3.2640 \(\int (A+B x) (d+e x)^m (a+b x+c x^2)^3 \, dx\)

Optimal. Leaf size=594 \[ -\frac{(d+e x)^{m+4} \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{e^8 (m+4)}-\frac{3 (d+e x)^{m+3} \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (m+3)}-\frac{(d+e x)^{m+5} \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{e^8 (m+6)}-\frac{(B d-A e) (d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^3}{e^8 (m+1)}-\frac{(d+e x)^{m+2} \left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{e^8 (m+2)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)} \]

[Out]

-(((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) - ((c*d^2 - b*d*e + a*e^2)^2*(3*A*e
*(2*c*d - b*e) - B*(7*c*d^2 - e*(4*b*d - a*e)))*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (3*(c*d^2 - b*d*e + a*e^2)*
(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*
(d + e*x)^(3 + m))/(e^8*(3 + m)) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*
c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*
(d + e*x)^(4 + m))/(e^8*(4 + m)) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d -
a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^(5 + m))/(e^8*(5 + m)) - (3*c*(A*c*e*(2*
c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (c^2*(7*B*c*d - 3
*b*B*e - A*c*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (B*c^3*(d + e*x)^(8 + m))/(e^8*(8 + m))

________________________________________________________________________________________

Rubi [A]  time = 0.687204, antiderivative size = 591, normalized size of antiderivative = 0.99, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {771} \[ -\frac{(d+e x)^{m+4} \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{e^8 (m+4)}-\frac{3 (d+e x)^{m+3} \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (m+3)}-\frac{(d+e x)^{m+5} \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{e^8 (m+6)}-\frac{(B d-A e) (d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^3}{e^8 (m+1)}+\frac{(d+e x)^{m+2} \left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{e^8 (m+2)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)} \]

Antiderivative was successfully verified.

[In]

Int[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]

[Out]

-(((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c
*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (3*(c*d^2 - b*d*e + a*e^2)*
(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*
(d + e*x)^(3 + m))/(e^8*(3 + m)) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*
c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*
(d + e*x)^(4 + m))/(e^8*(4 + m)) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d -
a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^(5 + m))/(e^8*(5 + m)) - (3*c*(A*c*e*(2*
c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (c^2*(7*B*c*d - 3
*b*B*e - A*c*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (B*c^3*(d + e*x)^(8 + m))/(e^8*(8 + m))

Rule 771

Int[((d_.) + (e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> In
t[ExpandIntegrand[(d + e*x)^m*(f + g*x)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && N
eQ[b^2 - 4*a*c, 0] && IntegerQ[p] && (GtQ[p, 0] || (EqQ[a, 0] && IntegerQ[m]))

Rubi steps

\begin{align*} \int (A+B x) (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx &=\int \left (\frac{(-B d+A e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^m}{e^7}+\frac{\left (c d^2-b d e+a e^2\right )^2 \left (7 B c d^2-B e (4 b d-a e)-3 A e (2 c d-b e)\right ) (d+e x)^{1+m}}{e^7}+\frac{3 \left (c d^2-b d e+a e^2\right ) \left (-B \left (7 c^2 d^3-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)\right )+A e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^{2+m}}{e^7}+\frac{\left (-A e (2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right )+B \left (35 c^3 d^4-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+3 c e^2 \left (10 b^2 d^2-8 a b d e+a^2 e^2\right )\right )\right ) (d+e x)^{3+m}}{e^7}+\frac{\left (-B \left (35 c^3 d^3-b^3 e^3+3 b c e^2 (5 b d-2 a e)-15 c^2 d e (3 b d-a e)\right )+3 A c e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^{4+m}}{e^7}+\frac{3 c \left (-A c e (2 c d-b e)+B \left (7 c^2 d^2+b^2 e^2-c e (6 b d-a e)\right )\right ) (d+e x)^{5+m}}{e^7}+\frac{c^2 (-7 B c d+3 b B e+A c e) (d+e x)^{6+m}}{e^7}+\frac{B c^3 (d+e x)^{7+m}}{e^7}\right ) \, dx\\ &=-\frac{(B d-A e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^{1+m}}{e^8 (1+m)}+\frac{\left (c d^2-b d e+a e^2\right )^2 \left (7 B c d^2-B e (4 b d-a e)-3 A e (2 c d-b e)\right ) (d+e x)^{2+m}}{e^8 (2+m)}-\frac{3 \left (c d^2-b d e+a e^2\right ) \left (B \left (7 c^2 d^3-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)\right )-A e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^{3+m}}{e^8 (3+m)}-\frac{\left (A e (2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right )-B \left (35 c^3 d^4-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+3 c e^2 \left (10 b^2 d^2-8 a b d e+a^2 e^2\right )\right )\right ) (d+e x)^{4+m}}{e^8 (4+m)}-\frac{\left (B \left (35 c^3 d^3-b^3 e^3+3 b c e^2 (5 b d-2 a e)-15 c^2 d e (3 b d-a e)\right )-3 A c e \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right )\right ) (d+e x)^{5+m}}{e^8 (5+m)}-\frac{3 c \left (A c e (2 c d-b e)-B \left (7 c^2 d^2+b^2 e^2-c e (6 b d-a e)\right )\right ) (d+e x)^{6+m}}{e^8 (6+m)}-\frac{c^2 (7 B c d-3 b B e-A c e) (d+e x)^{7+m}}{e^8 (7+m)}+\frac{B c^3 (d+e x)^{8+m}}{e^8 (8+m)}\\ \end{align*}

