3.15 \(\int (e x)^m (a+b x^2)^3 (A+B x^2) (c+d x^2)^3 \, dx\)
Optimal. Leaf size=379 \[ \frac{3 a c (e x)^{m+5} \left (A \left (a^2 d^2+3 a b c d+b^2 c^2\right )+a B c (a d+b c)\right )}{e^5 (m+5)}+\frac{(e x)^{m+7} \left (A \left (9 a^2 b c d^2+a^3 d^3+9 a b^2 c^2 d+b^3 c^3\right )+3 a B c \left (a^2 d^2+3 a b c d+b^2 c^2\right )\right )}{e^7 (m+7)}+\frac{(e x)^{m+9} \left (3 a^2 b d^2 (A d+3 B c)+a^3 B d^3+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right )}{e^9 (m+9)}+\frac{3 b d (e x)^{m+11} \left (a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right )}{e^{11} (m+11)}+\frac{a^2 c^2 (e x)^{m+3} (3 A (a d+b c)+a B c)}{e^3 (m+3)}+\frac{a^3 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d^2 (e x)^{m+13} (3 a B d+A b d+3 b B c)}{e^{13} (m+13)}+\frac{b^3 B d^3 (e x)^{m+15}}{e^{15} (m+15)} \]
[Out]
(a^3*A*c^3*(e*x)^(1 + m))/(e*(1 + m)) + (a^2*c^2*(a*B*c + 3*A*(b*c + a*d))*(e*x)^(3 + m))/(e^3*(3 + m)) + (3*a
*c*(a*B*c*(b*c + a*d) + A*(b^2*c^2 + 3*a*b*c*d + a^2*d^2))*(e*x)^(5 + m))/(e^5*(5 + m)) + ((3*a*B*c*(b^2*c^2 +
3*a*b*c*d + a^2*d^2) + A*(b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3))*(e*x)^(7 + m))/(e^7*(7 + m)) +
((a^3*B*d^3 + 9*a*b^2*c*d*(B*c + A*d) + 3*a^2*b*d^2*(3*B*c + A*d) + b^3*c^2*(B*c + 3*A*d))*(e*x)^(9 + m))/(e^9
*(9 + m)) + (3*b*d*(a^2*B*d^2 + b^2*c*(B*c + A*d) + a*b*d*(3*B*c + A*d))*(e*x)^(11 + m))/(e^11*(11 + m)) + (b^
2*d^2*(3*b*B*c + A*b*d + 3*a*B*d)*(e*x)^(13 + m))/(e^13*(13 + m)) + (b^3*B*d^3*(e*x)^(15 + m))/(e^15*(15 + m))
________________________________________________________________________________________
Rubi [A] time = 0.400774, antiderivative size = 379, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.032, Rules used =
{570} \[ \frac{3 a c (e x)^{m+5} \left (A \left (a^2 d^2+3 a b c d+b^2 c^2\right )+a B c (a d+b c)\right )}{e^5 (m+5)}+\frac{(e x)^{m+7} \left (A \left (9 a^2 b c d^2+a^3 d^3+9 a b^2 c^2 d+b^3 c^3\right )+3 a B c \left (a^2 d^2+3 a b c d+b^2 c^2\right )\right )}{e^7 (m+7)}+\frac{(e x)^{m+9} \left (3 a^2 b d^2 (A d+3 B c)+a^3 B d^3+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right )}{e^9 (m+9)}+\frac{3 b d (e x)^{m+11} \left (a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right )}{e^{11} (m+11)}+\frac{a^2 c^2 (e x)^{m+3} (3 A (a d+b c)+a B c)}{e^3 (m+3)}+\frac{a^3 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d^2 (e x)^{m+13} (3 a B d+A b d+3 b B c)}{e^{13} (m+13)}+\frac{b^3 B d^3 (e x)^{m+15}}{e^{15} (m+15)} \]
Antiderivative was successfully verified.
[In]
Int[(e*x)^m*(a + b*x^2)^3*(A + B*x^2)*(c + d*x^2)^3,x]
[Out]
(a^3*A*c^3*(e*x)^(1 + m))/(e*(1 + m)) + (a^2*c^2*(a*B*c + 3*A*(b*c + a*d))*(e*x)^(3 + m))/(e^3*(3 + m)) + (3*a
*c*(a*B*c*(b*c + a*d) + A*(b^2*c^2 + 3*a*b*c*d + a^2*d^2))*(e*x)^(5 + m))/(e^5*(5 + m)) + ((3*a*B*c*(b^2*c^2 +
3*a*b*c*d + a^2*d^2) + A*(b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3))*(e*x)^(7 + m))/(e^7*(7 + m)) +
