3} + 130 \, {\left({\left(2 \, B a b + A b^{2}\right)} c + {\left(B a^{2} + 2 \, A a b\right)} d\right)} m^{2} + 189 \, {\left(2 \, B a b + A b^{2}\right)} c + 189 \, {\left(B a^{2} + 2 \, A a b\right)} d + 300 \, {\left({\left(2 \, B a b + A b^{2}\right)} c + {\left(B a^{2} + 2 \, A a b\right)} d\right)} m\right)} x^{5} + {\left({\left(A a^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{4} + 315 \, A a^{2} d + 22 \, {\left(A a^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{3} + 164 \, {\left(A a^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{2} + 315 \, {\left(B a^{2} + 2 \, A a b\right)} c + 458 \, {\left(A a^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c\right)} m\right)} x^{3} + {\left(A a^{2} c m^{4} + 24 \, A a^{2} c m^{3} + 206 \, A a^{2} c m^{2} + 744 \, A a^{2} c m + 945 \, A a^{2} c\right)} x\right)} \left(e x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((B*b^2*d*m^4 + 16*B*b^2*d*m^3 + 86*B*b^2*d*m^2 + 176*B*b^2*d*m + 105*B*b^2*d)*x^9 + ((B*b^2*c + (2*B*a*b + A*b^2)*d)*m^4 + 135*B*b^2*c + 18*(B*b^2*c + (2*B*a*b + A*b^2)*d)*m^3 + 104*(B*b^2*c + (2*B*a*b + A*b^2)*d)*m^2 + 135*(2*B*a*b + A*b^2)*d + 222*(B*b^2*c + (2*B*a*b + A*b^2)*d)*m)*x^7 + (((2*B*a*b + A*b^2)*c + (B*a^2 + 2*A*a*b)*d)*m^4 + 20*((2*B*a*b + A*b^2)*c + (B*a^2 + 2*A*a*b)*d)*m^3 + 130*((2*B*a*b + A*b^2)*c + (B*a^2 + 2*A*a*b)*d)*m^2 + 189*(2*B*a*b + A*b^2)*c + 189*(B*a^2 + 2*A*a*b)*d + 300*((2*B*a*b + A*b^2)*c + (B*a^2 + 2*A*a*b)*d)*m)*x^5 + ((A*a^2*d + (B*a^2 + 2*A*a*b)*c)*m^4 + 315*A*a^2*d + 22*(A*a^2*d + (B*a^2 + 2*A*a*b)*c)*m^3 + 164*(A*a^2*d + (B*a^2 + 2*A*a*b)*c)*m^2 + 315*(B*a^2 + 2*A*a*b)*c + 458*(A*a^2*d + (B*a^2 + 2*A*a*b)*c)*m)*x^3 + (A*a^2*c*m^4 + 24*A*a^2*c*m^3 + 206*A*a^2*c*m^2 + 744*A*a^2*c*m + 945*A*a^2*c)*x)*(e*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
3,1,235,0,0.755554," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left({\left(B b d m^{3} + 9 \, B b d m^{2} + 23 \, B b d m + 15 \, B b d\right)} x^{7} + {\left({\left(B b c + {\left(B a + A b\right)} d\right)} m^{3} + 21 \, B b c + 11 \, {\left(B b c + {\left(B a + A b\right)} d\right)} m^{2} + 21 \, {\left(B a + A b\right)} d + 31 \, {\left(B b c + {\left(B a + A b\right)} d\right)} m\right)} x^{5} + {\left({\left(A a d + {\left(B a + A b\right)} c\right)} m^{3} + 35 \, A a d + 13 \, {\left(A a d + {\left(B a + A b\right)} c\right)} m^{2} + 35 \, {\left(B a + A b\right)} c + 47 \, {\left(A a d + {\left(B a + A b\right)} c\right)} m\right)} x^{3} + {\left(A a c m^{3} + 15 \, A a c m^{2} + 71 \, A a c m + 105 \, A a c\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((B*b*d*m^3 + 9*B*b*d*m^2 + 23*B*b*d*m + 15*B*b*d)*x^7 + ((B*b*c + (B*a + A*b)*d)*m^3 + 21*B*b*c + 11*(B*b*c + (B*a + A*b)*d)*m^2 + 21*(B*a + A*b)*d + 31*(B*b*c + (B*a + A*b)*d)*m)*x^5 + ((A*a*d + (B*a + A*b)*c)*m^3 + 35*A*a*d + 13*(A*a*d + (B*a + A*b)*c)*m^2 + 35*(B*a + A*b)*c + 47*(A*a*d + (B*a + A*b)*c)*m)*x^3 + (A*a*c*m^3 + 15*A*a*c*m^2 + 71*A*a*c*m + 105*A*a*c)*x)*(e*x)^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
4,1,94,0,0.887379," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left({\left(B d m^{2} + 4 \, B d m + 3 \, B d\right)} x^{5} + {\left({\left(B c + A d\right)} m^{2} + 5 \, B c + 5 \, A d + 6 \, {\left(B c + A d\right)} m\right)} x^{3} + {\left(A c m^{2} + 8 \, A c m + 15 \, A c\right)} x\right)} \left(e x\right)^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((B*d*m^2 + 4*B*d*m + 3*B*d)*x^5 + ((B*c + A*d)*m^2 + 5*B*c + 5*A*d + 6*(B*c + A*d)*m)*x^3 + (A*c*m^2 + 8*A*c*m + 15*A*c)*x)*(e*x)^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
5,0,0,0,0.923377," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d x^{4} + {\left(B c + A d\right)} x^{2} + A c\right)} \left(e x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((B*d*x^4 + (B*c + A*d)*x^2 + A*c)*(e*x)^m/(b*x^2 + a), x)","F",0
6,0,0,0,0.900688," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d x^{4} + {\left(B c + A d\right)} x^{2} + A c\right)} \left(e x\right)^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*d*x^4 + (B*c + A*d)*x^2 + A*c)*(e*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
7,0,0,0,0.675930," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d x^{4} + {\left(B c + A d\right)} x^{2} + A c\right)} \left(e x\right)^{m}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*d*x^4 + (B*c + A*d)*x^2 + A*c)*(e*x)^m/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
8,1,1711,0,1.204664," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{3} d^{2} m^{6} + 36 \, B b^{3} d^{2} m^{5} + 505 \, B b^{3} d^{2} m^{4} + 3480 \, B b^{3} d^{2} m^{3} + 12139 \, B b^{3} d^{2} m^{2} + 19524 \, B b^{3} d^{2} m + 10395 \, B b^{3} d^{2}\right)} x^{13} + {\left({\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m^{6} + 24570 \, B b^{3} c d + 38 \, {\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m^{5} + 555 \, {\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m^{4} + 3940 \, {\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m^{3} + 12285 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} + 14039 \, {\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m^{2} + 22902 \, {\left(2 \, B b^{3} c d + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2}\right)} m\right)} x^{11} + {\left({\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m^{6} + 15015 \, B b^{3} c^{2} + 40 \, {\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m^{5} + 613 \, {\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m^{4} + 4528 \, {\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m^{3} + 30030 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 45045 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} + 16627 \, {\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m^{2} + 27688 \, {\left(B b^{3} c^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2}\right)} m\right)} x^{9} + {\left({\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m^{6} + 42 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m^{5} + 679 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m^{4} + 5292 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m^{3} + 19305 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 115830 \, {\left(B a^{2} b + A a b^{2}\right)} c d + 19305 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} + 20335 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m^{2} + 34986 \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} m\right)} x^{7} + {\left({\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m^{6} + 27027 \, A a^{3} d^{2} + 44 \, {\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m^{5} + 753 \, {\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m^{4} + 6280 \, {\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m^{3} + 81081 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 54054 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d + 25979 \, {\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m^{2} + 47436 \, {\left(A a^{3} d^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d\right)} m\right)} x^{5} + {\left({\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m^{6} + 90090 \, A a^{3} c d + 46 \, {\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m^{5} + 835 \, {\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m^{4} + 7540 \, {\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m^{3} + 45045 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} + 34759 \, {\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m^{2} + 73054 \, {\left(2 \, A a^{3} c d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2}\right)} m\right)} x^{3} + {\left(A a^{3} c^{2} m^{6} + 48 \, A a^{3} c^{2} m^{5} + 925 \, A a^{3} c^{2} m^{4} + 9120 \, A a^{3} c^{2} m^{3} + 48259 \, A a^{3} c^{2} m^{2} + 129072 \, A a^{3} c^{2} m + 135135 \, A a^{3} c^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((B*b^3*d^2*m^6 + 36*B*b^3*d^2*m^5 + 505*B*b^3*d^2*m^4 + 3480*B*b^3*d^2*m^3 + 12139*B*b^3*d^2*m^2 + 19524*B*b^3*d^2*m + 10395*B*b^3*d^2)*x^13 + ((2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^6 + 24570*B*b^3*c*d + 38*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^5 + 555*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^4 + 3940*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^3 + 12285*(3*B*a*b^2 + A*b^3)*d^2 + 14039*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^2 + 22902*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m)*x^11 + ((B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m^6 + 15015*B*b^3*c^2 + 40*(B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m^5 + 613*(B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m^4 + 4528*(B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m^3 + 30030*(3*B*a*b^2 + A*b^3)*c*d + 45045*(B*a^2*b + A*a*b^2)*d^2 + 16627*(B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m^2 + 27688*(B*b^3*c^2 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2)*m)*x^9 + (((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m^6 + 42*((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m^5 + 679*((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m^4 + 5292*((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m^3 + 19305*(3*B*a*b^2 + A*b^3)*c^2 + 115830*(B*a^2*b + A*a*b^2)*c*d + 19305*(B*a^3 + 3*A*a^2*b)*d^2 + 20335*((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m^2 + 34986*((3*B*a*b^2 + A*b^3)*c^2 + 6*(B*a^2*b + A*a*b^2)*c*d + (B*a^3 + 3*A*a^2*b)*d^2)*m)*x^7 + ((A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m^6 + 27027*A*a^3*d^2 + 44*(A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m^5 + 753*(A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m^4 + 6280*(A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m^3 + 81081*(B*a^2*b + A*a*b^2)*c^2 + 54054*(B*a^3 + 3*A*a^2*b)*c*d + 25979*(A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m^2 + 47436*(A*a^3*d^2 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d)*m)*x^5 + ((2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^6 + 90090*A*a^3*c*d + 46*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^5 + 835*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^4 + 7540*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^3 + 45045*(B*a^3 + 3*A*a^2*b)*c^2 + 34759*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^2 + 73054*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*x^3 + (A*a^3*c^2*m^6 + 48*A*a^3*c^2*m^5 + 925*A*a^3*c^2*m^4 + 9120*A*a^3*c^2*m^3 + 48259*A*a^3*c^2*m^2 + 129072*A*a^3*c^2*m + 135135*A*a^3*c^2)*x)*(e*x)^m/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
9,1,1043,0,1.025419," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} d^{2} m^{5} + 25 \, B b^{2} d^{2} m^{4} + 230 \, B b^{2} d^{2} m^{3} + 950 \, B b^{2} d^{2} m^{2} + 1689 \, B b^{2} d^{2} m + 945 \, B b^{2} d^{2}\right)} x^{11} + {\left({\left(2 \, B b^{2} c d + {\left(2 \, B a b + A b^{2}\right)} d^{2}\right)} m^{5} + 2310 \, B b^{2} c d + 27 \, {\left(2 \, B b^{2} c d + {\left(2 \, B a b + A b^{2}\right)} d^{2}\right)} m^{4} + 262 \, {\left(2 \, B b^{2} c d + {\left(2 \, B a b + A b^{2}\right)} d^{2}\right)} m^{3} + 1155 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} + 1122 \, {\left(2 \, B b^{2} c d + {\left(2 \, B a b + A b^{2}\right)} d^{2}\right)} m^{2} + 2041 \, {\left(2 \, B b^{2} c d + {\left(2 \, B a b + A b^{2}\right)} d^{2}\right)} m\right)} x^{9} + {\left({\left(B b^{2} c^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c d + {\left(B a^{2} + 2 \, A a b\right)} d^{2}\right)} m^{5} + 1485 \, B b^{2} c^{2} + 29 \, {\left(B b^{2} c^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c d + {\left(B a^{2} + 2 \, A a b\right)} d^{2}\right)} m^{4} + 302 \, {\left(B b^{2} c^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c d + {\left(B a^{2} + 2 \, A a b\right)} d^{2}\right)} m^{3} + 2970 \, {\left(2 \, B a b + A b^{2}\right)} c d + 1485 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} + 1366 \, {\left(B b^{2} c^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c d + {\left(B a^{2} + 2 \, A a b\right)} d^{2}\right)} m^{2} + 2577 \, {\left(B b^{2} c^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c d + {\left(B a^{2} + 2 \, A a b\right)} d^{2}\right)} m\right)} x^{7} + {\left({\left(A a^{2} d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d\right)} m^{5} + 2079 \, A a^{2} d^{2} + 31 \, {\left(A a^{2} d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d\right)} m^{4} + 350 \, {\left(A a^{2} d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d\right)} m^{3} + 2079 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} + 4158 \, {\left(B a^{2} + 2 \, A a b\right)} c d + 1730 \, {\left(A a^{2} d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d\right)} m^{2} + 3489 \, {\left(A a^{2} d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d\right)} m\right)} x^{5} + {\left({\left(2 \, A a^{2} c d + {\left(B a^{2} + 2 \, A a b\right)} c^{2}\right)} m^{5} + 6930 \, A a^{2} c d + 33 \, {\left(2 \, A a^{2} c d + {\left(B a^{2} + 2 \, A a b\right)} c^{2}\right)} m^{4} + 406 \, {\left(2 \, A a^{2} c d + {\left(B a^{2} + 2 \, A a b\right)} c^{2}\right)} m^{3} + 3465 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} + 