Mathematica [B]  time = 6.81703, size = 4291, normalized size = 7.22 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]

Integrate[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]

[Out]

((d + e*x)^(1 + m)*(-(B*(7*c*d - 3*b*e)) + A*c*e*(8 + m) + B*c*e*(7 + m)*x)*(a + b*x + c*x^2)^3)/(c*e^2*(7 + m
)*(8 + m)) - (3*(((d + e*x)^(1 + m)*(c*e*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B
*e*(2*c*d*m - b*e*(1 + m))) - (5*c*d - 2*b*e)*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) -
c*e*(b*d*(6 - m) - 2*a*e*(7 + m)))) + c*e*(5 + m)*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 +
m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))*x)*(a + b*x + c*x^2)^2)/(c*e^2*(5 + m)*(6 + m)) - (2*(((d + e*x)^(1
+ m)*(c*e*(4 + m)*(c*e*(b*d - 2*a*e)*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(
2*c*d*m - b*e*(1 + m))) + (b*d*(-5*c*d + 2*b*e) + a*e*(b*e - 2*c*d*m + b*e*m))*(A*c*e*(2*c*d - b*e)*(8 + m) -
B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))) - (3*c*d - b*e)*(c*e*(2*c*d - b*e)*(6 +
m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) + (-10*c^2*d^2 +
b^2*e^2*(3 + m) - c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(
4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))) + c*e*(3 + m)*(c*e*(2*c*d - b*e)*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e
)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) + (-10*c^2*d^2 + b^2*e^2*(3 + m) - c*e*(b*d*
(-4 + m) + 2*a*e*(5 + m)))*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) -
2*a*e*(7 + m)))))*x)*(a + b*x + c*x^2))/(c*e^2*(3 + m)*(4 + m)) - (((840*B*c^6*d^7 - 2460*b*B*c^5*d^6*e - 960
*A*c^6*d^6*e + 2340*b^2*B*c^4*d^5*e^2 + 2880*A*b*c^5*d^5*e^2 + 2520*a*B*c^5*d^5*e^2 - 684*b^3*B*c^3*d^4*e^3 -
2832*A*b^2*c^4*d^4*e^3 - 4764*a*b*B*c^4*d^4*e^3 - 3072*a*A*c^5*d^4*e^3 - 12*b^4*B*c^2*d^3*e^4 + 864*A*b^3*c^3*
d^3*e^4 + 1968*a*b^2*B*c^3*d^3*e^4 + 6144*a*A*b*c^4*d^3*e^4 + 2520*a^2*B*c^4*d^3*e^4 - 12*b^5*B*c*d^2*e^5 + 24