((a^3*B*d^3 + 9*a*b^2*c*d*(B*c + A*d) + 3*a^2*b*d^2*(3*B*c + A*d) + b^3*c^2*(B*c + 3*A*d))*(e*x)^(9 + m))/(e^9
*(9 + m)) + (3*b*d*(a^2*B*d^2 + b^2*c*(B*c + A*d) + a*b*d*(3*B*c + A*d))*(e*x)^(11 + m))/(e^11*(11 + m)) + (b^
2*d^2*(3*b*B*c + A*b*d + 3*a*B*d)*(e*x)^(13 + m))/(e^13*(13 + m)) + (b^3*B*d^3*(e*x)^(15 + m))/(e^15*(15 + m))
Rule 570
Int[((g_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_.)*((c_) + (d_.)*(x_)^(n_))^(q_.)*((e_) + (f_.)*(x_)^(n_))^
(r_.), x_Symbol] :> Int[ExpandIntegrand[(g*x)^m*(a + b*x^n)^p*(c + d*x^n)^q*(e + f*x^n)^r, x], x] /; FreeQ[{a,
b, c, d, e, f, g, m, n}, x] && IGtQ[p, -2] && IGtQ[q, 0] && IGtQ[r, 0]
Rubi steps
\begin{align*} \int (e x)^m \left (a+b x^2\right )^3 \left (A+B x^2\right ) \left (c+d x^2\right )^3 \, dx &=\int \left (a^3 A c^3 (e x)^m+\frac{a^2 c^2 (a B c+3 A (b c+a d)) (e x)^{2+m}}{e^2}+\frac{3 a c \left (a B c (b c+a d)+A \left (b^2 c^2+3 a b c d+a^2 d^2\right )\right ) (e x)^{4+m}}{e^4}+\frac{\left (3 a B c \left (b^2 c^2+3 a b c d+a^2 d^2\right )+A \left (b^3 c^3+9 a b^2 c^2 d+9 a^2 b c d^2+a^3 d^3\right )\right ) (e x)^{6+m}}{e^6}+\frac{\left (a^3 B d^3+9 a b^2 c d (B c+A d)+3 a^2 b d^2 (3 B c+A d)+b^3 c^2 (B c+3 A d)\right ) (e x)^{8+m}}{e^8}+\frac{3 b d \left (a^2 B d^2+b^2 c (B c+A d)+a b d (3 B c+A d)\right ) (e x)^{10+m}}{e^{10}}+\frac{b^2 d^2 (3 b B c+A b d+3 a B d) (e x)^{12+m}}{e^{12}}+\frac{b^3 B d^3 (e x)^{14+m}}{e^{14}}\right ) \, dx\\ &=\frac{a^3 A c^3 (e x)^{1+m}}{e (1+m)}+\frac{a^2 c^2 (a B c+3 A (b c+a d)) (e x)^{3+m}}{e^3 (3+m)}+\frac{3 a c \left (a B c (b c+a d)+A \left (b^2 c^2+3 a b c d+a^2 d^2\right )\right ) (e x)^{5+m}}{e^5 (5+m)}+\frac{\left (3 a B c \left (b^2 c^2+3 a b c d+a^2 d^2\right )+A \left (b^3 c^3+9 a b^2 c^2 d+9 a^2 b c d^2+a^3 d^3\right )\right ) (e x)^{7+m}}{e^7 (7+m)}+\frac{\left (a^3 B d^3+9 a b^2 c d (B c+A d)+3 a^2 b d^2 (3 B c+A d)+b^3 c^2 (B c+3 A d)\right ) (e x)^{9+m}}{e^9 (9+m)}+\frac{3 b d \left (a^2 B d^2+b^2 c (B c+A d)+a b d (3 B c+A d)\right ) (e x)^{11+m}}{e^{11} (11+m)}+\frac{b^2 d^2 (3 b B c+A b d+3 a B d) (e x)^{13+m}}{e^{13} (13+m)}+\frac{b^3 B d^3 (e x)^{15+m}}{e^{15} (15+m)}\\ \end{align*}
Mathematica [A] time = 0.694751, size = 327, normalized size = 0.86 \[ x (e x)^m \left (\frac{x^8 \left (3 a^2 b d^2 (A d+3 B c)+a^3 B d^3+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right )}{m+9}+\frac{x^6 \left (A \left (9 a^2 b c d^2+a^3 d^3+9 a b^2 c^2 d+b^3 c^3\right )+3 a B c \left (a^2 d^2+3 a b c d+b^2 c^2\right )\right )}{m+7}+\frac{3 a c x^4 \left (A \left (a^2 d^2+3 a b c d+b^2 c^2\right )+a B c (a d+b c)\right )}{m+5}+\frac{3 b d x^{10} \left (a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right )}{m+11}+\frac{a^2 c^2 x^2 (3 A (a d+b c)+a B c)}{m+3}+\frac{a^3 A c^3}{m+1}+\frac{b^2 d^2 x^{12} (3 a B d+A b d+3 b B c)}{m+13}+\frac{b^3 B d^3 x^{14}}{m+15}\right ) \]
Antiderivative was successfully verified.
[In]