2262 \, {\left(2 \, A a^{2} c d + {\left(B a^{2} + 2 \, A a b\right)} c^{2}\right)} m^{2} + 5353 \, {\left(2 \, A a^{2} c d + {\left(B a^{2} + 2 \, A a b\right)} c^{2}\right)} m\right)} x^{3} + {\left(A a^{2} c^{2} m^{5} + 35 \, A a^{2} c^{2} m^{4} + 470 \, A a^{2} c^{2} m^{3} + 3010 \, A a^{2} c^{2} m^{2} + 9129 \, A a^{2} c^{2} m + 10395 \, A a^{2} c^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((B*b^2*d^2*m^5 + 25*B*b^2*d^2*m^4 + 230*B*b^2*d^2*m^3 + 950*B*b^2*d^2*m^2 + 1689*B*b^2*d^2*m + 945*B*b^2*d^2)*x^11 + ((2*B*b^2*c*d + (2*B*a*b + A*b^2)*d^2)*m^5 + 2310*B*b^2*c*d + 27*(2*B*b^2*c*d + (2*B*a*b + A*b^2)*d^2)*m^4 + 262*(2*B*b^2*c*d + (2*B*a*b + A*b^2)*d^2)*m^3 + 1155*(2*B*a*b + A*b^2)*d^2 + 1122*(2*B*b^2*c*d + (2*B*a*b + A*b^2)*d^2)*m^2 + 2041*(2*B*b^2*c*d + (2*B*a*b + A*b^2)*d^2)*m)*x^9 + ((B*b^2*c^2 + 2*(2*B*a*b + A*b^2)*c*d + (B*a^2 + 2*A*a*b)*d^2)*m^5 + 1485*B*b^2*c^2 + 29*(B*b^2*c^2 + 2*(2*B*a*b + A*b^2)*c*d + (B*a^2 + 2*A*a*b)*d^2)*m^4 + 302*(B*b^2*c^2 + 2*(2*B*a*b + A*b^2)*c*d + (B*a^2 + 2*A*a*b)*d^2)*m^3 + 2970*(2*B*a*b + A*b^2)*c*d + 1485*(B*a^2 + 2*A*a*b)*d^2 + 1366*(B*b^2*c^2 + 2*(2*B*a*b + A*b^2)*c*d + (B*a^2 + 2*A*a*b)*d^2)*m^2 + 2577*(B*b^2*c^2 + 2*(2*B*a*b + A*b^2)*c*d + (B*a^2 + 2*A*a*b)*d^2)*m)*x^7 + ((A*a^2*d^2 + (2*B*a*b + A*b^2)*c^2 + 2*(B*a^2 + 2*A*a*b)*c*d)*m^5 + 2079*A*a^2*d^2 + 31*(A*a^2*d^2 + (2*B*a*b + A*b^2)*c^2 + 2*(B*a^2 + 2*A*a*b)*c*d)*m^4 + 350*(A*a^2*d^2 + (2*B*a*b + A*b^2)*c^2 + 2*(B*a^2 + 2*A*a*b)*c*d)*m^3 + 2079*(2*B*a*b + A*b^2)*c^2 + 4158*(B*a^2 + 2*A*a*b)*c*d + 1730*(A*a^2*d^2 + (2*B*a*b + A*b^2)*c^2 + 2*(B*a^2 + 2*A*a*b)*c*d)*m^2 + 3489*(A*a^2*d^2 + (2*B*a*b + A*b^2)*c^2 + 2*(B*a^2 + 2*A*a*b)*c*d)*m)*x^5 + ((2*A*a^2*c*d + (B*a^2 + 2*A*a*b)*c^2)*m^5 + 6930*A*a^2*c*d + 33*(2*A*a^2*c*d + (B*a^2 + 2*A*a*b)*c^2)*m^4 + 406*(2*A*a^2*c*d + (B*a^2 + 2*A*a*b)*c^2)*m^3 + 3465*(B*a^2 + 2*A*a*b)*c^2 + 2262*(2*A*a^2*c*d + (B*a^2 + 2*A*a*b)*c^2)*m^2 + 5353*(2*A*a^2*c*d + (B*a^2 + 2*A*a*b)*c^2)*m)*x^3 + (A*a^2*c^2*m^5 + 35*A*a^2*c^2*m^4 + 470*A*a^2*c^2*m^3 + 3010*A*a^2*c^2*m^2 + 9129*A*a^2*c^2*m + 10395*A*a^2*c^2)*x)*(e*x)^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
10,1,495,0,1.009202," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B b d^{2} m^{4} + 16 \, B b d^{2} m^{3} + 86 \, B b d^{2} m^{2} + 176 \, B b d^{2} m + 105 \, B b d^{2}\right)} x^{9} + {\left({\left(2 \, B b c d + {\left(B a + A b\right)} d^{2}\right)} m^{4} + 270 \, B b c d + 18 \, {\left(2 \, B b c d + {\left(B a + A b\right)} d^{2}\right)} m^{3} + 135 \, {\left(B a + A b\right)} d^{2} + 104 \, {\left(2 \, B b c d + {\left(B a + A b\right)} d^{2}\right)} m^{2} + 222 \, {\left(2 \, B b c d + {\left(B a + A b\right)} d^{2}\right)} m\right)} x^{7} + {\left({\left(B b c^{2} + A a d^{2} + 2 \, {\left(B a + A b\right)} c d\right)} m^{4} + 189 \, B b c^{2} + 189 \, A a d^{2} + 20 \, {\left(B b c^{2} + A a d^{2} + 2 \, {\left(B a + A b\right)} c d\right)} m^{3} + 378 \, {\left(B a + A b\right)} c d + 130 \, {\left(B b c^{2} + A a d^{2} + 2 \, {\left(B a + A b\right)} c d\right)} m^{2} + 300 \, {\left(B b c^{2} + A a d^{2} + 2 \, {\left(B a + A b\right)} c d\right)} m\right)} x^{5} + {\left({\left(2 \, A a c d + {\left(B a + A b\right)} c^{2}\right)} m^{4} + 630 \, A a c d + 22 \, {\left(2 \, A a c d + {\left(B a + A b\right)} c^{2}\right)} m^{3} + 315 \, {\left(B a + A b\right)} c^{2} + 164 \, {\left(2 \, A a c d + {\left(B a + A b\right)} c^{2}\right)} m^{2} + 458 \, {\left(2 \, A a c d + {\left(B a + A b\right)} c^{2}\right)} m\right)} x^{3} + {\left(A a c^{2} m^{4} + 24 \, A a c^{2} m^{3} + 206 \, A a c^{2} m^{2} + 744 \, A a c^{2} m + 945 \, A a c^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((B*b*d^2*m^4 + 16*B*b*d^2*m^3 + 86*B*b*d^2*m^2 + 176*B*b*d^2*m + 105*B*b*d^2)*x^9 + ((2*B*b*c*d + (B*a + A*b)*d^2)*m^4 + 270*B*b*c*d + 18*(2*B*b*c*d + (B*a + A*b)*d^2)*m^3 + 135*(B*a + A*b)*d^2 + 104*(2*B*b*c*d + (B*a + A*b)*d^2)*m^2 + 222*(2*B*b*c*d + (B*a + A*b)*d^2)*m)*x^7 + ((B*b*c^2 + A*a*d^2 + 2*(B*a + A*b)*c*d)*m^4 + 189*B*b*c^2 + 189*A*a*d^2 + 20*(B*b*c^2 + A*a*d^2 + 2*(B*a + A*b)*c*d)*m^3 + 378*(B*a + A*b)*c*d + 130*(B*b*c^2 + A*a*d^2 + 2*(B*a + A*b)*c*d)*m^2 + 300*(B*b*c^2 + A*a*d^2 + 2*(B*a + A*b)*c*d)*m)*x^5 + ((2*A*a*c*d + (B*a + A*b)*c^2)*m^4 + 630*A*a*c*d + 22*(2*A*a*c*d + (B*a + A*b)*c^2)*m^3 + 315*(B*a + A*b)*c^2 + 164*(2*A*a*c*d + (B*a + A*b)*c^2)*m^2 + 458*(2*A*a*c*d + (B*a + A*b)*c^2)*m)*x^3 + (A*a*c^2*m^4 + 24*A*a*c^2*m^3 + 206*A*a*c^2*m^2 + 744*A*a*c^2*m + 945*A*a*c^2)*x)*(e*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
11,1,217,0,0.900270," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B d^{2} m^{3} + 9 \, B d^{2} m^{2} + 23 \, B d^{2} m + 15 \, B d^{2}\right)} x^{7} + {\left({\left(2 \, B c d + A d^{2}\right)} m^{3} + 42 \, B c d + 21 \, A d^{2} + 11 \, {\left(2 \, B c d + A d^{2}\right)} m^{2} + 31 \, {\left(2 \, B c d + A d^{2}\right)} m\right)} x^{5} + {\left({\left(B c^{2} + 2 \, A c d\right)} m^{3} + 35 \, B c^{2} + 70 \, A c d + 13 \, {\left(B c^{2} + 2 \, A c d\right)} m^{2} + 47 \, {\left(B c^{2} + 2 \, A c d\right)} m\right)} x^{3} + {\left(A c^{2} m^{3} + 15 \, A c^{2} m^{2} + 71 \, A c^{2} m + 105 \, A c^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((B*d^2*m^3 + 9*B*d^2*m^2 + 23*B*d^2*m + 15*B*d^2)*x^7 + ((2*B*c*d + A*d^2)*m^3 + 42*B*c*d + 21*A*d^2 + 11*(2*B*c*d + A*d^2)*m^2 + 31*(2*B*c*d + A*d^2)*m)*x^5 + ((B*c^2 + 2*A*c*d)*m^3 + 35*B*c^2 + 70*A*c*d + 13*(B*c^2 + 2*A*c*d)*m^2 + 47*(B*c^2 + 2*A*c*d)*m)*x^3 + (A*c^2*m^3 + 15*A*c^2*m^2 + 71*A*c^2*m + 105*A*c^2)*x)*(e*x)^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
12,0,0,0,0.532575," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{2} x^{6} + {\left(2 \, B c d + A d^{2}\right)} x^{4} + A c^{2} + {\left(B c^{2} + 2 \, A c d\right)} x^{2}\right)} \left(e x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((B*d^2*x^6 + (2*B*c*d + A*d^2)*x^4 + A*c^2 + (B*c^2 + 2*A*c*d)*x^2)*(e*x)^m/(b*x^2 + a), x)","F",0
13,0,0,0,0.602947," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{2} x^{6} + {\left(2 \, B c d + A d^{2}\right)} x^{4} + A c^{2} + {\left(B c^{2} + 2 \, A c d\right)} x^{2}\right)} \left(e x\right)^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*d^2*x^6 + (2*B*c*d + A*d^2)*x^4 + A*c^2 + (B*c^2 + 2*A*c*d)*x^2)*(e*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
14,0,0,0,0.644336," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{2} x^{6} + {\left(2 \, B c d + A d^{2}\right)} x^{4} + A c^{2} + {\left(B c^{2} + 2 \, A c d\right)} x^{2}\right)} \left(e x\right)^{m}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*d^2*x^6 + (2*B*c*d + A*d^2)*x^4 + A*c^2 + (B*c^2 + 2*A*c*d)*x^2)*(e*x)^m/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