*A*b^4*c^2*d^2*e^5 + 132*a*b^3*B*c^2*d^2*e^5 - 2784*a*A*b^2*c^3*d^2*e^5 - 1956*a^2*b*B*c^3*d^2*e^5 - 3648*a^2*
A*c^4*d^2*e^5 - 12*b^6*B*d*e^6 + 24*A*b^5*c*d*e^6 + 144*a*b^4*B*c*d*e^6 - 288*a*A*b^3*c^2*d*e^6 - 564*a^2*b^2*
B*c^2*d*e^6 + 3648*a^2*A*b*c^3*d*e^6 + 840*a^3*B*c^3*d*e^6 + 12*a*b^5*B*e^7 - 24*a*A*b^4*c*e^7 - 120*a^2*b^3*B
*c*e^7 + 240*a^2*A*b^2*c^2*e^7 + 348*a^3*b*B*c^2*e^7 - 1536*a^3*A*c^3*e^7 + 60*b*B*c^5*d^6*e*m - 120*A*c^6*d^6
*e*m - 160*b^2*B*c^4*d^5*e^2*m + 360*A*b*c^5*d^5*e^2*m - 80*a*B*c^5*d^5*e^2*m + 111*b^3*B*c^3*d^4*e^3*m - 322*
A*b^2*c^4*d^4*e^3*m + 456*a*b*B*c^4*d^4*e^3*m - 512*a*A*c^5*d^4*e^3*m + 15*b^4*B*c^2*d^3*e^4*m + 44*A*b^3*c^3*
d^3*e^4*m - 608*a*b^2*B*c^3*d^3*e^4*m + 1024*a*A*b*c^4*d^3*e^4*m - 208*a^2*B*c^4*d^3*e^4*m - 7*b^5*B*c*d^2*e^5
*m + 3*A*b^4*c^2*d^2*e^5*m + 22*a*b^3*B*c^2*d^2*e^5*m - 156*a*A*b^2*c^3*d^2*e^5*m + 924*a^2*b*B*c^3*d^2*e^5*m
- 1224*a^2*A*c^4*d^2*e^5*m - 19*b^6*B*d*e^6*m + 35*A*b^5*c*d*e^6*m + 207*a*b^4*B*c*d*e^6*m - 356*a*A*b^3*c^2*d
*e^6*m - 672*a^2*b^2*B*c^2*d*e^6*m + 1224*a^2*A*b*c^3*d*e^6*m - 128*a^3*B*c^3*d*e^6*m + 19*a*b^5*B*e^7*m - 35*
a*A*b^4*c*e^7*m - 181*a^2*b^3*B*c*e^7*m + 318*a^2*A*b^2*c^2*e^7*m + 480*a^3*b*B*c^2*e^7*m - 832*a^3*A*c^3*e^7*
m + 20*b^2*B*c^4*d^5*e^2*m^2 - 80*a*B*c^5*d^5*e^2*m^2 - 44*b^3*B*c^3*d^4*e^3*m^2 - 12*A*b^2*c^4*d^4*e^3*m^2 +
176*a*b*B*c^4*d^4*e^3*m^2 + 48*a*A*c^5*d^4*e^3*m^2 + 24*b^4*B*c^2*d^3*e^4*m^2 + 24*A*b^3*c^3*d^3*e^4*m^2 - 40*
a*b^2*B*c^3*d^3*e^4*m^2 - 96*a*A*b*c^4*d^3*e^4*m^2 - 224*a^2*B*c^4*d^3*e^4*m^2 + 8*b^5*B*c*d^2*e^5*m^2 - 24*A*
b^4*c^2*d^2*e^5*m^2 - 128*a*b^3*B*c^2*d^2*e^5*m^2 + 120*a*A*b^2*c^3*d^2*e^5*m^2 + 384*a^2*b*B*c^3*d^2*e^5*m^2
- 96*a^2*A*c^4*d^2*e^5*m^2 - 8*b^6*B*d*e^6*m^2 + 12*A*b^5*c*d*e^6*m^2 + 68*a*b^4*B*c*d*e^6*m^2 - 72*a*A*b^3*c^
2*d*e^6*m^2 - 108*a^2*b^2*B*c^2*d*e^6*m^2 + 96*a^2*A*b*c^3*d*e^6*m^2 - 144*a^3*B*c^3*d*e^6*m^2 + 8*a*b^5*B*e^7
*m^2 - 12*a*A*b^4*c*e^7*m^2 - 68*a^2*b^3*B*c*e^7*m^2 + 84*a^2*A*b^2*c^2*e^7*m^2 + 144*a^3*b*B*c^2*e^7*m^2 - 14