Integrate[(e*x)^m*(a + b*x^2)^3*(A + B*x^2)*(c + d*x^2)^3,x]
[Out]
x*(e*x)^m*((a^3*A*c^3)/(1 + m) + (a^2*c^2*(a*B*c + 3*A*(b*c + a*d))*x^2)/(3 + m) + (3*a*c*(a*B*c*(b*c + a*d) +
A*(b^2*c^2 + 3*a*b*c*d + a^2*d^2))*x^4)/(5 + m) + ((3*a*B*c*(b^2*c^2 + 3*a*b*c*d + a^2*d^2) + A*(b^3*c^3 + 9*
a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3))*x^6)/(7 + m) + ((a^3*B*d^3 + 9*a*b^2*c*d*(B*c + A*d) + 3*a^2*b*d^2*(3*
B*c + A*d) + b^3*c^2*(B*c + 3*A*d))*x^8)/(9 + m) + (3*b*d*(a^2*B*d^2 + b^2*c*(B*c + A*d) + a*b*d*(3*B*c + A*d)
)*x^10)/(11 + m) + (b^2*d^2*(3*b*B*c + A*b*d + 3*a*B*d)*x^12)/(13 + m) + (b^3*B*d^3*x^14)/(15 + m))
________________________________________________________________________________________
Maple [B] time = 0.01, size = 3953, normalized size = 10.4 \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x)
[Out]
x*(B*b^3*d^3*m^7*x^14+49*B*b^3*d^3*m^6*x^14+A*b^3*d^3*m^7*x^12+3*B*a*b^2*d^3*m^7*x^12+3*B*b^3*c*d^2*m^7*x^12+9
73*B*b^3*d^3*m^5*x^14+51*A*b^3*d^3*m^6*x^12+153*B*a*b^2*d^3*m^6*x^12+153*B*b^3*c*d^2*m^6*x^12+10045*B*b^3*d^3*
m^4*x^14+3*A*a*b^2*d^3*m^7*x^10+3*A*b^3*c*d^2*m^7*x^10+1045*A*b^3*d^3*m^5*x^12+3*B*a^2*b*d^3*m^7*x^10+9*B*a*b^
2*c*d^2*m^7*x^10+3135*B*a*b^2*d^3*m^5*x^12+3*B*b^3*c^2*d*m^7*x^10+3135*B*b^3*c*d^2*m^5*x^12+57379*B*b^3*d^3*m^
3*x^14+159*A*a*b^2*d^3*m^6*x^10+159*A*b^3*c*d^2*m^6*x^10+11055*A*b^3*d^3*m^4*x^12+159*B*a^2*b*d^3*m^6*x^10+477
*B*a*b^2*c*d^2*m^6*x^10+33165*B*a*b^2*d^3*m^4*x^12+159*B*b^3*c^2*d*m^6*x^10+33165*B*b^3*c*d^2*m^4*x^12+177331*
B*b^3*d^3*m^2*x^14+3*A*a^2*b*d^3*m^7*x^8+9*A*a*b^2*c*d^2*m^7*x^8+3375*A*a*b^2*d^3*m^5*x^10+3*A*b^3*c^2*d*m^7*x
^8+3375*A*b^3*c*d^2*m^5*x^10+64339*A*b^3*d^3*m^3*x^12+B*a^3*d^3*m^7*x^8+9*B*a^2*b*c*d^2*m^7*x^8+3375*B*a^2*b*d
^3*m^5*x^10+9*B*a*b^2*c^2*d*m^7*x^8+10125*B*a*b^2*c*d^2*m^5*x^10+193017*B*a*b^2*d^3*m^3*x^12+B*b^3*c^3*m^7*x^8
+3375*B*b^3*c^2*d*m^5*x^10+193017*B*b^3*c*d^2*m^3*x^12+264207*B*b^3*d^3*m*x^14+165*A*a^2*b*d^3*m^6*x^8+495*A*a
*b^2*c*d^2*m^6*x^8+36795*A*a*b^2*d^3*m^4*x^10+165*A*b^3*c^2*d*m^6*x^8+36795*A*b^3*c*d^2*m^4*x^10+201609*A*b^3*
d^3*m^2*x^12+55*B*a^3*d^3*m^6*x^8+495*B*a^2*b*c*d^2*m^6*x^8+36795*B*a^2*b*d^3*m^4*x^10+495*B*a*b^2*c^2*d*m^6*x
^8+110385*B*a*b^2*c*d^2*m^4*x^10+604827*B*a*b^2*d^3*m^2*x^12+55*B*b^3*c^3*m^6*x^8+36795*B*b^3*c^2*d*m^4*x^10+6
04827*B*b^3*c*d^2*m^2*x^12+135135*B*b^3*d^3*x^14+A*a^3*d^3*m^7*x^6+9*A*a^2*b*c*d^2*m^7*x^6+3639*A*a^2*b*d^3*m^
5*x^8+9*A*a*b^2*c^2*d*m^7*x^6+10917*A*a*b^2*c*d^2*m^5*x^8+219417*A*a*b^2*d^3*m^3*x^10+A*b^3*c^3*m^7*x^6+3639*A
*b^3*c^2*d*m^5*x^8+219417*A*b^3*c*d^2*m^3*x^10+303255*A*b^3*d^3*m*x^12+3*B*a^3*c*d^2*m^7*x^6+1213*B*a^3*d^3*m^
5*x^8+9*B*a^2*b*c^2*d*m^7*x^6+10917*B*a^2*b*c*d^2*m^5*x^8+219417*B*a^2*b*d^3*m^3*x^10+3*B*a*b^2*c^3*m^7*x^6+10
917*B*a*b^2*c^2*d*m^5*x^8+658251*B*a*b^2*c*d^2*m^3*x^10+909765*B*a*b^2*d^3*m*x^12+1213*B*b^3*c^3*m^5*x^8+21941
7*B*b^3*c^2*d*m^3*x^10+909765*B*b^3*c*d^2*m*x^12+57*A*a^3*d^3*m^6*x^6+513*A*a^2*b*c*d^2*m^6*x^6+41169*A*a^2*b*