15,1,2657,0,0.796247," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{3} d^{3} m^{7} + 49 \, B b^{3} d^{3} m^{6} + 973 \, B b^{3} d^{3} m^{5} + 10045 \, B b^{3} d^{3} m^{4} + 57379 \, B b^{3} d^{3} m^{3} + 177331 \, B b^{3} d^{3} m^{2} + 264207 \, B b^{3} d^{3} m + 135135 \, B b^{3} d^{3}\right)} x^{15} + {\left({\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{7} + 467775 \, B b^{3} c d^{2} + 51 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{6} + 1045 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{5} + 11055 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{4} + 155925 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} + 64339 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{3} + 201609 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m^{2} + 303255 \, {\left(3 \, B b^{3} c d^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3}\right)} m\right)} x^{13} + 3 \, {\left({\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{7} + 184275 \, B b^{3} c^{2} d + 53 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{6} + 1125 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{5} + 12265 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{4} + 184275 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + 184275 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} + 73139 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{3} + 233487 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m^{2} + 355815 \, {\left(B b^{3} c^{2} d + {\left(3 \, B a b^{2} + A b^{3}\right)} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3}\right)} m\right)} x^{11} + {\left({\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{7} + 225225 \, B b^{3} c^{3} + 55 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{6} + 1213 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{5} + 13723 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{4} + 675675 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 2027025 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + 225225 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} + 84547 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{3} + 277093 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m^{2} + 430335 \, {\left(B b^{3} c^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{2} d + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c d^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} m\right)} x^{9} + {\left({\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{7} + 289575 \, A a^{3} d^{3} + 57 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{6} + 1309 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{5} + 15477 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{4} + 289575 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 2606175 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 868725 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2} + 99715 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{3} + 340011 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m^{2} + 544095 \, {\left(A a^{3} d^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} c^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} d + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{2}\right)} m\right)} x^{7} + 3 \, {\left({\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{7} + 405405 \, A a^{3} c d^{2} + 59 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{6} + 1413 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{5} + 17575 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{4} + 405405 \, {\left(B a^{2} b + A a b^{2}\right)} c^{3} + 405405 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d + 120179 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{3} + 437121 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m^{2} + 738567 \, {\left(A a^{3} c d^{2} + {\left(B a^{2} b + A a b^{2}\right)} c^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d\right)} m\right)} x^{5} + {\left({\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{7} + 2027025 \, A a^{3} c^{2} d + 61 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{6} + 1525 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{5} + 20065 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{4} + 675675 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 147859 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{3} + 594439 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m^{2} + 1140855 \, {\left(3 \, A a^{3} c^{2} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3}\right)} m\right)} x^{3} + {\left(A a^{3} c^{3} m^{7} + 63 \, A a^{3} c^{3} m^{6} + 1645 \, A a^{3} c^{3} m^{5} + 22995 \, A a^{3} c^{3} m^{4} + 185059 \, A a^{3} c^{3} m^{3} + 852957 \, A a^{3} c^{3} m^{2} + 2071215 \, A a^{3} c^{3} m + 2027025 \, A a^{3} c^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{8} + 64 \, m^{7} + 1708 \, m^{6} + 24640 \, m^{5} + 208054 \, m^{4} + 1038016 \, m^{3} + 2924172 \, m^{2} + 4098240 \, m + 2027025}"," ",0,"((B*b^3*d^3*m^7 + 49*B*b^3*d^3*m^6 + 973*B*b^3*d^3*m^5 + 10045*B*b^3*d^3*m^4 + 57379*B*b^3*d^3*m^3 + 177331*B*b^3*d^3*m^2 + 264207*B*b^3*d^3*m + 135135*B*b^3*d^3)*x^15 + ((3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^7 + 467775*B*b^3*c*d^2 + 51*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^6 + 1045*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^5 + 11055*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^4 + 155925*(3*B*a*b^2 + A*b^3)*d^3 + 64339*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^3 + 201609*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m^2 + 303255*(3*B*b^3*c*d^2 + (3*B*a*b^2 + A*b^3)*d^3)*m)*x^13 + 3*((B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^7 + 184275*B*b^3*c^2*d + 53*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^6 + 1125*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^5 + 12265*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^4 + 184275*(3*B*a*b^2 + A*b^3)*c*d^2 + 184275*(B*a^2*b + A*a*b^2)*d^3 + 73139*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^3 + 233487*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m^2 + 355815*(B*b^3*c^2*d + (3*B*a*b^2 + A*b^3)*c*d^2 + (B*a^2*b + A*a*b^2)*d^3)*m)*x^11 + ((B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^7 + 225225*B*b^3*c^3 + 55*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^6 + 1213*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^5 + 