d^3*m^4*x^8+513*A*a*b^2*c^2*d*m^6*x^6+123507*A*a*b^2*c*d^2*m^4*x^8+700461*A*a*b^2*d^3*m^2*x^10+57*A*b^3*c^3*m^
6*x^6+41169*A*b^3*c^2*d*m^4*x^8+700461*A*b^3*c*d^2*m^2*x^10+155925*A*b^3*d^3*x^12+171*B*a^3*c*d^2*m^6*x^6+1372
3*B*a^3*d^3*m^4*x^8+513*B*a^2*b*c^2*d*m^6*x^6+123507*B*a^2*b*c*d^2*m^4*x^8+700461*B*a^2*b*d^3*m^2*x^10+171*B*a
*b^2*c^3*m^6*x^6+123507*B*a*b^2*c^2*d*m^4*x^8+2101383*B*a*b^2*c*d^2*m^2*x^10+467775*B*a*b^2*d^3*x^12+13723*B*b
^3*c^3*m^4*x^8+700461*B*b^3*c^2*d*m^2*x^10+467775*B*b^3*c*d^2*x^12+3*A*a^3*c*d^2*m^7*x^4+1309*A*a^3*d^3*m^5*x^
6+9*A*a^2*b*c^2*d*m^7*x^4+11781*A*a^2*b*c*d^2*m^5*x^6+253641*A*a^2*b*d^3*m^3*x^8+3*A*a*b^2*c^3*m^7*x^4+11781*A
*a*b^2*c^2*d*m^5*x^6+760923*A*a*b^2*c*d^2*m^3*x^8+1067445*A*a*b^2*d^3*m*x^10+1309*A*b^3*c^3*m^5*x^6+253641*A*b
^3*c^2*d*m^3*x^8+1067445*A*b^3*c*d^2*m*x^10+3*B*a^3*c^2*d*m^7*x^4+3927*B*a^3*c*d^2*m^5*x^6+84547*B*a^3*d^3*m^3
*x^8+3*B*a^2*b*c^3*m^7*x^4+11781*B*a^2*b*c^2*d*m^5*x^6+760923*B*a^2*b*c*d^2*m^3*x^8+1067445*B*a^2*b*d^3*m*x^10
+3927*B*a*b^2*c^3*m^5*x^6+760923*B*a*b^2*c^2*d*m^3*x^8+3202335*B*a*b^2*c*d^2*m*x^10+84547*B*b^3*c^3*m^3*x^8+10
67445*B*b^3*c^2*d*m*x^10+177*A*a^3*c*d^2*m^6*x^4+15477*A*a^3*d^3*m^4*x^6+531*A*a^2*b*c^2*d*m^6*x^4+139293*A*a^
2*b*c*d^2*m^4*x^6+831279*A*a^2*b*d^3*m^2*x^8+177*A*a*b^2*c^3*m^6*x^4+139293*A*a*b^2*c^2*d*m^4*x^6+2493837*A*a*
b^2*c*d^2*m^2*x^8+552825*A*a*b^2*d^3*x^10+15477*A*b^3*c^3*m^4*x^6+831279*A*b^3*c^2*d*m^2*x^8+552825*A*b^3*c*d^
2*x^10+177*B*a^3*c^2*d*m^6*x^4+46431*B*a^3*c*d^2*m^4*x^6+277093*B*a^3*d^3*m^2*x^8+177*B*a^2*b*c^3*m^6*x^4+1392
93*B*a^2*b*c^2*d*m^4*x^6+2493837*B*a^2*b*c*d^2*m^2*x^8+552825*B*a^2*b*d^3*x^10+46431*B*a*b^2*c^3*m^4*x^6+24938
37*B*a*b^2*c^2*d*m^2*x^8+1658475*B*a*b^2*c*d^2*x^10+277093*B*b^3*c^3*m^2*x^8+552825*B*b^3*c^2*d*x^10+3*A*a^3*c
^2*d*m^7*x^2+4239*A*a^3*c*d^2*m^5*x^4+99715*A*a^3*d^3*m^3*x^6+3*A*a^2*b*c^3*m^7*x^2+12717*A*a^2*b*c^2*d*m^5*x^
4+897435*A*a^2*b*c*d^2*m^3*x^6+1291005*A*a^2*b*d^3*m*x^8+4239*A*a*b^2*c^3*m^5*x^4+897435*A*a*b^2*c^2*d*m^3*x^6
+3873015*A*a*b^2*c*d^2*m*x^8+99715*A*b^3*c^3*m^3*x^6+1291005*A*b^3*c^2*d*m*x^8+B*a^3*c^3*m^7*x^2+4239*B*a^3*c^
2*d*m^5*x^4+299145*B*a^3*c*d^2*m^3*x^6+430335*B*a^3*d^3*m*x^8+4239*B*a^2*b*c^3*m^5*x^4+897435*B*a^2*b*c^2*d*m^
3*x^6+3873015*B*a^2*b*c*d^2*m*x^8+299145*B*a*b^2*c^3*m^3*x^6+3873015*B*a*b^2*c^2*d*m*x^8+430335*B*b^3*c^3*m*x^
8+183*A*a^3*c^2*d*m^6*x^2+52725*A*a^3*c*d^2*m^4*x^4+340011*A*a^3*d^3*m^2*x^6+183*A*a^2*b*c^3*m^6*x^2+158175*A*
a^2*b*c^2*d*m^4*x^4+3060099*A*a^2*b*c*d^2*m^2*x^6+675675*A*a^2*b*d^3*x^8+52725*A*a*b^2*c^3*m^4*x^4+3060099*A*a
*b^2*c^2*d*m^2*x^6+2027025*A*a*b^2*c*d^2*x^8+340011*A*b^3*c^3*m^2*x^6+675675*A*b^3*c^2*d*x^8+61*B*a^3*c^3*m^6*
x^2+52725*B*a^3*c^2*d*m^4*x^4+1020033*B*a^3*c*d^2*m^2*x^6+225225*B*a^3*d^3*x^8+52725*B*a^2*b*c^3*m^4*x^4+30600
99*B*a^2*b*c^2*d*m^2*x^6+2027025*B*a^2*b*c*d^2*x^8+1020033*B*a*b^2*c^3*m^2*x^6+2027025*B*a*b^2*c^2*d*x^8+22522
5*B*b^3*c^3*x^8+A*a^3*c^3*m^7+4575*A*a^3*c^2*d*m^5*x^2+360537*A*a^3*c*d^2*m^3*x^4+544095*A*a^3*d^3*m*x^6+4575*
A*a^2*b*c^3*m^5*x^2+1081611*A*a^2*b*c^2*d*m^3*x^4+4896855*A*a^2*b*c*d^2*m*x^6+360537*A*a*b^2*c^3*m^3*x^4+48968
55*A*a*b^2*c^2*d*m*x^6+544095*A*b^3*c^3*m*x^6+1525*B*a^3*c^3*m^5*x^2+360537*B*a^3*c^2*d*m^3*x^4+1632285*B*a^3*
c*d^2*m*x^6+360537*B*a^2*b*c^3*m^3*x^4+4896855*B*a^2*b*c^2*d*m*x^6+1632285*B*a*b^2*c^3*m*x^6+63*A*a^3*c^3*m^6+
60195*A*a^3*c^2*d*m^4*x^2+1311363*A*a^3*c*d^2*m^2*x^4+289575*A*a^3*d^3*x^6+60195*A*a^2*b*c^3*m^4*x^2+3934089*A
*a^2*b*c^2*d*m^2*x^4+2606175*A*a^2*b*c*d^2*x^6+1311363*A*a*b^2*c^3*m^2*x^4+2606175*A*a*b^2*c^2*d*x^6+289575*A*
b^3*c^3*x^6+20065*B*a^3*c^3*m^4*x^2+1311363*B*a^3*c^2*d*m^2*x^4+868725*B*a^3*c*d^2*x^6+1311363*B*a^2*b*c^3*m^2
*x^4+2606175*B*a^2*b*c^2*d*x^6+868725*B*a*b^2*c^3*x^6+1645*A*a^3*c^3*m^5+443577*A*a^3*c^2*d*m^3*x^2+2215701*A*
a^3*c*d^2*m*x^4+443577*A*a^2*b*c^3*m^3*x^2+6647103*A*a^2*b*c^2*d*m*x^4+2215701*A*a*b^2*c^3*m*x^4+147859*B*a^3*
c^3*m^3*x^2+2215701*B*a^3*c^2*d*m*x^4+2215701*B*a^2*b*c^3*m*x^4+22995*A*a^3*c^3*m^4+1783317*A*a^3*c^2*d*m^2*x^
2+1216215*A*a^3*c*d^2*x^4+1783317*A*a^2*b*c^3*m^2*x^2+3648645*A*a^2*b*c^2*d*x^4+1216215*A*a*b^2*c^3*x^4+594439
*B*a^3*c^3*m^2*x^2+1216215*B*a^3*c^2*d*x^4+1216215*B*a^2*b*c^3*x^4+185059*A*a^3*c^3*m^3+3422565*A*a^3*c^2*d*m*
x^2+3422565*A*a^2*b*c^3*m*x^2+1140855*B*a^3*c^3*m*x^2+852957*A*a^3*c^3*m^2+2027025*A*a^3*c^2*d*x^2+2027025*A*a
^2*b*c^3*x^2+675675*B*a^3*c^3*x^2+2071215*A*a^3*c^3*m+2027025*A*a^3*c^3)*(e*x)^m/(1+m)/(3+m)/(5+m)/(7+m)/(9+m)
/(11+m)/(13+m)/(15+m)
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x, algorithm="maxima")
[Out]
Exception raised: ValueError
________________________________________________________________________________________
Fricas [B] time = 1.93138, size = 5917, normalized size = 15.61 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x, algorithm="fricas")
[Out]
((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 + 4
67775*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 + 20
065*(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)
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x)**m*(b*x**2+a)**3*(B*x**2+A)*(d*x**2+c)**3,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] time = 1.36898, size = 7066, normalized size = 18.64 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x, algorithm="giac")
[Out]
(B*b^3*d^3*m^7*x^15*x^m*e^m + 49*B*b^3*d^3*m^6*x^15*x^m*e^m + 3*B*b^3*c*d^2*m^7*x^13*x^m*e^m + 3*B*a*b^2*d^3*m
^7*x^13*x^m*e^m + A*b^3*d^3*m^7*x^13*x^m*e^m + 973*B*b^3*d^3*m^5*x^15*x^m*e^m + 153*B*b^3*c*d^2*m^6*x^13*x^m*e
^m + 153*B*a*b^2*d^3*m^6*x^13*x^m*e^m + 51*A*b^3*d^3*m^6*x^13*x^m*e^m + 10045*B*b^3*d^3*m^4*x^15*x^m*e^m + 3*B
*b^3*c^2*d*m^7*x^11*x^m*e^m + 9*B*a*b^2*c*d^2*m^7*x^11*x^m*e^m + 3*A*b^3*c*d^2*m^7*x^11*x^m*e^m + 3*B*a^2*b*d^