13723*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^4 + 675675*(3*B*a*b^2 + A*b^3)*c^2*d + 2027025*(B*a^2*b + A*a*b^2)*c*d^2 + 225225*(B*a^3 + 3*A*a^2*b)*d^3 + 84547*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^3 + 277093*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m^2 + 430335*(B*b^3*c^3 + 3*(3*B*a*b^2 + A*b^3)*c^2*d + 9*(B*a^2*b + A*a*b^2)*c*d^2 + (B*a^3 + 3*A*a^2*b)*d^3)*m)*x^9 + ((A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^7 + 289575*A*a^3*d^3 + 57*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^6 + 1309*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^5 + 15477*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^4 + 289575*(3*B*a*b^2 + A*b^3)*c^3 + 2606175*(B*a^2*b + A*a*b^2)*c^2*d + 868725*(B*a^3 + 3*A*a^2*b)*c*d^2 + 99715*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^3 + 340011*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m^2 + 544095*(A*a^3*d^3 + (3*B*a*b^2 + A*b^3)*c^3 + 9*(B*a^2*b + A*a*b^2)*c^2*d + 3*(B*a^3 + 3*A*a^2*b)*c*d^2)*m)*x^7 + 3*((A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^7 + 405405*A*a^3*c*d^2 + 59*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^6 + 1413*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^5 + 17575*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^4 + 405405*(B*a^2*b + A*a*b^2)*c^3 + 405405*(B*a^3 + 3*A*a^2*b)*c^2*d + 120179*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^3 + 437121*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m^2 + 738567*(A*a^3*c*d^2 + (B*a^2*b + A*a*b^2)*c^3 + (B*a^3 + 3*A*a^2*b)*c^2*d)*m)*x^5 + ((3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^7 + 2027025*A*a^3*c^2*d + 61*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^6 + 1525*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^5 + 20065*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^4 + 675675*(B*a^3 + 3*A*a^2*b)*c^3 + 147859*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^3 + 594439*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m^2 + 1140855*(3*A*a^3*c^2*d + (B*a^3 + 3*A*a^2*b)*c^3)*m)*x^3 + (A*a^3*c^3*m^7 + 63*A*a^3*c^3*m^6 + 1645*A*a^3*c^3*m^5 + 22995*A*a^3*c^3*m^4 + 185059*A*a^3*c^3*m^3 + 852957*A*a^3*c^3*m^2 + 2071215*A*a^3*c^3*m + 2027025*A*a^3*c^3)*x)*(e*x)^m/(m^8 + 64*m^7 + 1708*m^6 + 24640*m^5 + 208054*m^4 + 1038016*m^3 + 2924172*m^2 + 4098240*m + 2027025)","B",0
16,1,1690,0,0.816180," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} d^{3} m^{6} + 36 \, B b^{2} d^{3} m^{5} + 505 \, B b^{2} d^{3} m^{4} + 3480 \, B b^{2} d^{3} m^{3} + 12139 \, B b^{2} d^{3} m^{2} + 19524 \, B b^{2} d^{3} m + 10395 \, B b^{2} d^{3}\right)} x^{13} + {\left({\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m^{6} + 36855 \, B b^{2} c d^{2} + 38 \, {\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m^{5} + 555 \, {\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m^{4} + 12285 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} + 3940 \, {\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m^{3} + 14039 \, {\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m^{2} + 22902 \, {\left(3 \, B b^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} d^{3}\right)} m\right)} x^{11} + {\left({\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m^{6} + 45045 \, B b^{2} c^{2} d + 40 \, {\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m^{5} + 613 \, {\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m^{4} + 45045 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + 15015 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} + 4528 \, {\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m^{3} + 16627 \, {\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m^{2} + 27688 \, {\left(3 \, B b^{2} c^{2} d + 3 \, {\left(2 \, B a b + A b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, A a b\right)} d^{3}\right)} m\right)} x^{9} + {\left({\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m^{6} + 19305 \, B b^{2} c^{3} + 19305 \, A a^{2} d^{3} + 42 \, {\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m^{5} + 679 \, {\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m^{4} + 57915 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 57915 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2} + 5292 \, {\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m^{3} + 20335 \, {\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m^{2} + 34986 \, {\left(B b^{2} c^{3} + A a^{2} d^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{2}\right)} m\right)} x^{7} + {\left({\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m^{6} + 81081 \, A a^{2} c d^{2} + 44 \, {\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m^{5} + 753 \, {\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m^{4} + 27027 \, {\left(2 \, B a b + A b^{2}\right)} c^{3} + 81081 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d + 6280 \, {\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m^{3} + 25979 \, {\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m^{2} + 47436 \, {\left(3 \, A a^{2} c d^{2} + {\left(2 \, B a b + A b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d\right)} m\right)} x^{5} + {\left({\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m^{6} + 135135 \, A a^{2} c^{2} d + 46 \, {\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m^{5} + 835 \, {\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m^{4} + 45045 \, {\left(B a^{2} + 2 \, A a b\right)} c^{3} + 7540 \, {\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m^{3} + 34759 \, {\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m^{2} + 73054 \, {\left(3 \, A a^{2} c^{2} d + {\left(B a^{2} + 2 \, A a b\right)} c^{3}\right)} m\right)} x^{3} + {\left(A a^{2} c^{3} m^{6} + 48 \, A a^{2} c^{3} m^{5} + 925 \, A a^{2} c^{3} m^{4} + 9120 \, A a^{2} c^{3} m^{3} + 48259 \, A a^{2} c^{3} m^{2} + 129072 \, A a^{2} c^{3} m + 135135 \, A a^{2} c^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((B*b^2*d^3*m^6 + 36*B*b^2*d^3*m^5 + 505*B*b^2*d^3*m^4 + 3480*B*b^2*d^3*m^3 + 12139*B*b^2*d^3*m^2 + 19524*B*b^2*d^3*m + 10395*B*b^2*d^3)*x^13 + ((3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m^6 + 36855*B*b^2*c*d^2 + 38*(3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m^5 + 555*(3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m^4 + 12285*(2*B*a*b + A*b^2)*d^3 + 3940*(3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m^3 + 14039*(3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m^2 + 22902*(3*B*b^2*c*d^2 + (2*B*a*b + A*b^2)*d^3)*m)*x^11 + ((3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m^6 + 45045*B*b^2*c^2*d + 40*(3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m^5 + 613*(3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m^4 + 45045*(2*B*a*b + A*b^2)*c*d^2 + 15015*(B*a^2 + 2*A*a*b)*d^3 + 4528*(3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m^3 + 16627*(3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m^2 + 27688*(3*B*b^2*c^2*d + 3*(2*B*a*b + A*b^2)*c*d^2 + (B*a^2 + 2*A*a*b)*d^3)*m)*x^9 + ((B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m^6 + 19305*B*b^2*c^3 + 19305*A*a^2*d^3 + 42*(B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m^5 + 679*(B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m^4 + 57915*(2*B*a*b + A*b^2)*c^2*d + 57915*(B*a^2 + 2*A*a*b)*c*d^2 + 5292*(B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m^3 + 20335*(B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m^2 + 34986*(B*b^2*c^3 + A*a^2*d^3 + 3*(2*B*a*b + A*b^2)*c^2*d + 3*(B*a^2 + 2*A*a*b)*c*d^2)*m)*x^7 + ((3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m^6 + 81081*A*a^2*c*d^2 + 44*(3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m^5 + 753*(3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m^4 + 27027*(2*B*a*b + A*b^2)*c^3 + 81081*(B*a^2 + 2*A*a*b)*c^2*d + 6280*(3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m^3 + 25979*(3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m^2 + 47436*(3*A*a^2*c*d^2 + (2*B*a*b + A*b^2)*c^3 + 3*(B*a^2 + 2*A*a*b)*c^2*d)*m)*x^5 + ((3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m^6 + 135135*A*a^2*c^2*d + 46*(3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m^5 + 835*(3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m^4 + 45045*(B*a^2 + 2*A*a*b)*c^3 + 7540*(3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m^3 + 34759*(3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m^2 + 73054*(3*A*a^2*c^2*d + (B*a^2 + 2*A*a*b)*c^3)*m)*x^3 + (A*a^2*c^3*m^6 + 48*A*a^2*c^3*m^5 + 925*A*a^2*c^3*m^4 + 9120*A*a^2*c^3*m^3 + 48259*A*a^2*c^3*m^2 + 129072*A*a^2*c^3*m + 135135*A*a^2*c^3)*x)*(e*x)^m/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
17,1,837,0,0.644792," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B b d^{3} m^{5} + 25 \, B b d^{3} m^{4} + 230 \, B b d^{3} m^{3} + 950 \, B b d^{3} m^{2} + 1689 \, B b d^{3} m + 945 \, B b d^{3}\right)} x^{11} + {\left({\left(3 \, B b c d^{2} + {\left(B a + A b\right)} d^{3}\right)} m^{5} + 3465 \, B b c d^{2} + 27 \, {\left(3 \, B b c d^{2} + {\left(B a + A b\right)} d^{3}\right)} m^{4} + 1155 \, {\left(B a + A b\right)} d^{3} + 262 \, {\left(3 \, B b c d^{2} + {\left(B a + A b\right)} d^{3}\right)} m^{3} + 1122 \, {\left(3 \, B b c d^{2} + {\left(B a + A b\right)} d^{3}\right)} m^{2} + 2041 \, {\left(3 \, B b c d^{2} + {\left(B a + A b\right)} d^{3}\right)} m\right)} x^{9} + {\left({\left(3 \, B b c^{2} d + A a d^{3} + 3 \, {\left(B a + A b\right)} c d^{2}\right)} m^{5} + 4455 \, B b c^{2} d + 1485 \, A a d^{3} + 29 \, {\left(3 \, B b c^{2} d + A a d^{3} + 3 \, {\left(B a + A b\right)} c d^{2}\right)} m^{4} + 4455 \, {\left(B a + A b\right)} c d^{2} + 302 \, {\left(3 \, B b c^{2} d + A a d^{3} + 3 \, {\left(B a + A b\right)} c d^{2}\right)} m^{3} + 1366 \, {\left(3 \, B b c^{2} d + A a d^{3} + 3 \, {\left(B a + A b\right)} c d^{2}\right)} m^{2} + 2577 \, {\left(3 \, B b c^{2} d + A a d^{3} + 3 \, {\left(B a + A b\right)} c d^{2}\right)} m\right)} x^{7} + {\left({\left(B b c^{3} + 3 \, A a c d^{2} + 3 \, {\left(B a + A b\right)} c^{2} d\right)} m^{5} + 2079 \, B b c^{3} + 6237 \, A a c d^{2} + 31 \, {\left(B b c^{3} + 3 \, A a c d^{2} + 3 \, {\left(B a + A b\right)} c^{2} d\right)} m^{4} + 6237 \, {\left(B a + A b\right)} c^{2} d + 350 \, {\left(B b c^{3} + 3 \, A a c d^{2} + 3 \, {\left(B a + A b\right)} c^{2} d\right)} m^{3} + 1730 \, {\left(B b c^{3} + 3 \, A a c d^{2} + 3 \, {\left(B a + A b\right)} c^{2} d\right)} m^{2} + 3489 \, {\left(B b c^{3} + 3 \, A a c d^{2} + 3 \, {\left(B a + A b\right)} c^{2} d\right)} m\right)} x^{5} + {\left({\left(3 \, A a c^{2} d + {\left(B a + A b\right)} c^{3}\right)} m^{5} + 10395 \, A a c^{2} d + 33 \, {\left(3 \, A a c^{2} d + {\left(B a + A b\right)} c^{3}\right)} m^{4} + 3465 \, {\left(B a + A b\right)} c^{3} + 406 \, {\left(3 \, A a c^{2} d + {\left(B a + A b\right)} c^{3}\right)} m^{3} + 2262 \, {\left(3 \, A a c^{2} d + {\left(B a + A b\right)} c^{3}\right)} m^{2} + 5353 \, {\left(3 \, A a c^{2} d + {\left(B a + A b\right)} c^{3}\right)} m\right)} x^{3} + {\left(A a c^{3} m^{5} + 35 \, A a c^{3} m^{4} + 470 \, A a c^{3} m^{3} + 3010 \, A a c^{3} m^{2} + 9129 \, A a c^{3} m + 10395 \, A a c^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((B*b*d^3*m^5 + 25*B*b*d^3*m^4 + 230*B*b*d^3*m^3 + 950*B*b*d^3*m^2 + 1689*B*b*d^3*m + 945*B*b*d^3)*x^11 + ((3*B*b*c*d^2 + (B*a + A*b)*d^3)*m^5 + 3465*B*b*c*d^2 + 27*(3*B*b*c*d^2 + (B*a + A*b)*d^3)*m^4 + 1155*(B*a + A*b)*d^3 + 262*(3*B*b*c*d^2 + (B*a + A*b)*d^3)*m^3 + 1122*(3*B*b*c*d^2 + (B*a + A*b)*d^3)*m^2 + 2041*(3*B*b*c*d^2 + (B*a + A*b)*d^3)*m)*x^9 + ((3*B*b*c^2*d + A*a*d^3 + 3*(B*a + A*b)*c*d^2)*m^5 + 4455*B*b*c^2*d + 1485*A*a*d^3 + 29*(3*B*b*c^2*d + A*a*d^3 + 3*(B*a + A*b)*c*d^2)*m^4 + 4455*(B*a + A*b)*c*d^2 + 302*(3*B*b*c^2*d + A*a*d^3 + 3*(B*a + A*b)*c*d^2)*m^3 + 1366*(3*B*b*c^2*d + A*a*d^3 + 3*(B*a + A*b)*c*d^2)*m^2 + 2577*(3*B*b*c^2*d + A*a*d^3 + 3*(B*a + A*b)*c*d^2)*m)*x^7 + ((B*b*c^3 + 3*A*a*c*d^2 + 3*(B*a + A*b)*c^2*d)*m^5 + 2079*B*b*c^3 + 6237*A*a*c*d^2 + 31*(B*b*c^3 + 3*A*a*c*d^2 + 3*(B*a + A*b)*c^2*d)*m^4 + 6237*(B*a + A*b)*c^2*d + 350*(B*b*c^3 + 3*A*a*c*d^2 + 3*(B*a + A*b)*c^2*d)*m^3 + 1730*(B*b*c^3 + 3*A*a*c*d^2 + 3*(B*a + A*b)*c^2*d)*m^2 + 3489*(B*b*c^3 + 3*A*a*c*d^2 + 3*(B*a + A*b)*c^2*d)*m)*x^5 + ((3*A*a*c^2*d + (B*a + A*b)*c^3)*m^5 + 10395*A*a*c^2*d + 33*(3*A*a*c^2*d + (B*a + A*b)*c^3)*m^4 + 3465*(B*a + A*b)*c^3 + 406*(3*A*a*c^2*d + (B*a + A*b)*c^3)*m^3 + 2262*(3*A*a*c^2*d + (B*a + A*b)*c^3)*m^2 + 5353*(3*A*a*c^2*d + (B*a + A*b)*c^3)*m)*x^3 + (A*a*c^3*m^5 + 35*A*a*c^3*m^4 + 470*A*a*c^3*m^3 + 3010*A*a*c^3*m^2 + 9129*A*a*c^3*m + 10395*A*a*c^3)*x)*(e*x)^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