3*m^7*x^11*x^m*e^m + 3*A*a*b^2*d^3*m^7*x^11*x^m*e^m + 3135*B*b^3*c*d^2*m^5*x^13*x^m*e^m + 3135*B*a*b^2*d^3*m^5
*x^13*x^m*e^m + 1045*A*b^3*d^3*m^5*x^13*x^m*e^m + 57379*B*b^3*d^3*m^3*x^15*x^m*e^m + 159*B*b^3*c^2*d*m^6*x^11*
x^m*e^m + 477*B*a*b^2*c*d^2*m^6*x^11*x^m*e^m + 159*A*b^3*c*d^2*m^6*x^11*x^m*e^m + 159*B*a^2*b*d^3*m^6*x^11*x^m
*e^m + 159*A*a*b^2*d^3*m^6*x^11*x^m*e^m + 33165*B*b^3*c*d^2*m^4*x^13*x^m*e^m + 33165*B*a*b^2*d^3*m^4*x^13*x^m*
e^m + 11055*A*b^3*d^3*m^4*x^13*x^m*e^m + 177331*B*b^3*d^3*m^2*x^15*x^m*e^m + B*b^3*c^3*m^7*x^9*x^m*e^m + 9*B*a
*b^2*c^2*d*m^7*x^9*x^m*e^m + 3*A*b^3*c^2*d*m^7*x^9*x^m*e^m + 9*B*a^2*b*c*d^2*m^7*x^9*x^m*e^m + 9*A*a*b^2*c*d^2
*m^7*x^9*x^m*e^m + B*a^3*d^3*m^7*x^9*x^m*e^m + 3*A*a^2*b*d^3*m^7*x^9*x^m*e^m + 3375*B*b^3*c^2*d*m^5*x^11*x^m*e
^m + 10125*B*a*b^2*c*d^2*m^5*x^11*x^m*e^m + 3375*A*b^3*c*d^2*m^5*x^11*x^m*e^m + 3375*B*a^2*b*d^3*m^5*x^11*x^m*
e^m + 3375*A*a*b^2*d^3*m^5*x^11*x^m*e^m + 193017*B*b^3*c*d^2*m^3*x^13*x^m*e^m + 193017*B*a*b^2*d^3*m^3*x^13*x^
m*e^m + 64339*A*b^3*d^3*m^3*x^13*x^m*e^m + 264207*B*b^3*d^3*m*x^15*x^m*e^m + 55*B*b^3*c^3*m^6*x^9*x^m*e^m + 49
5*B*a*b^2*c^2*d*m^6*x^9*x^m*e^m + 165*A*b^3*c^2*d*m^6*x^9*x^m*e^m + 495*B*a^2*b*c*d^2*m^6*x^9*x^m*e^m + 495*A*
a*b^2*c*d^2*m^6*x^9*x^m*e^m + 55*B*a^3*d^3*m^6*x^9*x^m*e^m + 165*A*a^2*b*d^3*m^6*x^9*x^m*e^m + 36795*B*b^3*c^2
*d*m^4*x^11*x^m*e^m + 110385*B*a*b^2*c*d^2*m^4*x^11*x^m*e^m + 36795*A*b^3*c*d^2*m^4*x^11*x^m*e^m + 36795*B*a^2
*b*d^3*m^4*x^11*x^m*e^m + 36795*A*a*b^2*d^3*m^4*x^11*x^m*e^m + 604827*B*b^3*c*d^2*m^2*x^13*x^m*e^m + 604827*B*
a*b^2*d^3*m^2*x^13*x^m*e^m + 201609*A*b^3*d^3*m^2*x^13*x^m*e^m + 135135*B*b^3*d^3*x^15*x^m*e^m + 3*B*a*b^2*c^3
*m^7*x^7*x^m*e^m + A*b^3*c^3*m^7*x^7*x^m*e^m + 9*B*a^2*b*c^2*d*m^7*x^7*x^m*e^m + 9*A*a*b^2*c^2*d*m^7*x^7*x^m*e
^m + 3*B*a^3*c*d^2*m^7*x^7*x^m*e^m + 9*A*a^2*b*c*d^2*m^7*x^7*x^m*e^m + A*a^3*d^3*m^7*x^7*x^m*e^m + 1213*B*b^3*
c^3*m^5*x^9*x^m*e^m + 10917*B*a*b^2*c^2*d*m^5*x^9*x^m*e^m + 3639*A*b^3*c^2*d*m^5*x^9*x^m*e^m + 10917*B*a^2*b*c
*d^2*m^5*x^9*x^m*e^m + 10917*A*a*b^2*c*d^2*m^5*x^9*x^m*e^m + 1213*B*a^3*d^3*m^5*x^9*x^m*e^m + 3639*A*a^2*b*d^3
*m^5*x^9*x^m*e^m + 219417*B*b^3*c^2*d*m^3*x^11*x^m*e^m + 658251*B*a*b^2*c*d^2*m^3*x^11*x^m*e^m + 219417*A*b^3*
c*d^2*m^3*x^11*x^m*e^m + 219417*B*a^2*b*d^3*m^3*x^11*x^m*e^m + 219417*A*a*b^2*d^3*m^3*x^11*x^m*e^m + 909765*B*
b^3*c*d^2*m*x^13*x^m*e^m + 909765*B*a*b^2*d^3*m*x^13*x^m*e^m + 303255*A*b^3*d^3*m*x^13*x^m*e^m + 171*B*a*b^2*c
^3*m^6*x^7*x^m*e^m + 57*A*b^3*c^3*m^6*x^7*x^m*e^m + 513*B*a^2*b*c^2*d*m^6*x^7*x^m*e^m + 513*A*a*b^2*c^2*d*m^6*
x^7*x^m*e^m + 171*B*a^3*c*d^2*m^6*x^7*x^m*e^m + 513*A*a^2*b*c*d^2*m^6*x^7*x^m*e^m + 57*A*a^3*d^3*m^6*x^7*x^m*e
^m + 13723*B*b^3*c^3*m^4*x^9*x^m*e^m + 123507*B*a*b^2*c^2*d*m^4*x^9*x^m*e^m + 41169*A*b^3*c^2*d*m^4*x^9*x^m*e^
m + 123507*B*a^2*b*c*d^2*m^4*x^9*x^m*e^m + 123507*A*a*b^2*c*d^2*m^4*x^9*x^m*e^m + 13723*B*a^3*d^3*m^4*x^9*x^m*
e^m + 41169*A*a^2*b*d^3*m^4*x^9*x^m*e^m + 700461*B*b^3*c^2*d*m^2*x^11*x^m*e^m + 2101383*B*a*b^2*c*d^2*m^2*x^11