18,1,381,0,0.911616," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B d^{3} m^{4} + 16 \, B d^{3} m^{3} + 86 \, B d^{3} m^{2} + 176 \, B d^{3} m + 105 \, B d^{3}\right)} x^{9} + {\left({\left(3 \, B c d^{2} + A d^{3}\right)} m^{4} + 405 \, B c d^{2} + 135 \, A d^{3} + 18 \, {\left(3 \, B c d^{2} + A d^{3}\right)} m^{3} + 104 \, {\left(3 \, B c d^{2} + A d^{3}\right)} m^{2} + 222 \, {\left(3 \, B c d^{2} + A d^{3}\right)} m\right)} x^{7} + 3 \, {\left({\left(B c^{2} d + A c d^{2}\right)} m^{4} + 189 \, B c^{2} d + 189 \, A c d^{2} + 20 \, {\left(B c^{2} d + A c d^{2}\right)} m^{3} + 130 \, {\left(B c^{2} d + A c d^{2}\right)} m^{2} + 300 \, {\left(B c^{2} d + A c d^{2}\right)} m\right)} x^{5} + {\left({\left(B c^{3} + 3 \, A c^{2} d\right)} m^{4} + 315 \, B c^{3} + 945 \, A c^{2} d + 22 \, {\left(B c^{3} + 3 \, A c^{2} d\right)} m^{3} + 164 \, {\left(B c^{3} + 3 \, A c^{2} d\right)} m^{2} + 458 \, {\left(B c^{3} + 3 \, A c^{2} d\right)} m\right)} x^{3} + {\left(A c^{3} m^{4} + 24 \, A c^{3} m^{3} + 206 \, A c^{3} m^{2} + 744 \, A c^{3} m + 945 \, A c^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((B*d^3*m^4 + 16*B*d^3*m^3 + 86*B*d^3*m^2 + 176*B*d^3*m + 105*B*d^3)*x^9 + ((3*B*c*d^2 + A*d^3)*m^4 + 405*B*c*d^2 + 135*A*d^3 + 18*(3*B*c*d^2 + A*d^3)*m^3 + 104*(3*B*c*d^2 + A*d^3)*m^2 + 222*(3*B*c*d^2 + A*d^3)*m)*x^7 + 3*((B*c^2*d + A*c*d^2)*m^4 + 189*B*c^2*d + 189*A*c*d^2 + 20*(B*c^2*d + A*c*d^2)*m^3 + 130*(B*c^2*d + A*c*d^2)*m^2 + 300*(B*c^2*d + A*c*d^2)*m)*x^5 + ((B*c^3 + 3*A*c^2*d)*m^4 + 315*B*c^3 + 945*A*c^2*d + 22*(B*c^3 + 3*A*c^2*d)*m^3 + 164*(B*c^3 + 3*A*c^2*d)*m^2 + 458*(B*c^3 + 3*A*c^2*d)*m)*x^3 + (A*c^3*m^4 + 24*A*c^3*m^3 + 206*A*c^3*m^2 + 744*A*c^3*m + 945*A*c^3)*x)*(e*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
19,0,0,0,0.644587," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{3} x^{8} + {\left(3 \, B c d^{2} + A d^{3}\right)} x^{6} + 3 \, {\left(B c^{2} d + A c d^{2}\right)} x^{4} + A c^{3} + {\left(B c^{3} + 3 \, A c^{2} d\right)} x^{2}\right)} \left(e x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((B*d^3*x^8 + (3*B*c*d^2 + A*d^3)*x^6 + 3*(B*c^2*d + A*c*d^2)*x^4 + A*c^3 + (B*c^3 + 3*A*c^2*d)*x^2)*(e*x)^m/(b*x^2 + a), x)","F",0
20,0,0,0,0.629981," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{3} x^{8} + {\left(3 \, B c d^{2} + A d^{3}\right)} x^{6} + 3 \, {\left(B c^{2} d + A c d^{2}\right)} x^{4} + A c^{3} + {\left(B c^{3} + 3 \, A c^{2} d\right)} x^{2}\right)} \left(e x\right)^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*d^3*x^8 + (3*B*c*d^2 + A*d^3)*x^6 + 3*(B*c^2*d + A*c*d^2)*x^4 + A*c^3 + (B*c^3 + 3*A*c^2*d)*x^2)*(e*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
21,0,0,0,0.724156," ","integrate((e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B d^{3} x^{8} + {\left(3 \, B c d^{2} + A d^{3}\right)} x^{6} + 3 \, {\left(B c^{2} d + A c d^{2}\right)} x^{4} + A c^{3} + {\left(B c^{3} + 3 \, A c^{2} d\right)} x^{2}\right)} \left(e x\right)^{m}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*d^3*x^8 + (3*B*c*d^2 + A*d^3)*x^6 + 3*(B*c^2*d + A*c*d^2)*x^4 + A*c^3 + (B*c^3 + 3*A*c^2*d)*x^2)*(e*x)^m/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
22,0,0,0,0.661345," ","integrate((e*x)^m*(b*x^2+a)^4*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{4} x^{10} + {\left(4 \, B a b^{3} + A b^{4}\right)} x^{8} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{6} + A a^{4} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{4} + {\left(B a^{4} + 4 \, A a^{3} b\right)} x^{2}\right)} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*b^4*x^10 + (4*B*a*b^3 + A*b^4)*x^8 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*x^6 + A*a^4 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*x^4 + (B*a^4 + 4*A*a^3*b)*x^2)*(e*x)^m/(d*x^2 + c), x)","F",0
23,0,0,0,0.660342," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{3} x^{8} + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + A a^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*b^3*x^8 + (3*B*a*b^2 + A*b^3)*x^6 + 3*(B*a^2*b + A*a*b^2)*x^4 + A*a^3 + (B*a^3 + 3*A*a^2*b)*x^2)*(e*x)^m/(d*x^2 + c), x)","F",0
24,0,0,0,0.667164," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{6} + {\left(2 \, B a b + A b^{2}\right)} x^{4} + A a^{2} + {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*b^2*x^6 + (2*B*a*b + A*b^2)*x^4 + A*a^2 + (B*a^2 + 2*A*a*b)*x^2)*(e*x)^m/(d*x^2 + c), x)","F",0
25,0,0,0,0.560418," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*(e*x)^m/(d*x^2 + c), x)","F",0
26,0,0,0,0.722498," ","integrate((e*x)^m*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(d*x^2 + c), x)","F",0
27,0,0,0,0.764829," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
28,0,0,0,0.620803," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2), x)","F",0
29,0,0,0,0.665028," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{3} d x^{8} + {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{6} + 3 \, {\left(a b^{2} c + a^{2} b d\right)} x^{4} + a^{3} c + {\left(3 \, a^{2} b c + a^{3} d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^3*d*x^8 + (b^3*c + 3*a*b^2*d)*x^6 + 3*(a*b^2*c + a^2*b*d)*x^4 + a^3*c + (3*a^2*b*c + a^3*d)*x^2), x)","F",0
30,0,0,0,0.611072," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{3} x^{8} + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + A a^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \left(e x\right)^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((B*b^3*x^8 + (3*B*a*b^2 + A*b^3)*x^6 + 3*(B*a^2*b + A*a*b^2)*x^4 + A*a^3 + (B*a^3 + 3*A*a^2*b)*x^2)*(e*x)^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
31,0,0,0,0.680125," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{6} + {\left(2 \, B a b + A b^{2}\right)} x^{4} + A a^{2} + {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \left(e x\right)^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((B*b^2*x^6 + (2*B*a*b + A*b^2)*x^4 + A*a^2 + (B*a^2 + 2*A*a*b)*x^2)*(e*x)^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
32,0,0,0,0.730410," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \left(e x\right)^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*(e*x)^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
33,0,0,0,0.664234," ","integrate((e*x)^m*(B*x^2+A)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
34,0,0,0,0.801593," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b d^{2} x^{6} + {\left(2 \, b c d + a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b*d^2*x^6 + (2*b*c*d + a*d^2)*x^4 + a*c^2 + (b*c^2 + 2*a*c*d)*x^2), x)","F",0
35,0,0,0,0.801427," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{2} d^{2} x^{8} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^2*d^2*x^8 + 2*(b^2*c*d + a*b*d^2)*x^6 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(a*b*c^2 + a^2*c*d)*x^2), x)","F",0
36,0,0,0,0.614867," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{3} d^{2} x^{10} + {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} x^{8} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x^{6} + a^{3} c^{2} + {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{4} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^3*d^2*x^10 + (2*b^3*c*d + 3*a*b^2*d^2)*x^8 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*x^6 + a^3*c^2 + (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*x^4 + (3*a^2*b*c^2 + 2*a^3*c*d)*x^2), x)","F",0
37,0,0,0,0.714812," ","integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{3} x^{8} + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + A a^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \left(e x\right)^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((B*b^3*x^8 + (3*B*a*b^2 + A*b^3)*x^6 + 3*(B*a^2*b + A*a*b^2)*x^4 + A*a^3 + (B*a^3 + 3*A*a^2*b)*x^2)*(e*x)^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
38,0,0,0,0.851384," ","integrate((e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{6} + {\left(2 \, B a b + A b^{2}\right)} x^{4} + A a^{2} + {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \left(e x\right)^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((B*b^2*x^6 + (2*B*a*b + A*b^2)*x^4 + A*a^2 + (B*a^2 + 2*A*a*b)*x^2)*(e*x)^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
39,0,0,0,0.646489," ","integrate((e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \left(e x\right)^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*(e*x)^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
40,0,0,0,1.034712," ","integrate((e*x)^m*(B*x^2+A)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
41,0,0,0,0.974428," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b d^{3} x^{8} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{6} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} x^{4} + a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b*d^3*x^8 + (3*b*c*d^2 + a*d^3)*x^6 + 3*(b*c^2*d + a*c*d^2)*x^4 + a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2), x)","F",0
42,0,0,0,1.157887," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{2} d^{3} x^{10} + {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} + a^{2} c^{3} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^2*d^3*x^10 + (3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 + a^2*c^3 + (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + (2*a*b*c^3 + 3*a^2*c^2*d)*x^2), x)","F",0
43,0,0,0,1.076128," ","integrate((e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \left(e x\right)^{m}}{b^{3} d^{3} x^{12} + 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{10} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{8} + {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{6} + a^{3} c^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} x^{4} + 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x)^m/(b^3*d^3*x^12 + 3*(b^3*c*d^2 + a*b^2*d^3)*x^10 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*x^8 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*x^6 + a^3*c^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*x^4 + 3*(a^2*b*c^3 + a^3*c^2*d)*x^2), x)","F",0
44,0,0,0,1.043681," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B d^{3} x^{8} + {\left(3 \, B c d^{2} + A d^{3}\right)} x^{6} + 3 \, {\left(B c^{2} d + A c d^{2}\right)} x^{4} + A c^{3} + {\left(B c^{3} + 3 \, A c^{2} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*d^3*x^8 + (3*B*c*d^2 + A*d^3)*x^6 + 3*(B*c^2*d + A*c*d^2)*x^4 + A*c^3 + (B*c^3 + 3*A*c^2*d)*x^2)*(b*x^2 + a)^p*(e*x)^m, x)","F",0
45,0,0,0,0.971861," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B d^{2} x^{6} + {\left(2 \, B c d + A d^{2}\right)} x^{4} + A c^{2} + {\left(B c^{2} + 2 \, A c d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*d^2*x^6 + (2*B*c*d + A*d^2)*x^4 + A*c^2 + (B*c^2 + 2*A*c*d)*x^2)*(b*x^2 + a)^p*(e*x)^m, x)","F",0
46,0,0,0,0.642300," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B d x^{4} + {\left(B c + A d\right)} x^{2} + A c\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*d*x^4 + (B*c + A*d)*x^2 + A*c)*(b*x^2 + a)^p*(e*x)^m, x)","F",0
47,0,0,0,0.844293," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((B*x^2 + A)*(b*x^2 + a)^p*(e*x)^m/(d*x^2 + c), x)","F",0
48,0,0,0,0.990575," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*(b*x^2 + a)^p*(e*x)^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
49,0,0,0,0.851516," ","integrate((e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{p} \left(e x\right)^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*(b*x^2 + a)^p*(e*x)^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
50,1,231,0,0.951464," ","integrate((B*x^2+A)*(d*x^2+c)*(b*x^2+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, A \sqrt{a} b^{2} c \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, B b^{2} d x^{4} + {\left(5 \, B b^{2} c + {\left(B a b + 5 \, A b^{2}\right)} d\right)} x^{2} + 5 \, {\left(B a b + 3 \, A b^{2}\right)} c - {\left(2 \, B a^{2} - 5 \, A a b\right)} d\right)} \sqrt{b x^{2} + a}}{30 \, b^{2}}, \frac{15 \, A \sqrt{-a} b^{2} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, B b^{2} d x^{4} + {\left(5 \, B b^{2} c + {\left(B a b + 5 \, A b^{2}\right)} d\right)} x^{2} + 5 \, {\left(B a b + 3 \, A b^{2}\right)} c - {\left(2 \, B a^{2} - 5 \, A a b\right)} d\right)} \sqrt{b x^{2} + a}}{15 \, b^{2}}\right]"," ",0,"[1/30*(15*A*sqrt(a)*b^2*c*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*B*b^2*d*x^4 + (5*B*b^2*c + (B*a*b + 5*A*b^2)*d)*x^2 + 5*(B*a*b + 3*A*b^2)*c - (2*B*a^2 - 5*A*a*b)*d)*sqrt(b*x^2 + a))/b^2, 1/15*(15*A*sqrt(-a)*b^2*c*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*B*b^2*d*x^4 + (5*B*b^2*c + (B*a*b + 5*A*b^2)*d)*x^2 + 5*(B*a*b + 3*A*b^2)*c - (2*B*a^2 - 5*A*a*b)*d)*sqrt(b*x^2 + a))/b^2]","A",0
51,1,217,0,0.928528," ","integrate((b*x^2+a)*(B*x^2+A)*(d*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, A a \sqrt{c} d^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(3 \, B b d^{2} x^{4} - 2 \, B b c^{2} + 15 \, A a d^{2} + 5 \, {\left(B a + A b\right)} c d + {\left(B b c d + 5 \, {\left(B a + A b\right)} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, d^{2}}, \frac{15 \, A a \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, B b d^{2} x^{4} - 2 \, B b c^{2} + 15 \, A a d^{2} + 5 \, {\left(B a + A b\right)} c d + {\left(B b c d + 5 \, {\left(B a + A b\right)} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, d^{2}}\right]"," ",0,"[1/30*(15*A*a*sqrt(c)*d^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(3*B*b*d^2*x^4 - 2*B*b*c^2 + 15*A*a*d^2 + 5*(B*a + A*b)*c*d + (B*b*c*d + 5*(B*a + A*b)*d^2)*x^2)*sqrt(d*x^2 + c))/d^2, 1/15*(15*A*a*sqrt(-c)*d^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (3*B*b*d^2*x^4 - 2*B*b*c^2 + 15*A*a*d^2 + 5*(B*a + A*b)*c*d + (B*b*c*d + 5*(B*a + A*b)*d^2)*x^2)*sqrt(d*x^2 + c))/d^2]","A",0