*x^m*e^m + 700461*A*b^3*c*d^2*m^2*x^11*x^m*e^m + 700461*B*a^2*b*d^3*m^2*x^11*x^m*e^m + 700461*A*a*b^2*d^3*m^2*
x^11*x^m*e^m + 467775*B*b^3*c*d^2*x^13*x^m*e^m + 467775*B*a*b^2*d^3*x^13*x^m*e^m + 155925*A*b^3*d^3*x^13*x^m*e
^m + 3*B*a^2*b*c^3*m^7*x^5*x^m*e^m + 3*A*a*b^2*c^3*m^7*x^5*x^m*e^m + 3*B*a^3*c^2*d*m^7*x^5*x^m*e^m + 9*A*a^2*b
*c^2*d*m^7*x^5*x^m*e^m + 3*A*a^3*c*d^2*m^7*x^5*x^m*e^m + 3927*B*a*b^2*c^3*m^5*x^7*x^m*e^m + 1309*A*b^3*c^3*m^5
*x^7*x^m*e^m + 11781*B*a^2*b*c^2*d*m^5*x^7*x^m*e^m + 11781*A*a*b^2*c^2*d*m^5*x^7*x^m*e^m + 3927*B*a^3*c*d^2*m^
5*x^7*x^m*e^m + 11781*A*a^2*b*c*d^2*m^5*x^7*x^m*e^m + 1309*A*a^3*d^3*m^5*x^7*x^m*e^m + 84547*B*b^3*c^3*m^3*x^9
*x^m*e^m + 760923*B*a*b^2*c^2*d*m^3*x^9*x^m*e^m + 253641*A*b^3*c^2*d*m^3*x^9*x^m*e^m + 760923*B*a^2*b*c*d^2*m^
3*x^9*x^m*e^m + 760923*A*a*b^2*c*d^2*m^3*x^9*x^m*e^m + 84547*B*a^3*d^3*m^3*x^9*x^m*e^m + 253641*A*a^2*b*d^3*m^
3*x^9*x^m*e^m + 1067445*B*b^3*c^2*d*m*x^11*x^m*e^m + 3202335*B*a*b^2*c*d^2*m*x^11*x^m*e^m + 1067445*A*b^3*c*d^
2*m*x^11*x^m*e^m + 1067445*B*a^2*b*d^3*m*x^11*x^m*e^m + 1067445*A*a*b^2*d^3*m*x^11*x^m*e^m + 177*B*a^2*b*c^3*m
^6*x^5*x^m*e^m + 177*A*a*b^2*c^3*m^6*x^5*x^m*e^m + 177*B*a^3*c^2*d*m^6*x^5*x^m*e^m + 531*A*a^2*b*c^2*d*m^6*x^5
*x^m*e^m + 177*A*a^3*c*d^2*m^6*x^5*x^m*e^m + 46431*B*a*b^2*c^3*m^4*x^7*x^m*e^m + 15477*A*b^3*c^3*m^4*x^7*x^m*e
^m + 139293*B*a^2*b*c^2*d*m^4*x^7*x^m*e^m + 139293*A*a*b^2*c^2*d*m^4*x^7*x^m*e^m + 46431*B*a^3*c*d^2*m^4*x^7*x
^m*e^m + 139293*A*a^2*b*c*d^2*m^4*x^7*x^m*e^m + 15477*A*a^3*d^3*m^4*x^7*x^m*e^m + 277093*B*b^3*c^3*m^2*x^9*x^m
*e^m + 2493837*B*a*b^2*c^2*d*m^2*x^9*x^m*e^m + 831279*A*b^3*c^2*d*m^2*x^9*x^m*e^m + 2493837*B*a^2*b*c*d^2*m^2*
x^9*x^m*e^m + 2493837*A*a*b^2*c*d^2*m^2*x^9*x^m*e^m + 277093*B*a^3*d^3*m^2*x^9*x^m*e^m + 831279*A*a^2*b*d^3*m^
2*x^9*x^m*e^m + 552825*B*b^3*c^2*d*x^11*x^m*e^m + 1658475*B*a*b^2*c*d^2*x^11*x^m*e^m + 552825*A*b^3*c*d^2*x^11
*x^m*e^m + 552825*B*a^2*b*d^3*x^11*x^m*e^m + 552825*A*a*b^2*d^3*x^11*x^m*e^m + B*a^3*c^3*m^7*x^3*x^m*e^m + 3*A
*a^2*b*c^3*m^7*x^3*x^m*e^m + 3*A*a^3*c^2*d*m^7*x^3*x^m*e^m + 4239*B*a^2*b*c^3*m^5*x^5*x^m*e^m + 4239*A*a*b^2*c
^3*m^5*x^5*x^m*e^m + 4239*B*a^3*c^2*d*m^5*x^5*x^m*e^m + 12717*A*a^2*b*c^2*d*m^5*x^5*x^m*e^m + 4239*A*a^3*c*d^2
*m^5*x^5*x^m*e^m + 299145*B*a*b^2*c^3*m^3*x^7*x^m*e^m + 99715*A*b^3*c^3*m^3*x^7*x^m*e^m + 897435*B*a^2*b*c^2*d
*m^3*x^7*x^m*e^m + 897435*A*a*b^2*c^2*d*m^3*x^7*x^m*e^m + 299145*B*a^3*c*d^2*m^3*x^7*x^m*e^m + 897435*A*a^2*b*
c*d^2*m^3*x^7*x^m*e^m + 99715*A*a^3*d^3*m^3*x^7*x^m*e^m + 430335*B*b^3*c^3*m*x^9*x^m*e^m + 3873015*B*a*b^2*c^2
*d*m*x^9*x^m*e^m + 1291005*A*b^3*c^2*d*m*x^9*x^m*e^m + 3873015*B*a^2*b*c*d^2*m*x^9*x^m*e^m + 3873015*A*a*b^2*c
*d^2*m*x^9*x^m*e^m + 430335*B*a^3*d^3*m*x^9*x^m*e^m + 1291005*A*a^2*b*d^3*m*x^9*x^m*e^m + 61*B*a^3*c^3*m^6*x^3
*x^m*e^m + 183*A*a^2*b*c^3*m^6*x^3*x^m*e^m + 183*A*a^3*c^2*d*m^6*x^3*x^m*e^m + 52725*B*a^2*b*c^3*m^4*x^5*x^m*e
^m + 52725*A*a*b^2*c^3*m^4*x^5*x^m*e^m + 52725*B*a^3*c^2*d*m^4*x^5*x^m*e^m + 158175*A*a^2*b*c^2*d*m^4*x^5*x^m*
e^m + 52725*A*a^3*c*d^2*m^4*x^5*x^m*e^m + 1020033*B*a*b^2*c^3*m^2*x^7*x^m*e^m + 340011*A*b^3*c^3*m^2*x^7*x^m*e
^m + 3060099*B*a^2*b*c^2*d*m^2*x^7*x^m*e^m + 3060099*A*a*b^2*c^2*d*m^2*x^7*x^m*e^m + 1020033*B*a^3*c*d^2*m^2*x
^7*x^m*e^m + 3060099*A*a^2*b*c*d^2*m^2*x^7*x^m*e^m + 340011*A*a^3*d^3*m^2*x^7*x^m*e^m + 225225*B*b^3*c^3*x^9*x
^m*e^m + 2027025*B*a*b^2*c^2*d*x^9*x^m*e^m + 675675*A*b^3*c^2*d*x^9*x^m*e^m + 2027025*B*a^2*b*c*d^2*x^9*x^m*e^
m + 2027025*A*a*b^2*c*d^2*x^9*x^m*e^m + 225225*B*a^3*d^3*x^9*x^m*e^m + 675675*A*a^2*b*d^3*x^9*x^m*e^m + A*a^3*
c^3*m^7*x*x^m*e^m + 1525*B*a^3*c^3*m^5*x^3*x^m*e^m + 4575*A*a^2*b*c^3*m^5*x^3*x^m*e^m + 4575*A*a^3*c^2*d*m^5*x
^3*x^m*e^m + 360537*B*a^2*b*c^3*m^3*x^5*x^m*e^m + 360537*A*a*b^2*c^3*m^3*x^5*x^m*e^m + 360537*B*a^3*c^2*d*m^3*
x^5*x^m*e^m + 1081611*A*a^2*b*c^2*d*m^3*x^5*x^m*e^m + 360537*A*a^3*c*d^2*m^3*x^5*x^m*e^m + 1632285*B*a*b^2*c^3
*m*x^7*x^m*e^m + 544095*A*b^3*c^3*m*x^7*x^m*e^m + 4896855*B*a^2*b*c^2*d*m*x^7*x^m*e^m + 4896855*A*a*b^2*c^2*d*
m*x^7*x^m*e^m + 1632285*B*a^3*c*d^2*m*x^7*x^m*e^m + 4896855*A*a^2*b*c*d^2*m*x^7*x^m*e^m + 544095*A*a^3*d^3*m*x
^7*x^m*e^m + 63*A*a^3*c^3*m^6*x*x^m*e^m + 20065*B*a^3*c^3*m^4*x^3*x^m*e^m + 60195*A*a^2*b*c^3*m^4*x^3*x^m*e^m
+ 60195*A*a^3*c^2*d*m^4*x^3*x^m*e^m + 1311363*B*a^2*b*c^3*m^2*x^5*x^m*e^m + 1311363*A*a*b^2*c^3*m^2*x^5*x^m*e^
m + 1311363*B*a^3*c^2*d*m^2*x^5*x^m*e^m + 3934089*A*a^2*b*c^2*d*m^2*x^5*x^m*e^m + 1311363*A*a^3*c*d^2*m^2*x^5*
x^m*e^m + 868725*B*a*b^2*c^3*x^7*x^m*e^m + 289575*A*b^3*c^3*x^7*x^m*e^m + 2606175*B*a^2*b*c^2*d*x^7*x^m*e^m +
2606175*A*a*b^2*c^2*d*x^7*x^m*e^m + 868725*B*a^3*c*d^2*x^7*x^m*e^m + 2606175*A*a^2*b*c*d^2*x^7*x^m*e^m + 28957
5*A*a^3*d^3*x^7*x^m*e^m + 1645*A*a^3*c^3*m^5*x*x^m*e^m + 147859*B*a^3*c^3*m^3*x^3*x^m*e^m + 443577*A*a^2*b*c^3
*m^3*x^3*x^m*e^m + 443577*A*a^3*c^2*d*m^3*x^3*x^m*e^m + 2215701*B*a^2*b*c^3*m*x^5*x^m*e^m + 2215701*A*a*b^2*c^
3*m*x^5*x^m*e^m + 2215701*B*a^3*c^2*d*m*x^5*x^m*e^m + 6647103*A*a^2*b*c^2*d*m*x^5*x^m*e^m + 2215701*A*a^3*c*d^
2*m*x^5*x^m*e^m + 22995*A*a^3*c^3*m^4*x*x^m*e^m + 594439*B*a^3*c^3*m^2*x^3*x^m*e^m + 1783317*A*a^2*b*c^3*m^2*x
^3*x^m*e^m + 1783317*A*a^3*c^2*d*m^2*x^3*x^m*e^m + 1216215*B*a^2*b*c^3*x^5*x^m*e^m + 1216215*A*a*b^2*c^3*x^5*x
^m*e^m + 1216215*B*a^3*c^2*d*x^5*x^m*e^m + 3648645*A*a^2*b*c^2*d*x^5*x^m*e^m + 1216215*A*a^3*c*d^2*x^5*x^m*e^m
+ 185059*A*a^3*c^3*m^3*x*x^m*e^m + 1140855*B*a^3*c^3*m*x^3*x^m*e^m + 3422565*A*a^2*b*c^3*m*x^3*x^m*e^m + 3422
565*A*a^3*c^2*d*m*x^3*x^m*e^m + 852957*A*a^3*c^3*m^2*x*x^m*e^m + 675675*B*a^3*c^3*x^3*x^m*e^m + 2027025*A*a^2*
b*c^3*x^3*x^m*e^m + 2027025*A*a^3*c^2*d*x^3*x^m*e^m + 2071215*A*a^3*c^3*m*x*x^m*e^m + 2027025*A*a^3*c^3*x*x^m*
e^m)/(m^8 + 64*m^7 + 1708*m^6 + 24640*m^5 + 208054*m^4 + 1038016*m^3 + 2924172*m^2 + 4098240*m + 2027025)