4*a^3*A*c^3*e^7*m^2 + b^3*B*c^3*d^4*e^3*m^3 - 2*A*b^2*c^4*d^4*e^3*m^3 - 4*a*b*B*c^4*d^4*e^3*m^3 + 8*a*A*c^5*d^
4*e^3*m^3 - 3*b^4*B*c^2*d^3*e^4*m^3 + 4*A*b^3*c^3*d^3*e^4*m^3 + 16*a*b^2*B*c^3*d^3*e^4*m^3 - 16*a*A*b*c^4*d^3*
e^4*m^3 - 16*a^2*B*c^4*d^3*e^4*m^3 + 3*b^5*B*c*d^2*e^5*m^3 - 3*A*b^4*c^2*d^2*e^5*m^3 - 18*a*b^3*B*c^2*d^2*e^5*
m^3 + 12*a*A*b^2*c^3*d^2*e^5*m^3 + 24*a^2*b*B*c^3*d^2*e^5*m^3 - b^6*B*d*e^6*m^3 + A*b^5*c*d*e^6*m^3 + 5*a*b^4*
B*c*d*e^6*m^3 - 4*a*A*b^3*c^2*d*e^6*m^3 - 16*a^3*B*c^3*d*e^6*m^3 + a*b^5*B*e^7*m^3 - a*A*b^4*c*e^7*m^3 - 7*a^2
*b^3*B*c*e^7*m^3 + 6*a^2*A*b^2*c^2*e^7*m^3 + 12*a^3*b*B*c^2*e^7*m^3 - 8*a^3*A*c^3*e^7*m^3)*(d + e*x)^(1 + m))/
(e^2*(1 + m)) + ((-840*B*c^6*d^6 + 2040*b*B*c^5*d^5*e + 960*A*c^6*d^5*e - 1320*b^2*B*c^4*d^4*e^2 - 2400*A*b*c^
5*d^4*e^2 - 2520*a*B*c^5*d^4*e^2 + 24*b^3*B*c^3*d^3*e^3 + 1632*A*b^2*c^4*d^3*e^3 + 3504*a*b*B*c^4*d^3*e^3 + 30
72*a*A*c^5*d^3*e^3 + 24*b^4*B*c^2*d^2*e^4 - 48*A*b^3*c^3*d^2*e^4 - 216*a*b^2*B*c^3*d^2*e^4 - 4608*a*A*b*c^4*d^
2*e^4 - 2520*a^2*B*c^4*d^2*e^4 + 24*b^5*B*c*d*e^5 - 48*A*b^4*c^2*d*e^5 - 240*a*b^3*B*c^2*d*e^5 + 480*a*A*b^2*c
^3*d*e^5 + 696*a^2*b*B*c^3*d*e^5 + 3648*a^2*A*c^4*d*e^5 + 24*b^6*B*e^6 - 48*A*b^5*c*e^6 - 264*a*b^4*B*c*e^6 +
528*a*A*b^3*c^2*e^6 + 912*a^2*b^2*B*c^2*e^6 - 1824*a^2*A*b*c^3*e^6 - 840*a^3*B*c^3*e^6 - 60*b*B*c^5*d^5*e*m +
120*A*c^6*d^5*e*m + 200*b^2*B*c^4*d^4*e^2*m - 300*A*b*c^5*d^4*e^2*m - 200*a*B*c^5*d^4*e^2*m - 146*b^3*B*c^3*d^
3*e^3*m + 92*A*b^2*c^4*d^3*e^3*m - 16*a*b*B*c^4*d^3*e^3*m + 832*a*A*c^5*d^3*e^3*m - 42*b^4*B*c^2*d^2*e^4*m + 1
62*A*b^3*c^3*d^2*e^4*m + 612*a*b^2*B*c^3*d^2*e^4*m - 1248*a*A*b*c^4*d^2*e^4*m - 576*a^2*B*c^4*d^2*e^4*m + 2*b^
5*B*c*d*e^5*m + 18*A*b^4*c^2*d*e^5*m + 46*a*b^3*B*c^2*d*e^5*m - 468*a*A*b^2*c^3*d*e^5*m - 516*a^2*b*B*c^3*d*e^
5*m + 2184*a^2*A*c^4*d*e^5*m + 26*b^6*B*e^6*m - 46*A*b^5*c*e^6*m - 268*a*b^4*B*c*e^6*m + 442*a*A*b^3*c^2*e^6*m
+ 828*a^2*b^2*B*c^2*e^6*m - 1092*a^2*A*b*c^3*e^6*m - 568*a^3*B*c^3*e^6*m - 20*b^2*B*c^4*d^4*e^2*m^2 + 80*a*B*
c^5*d^4*e^2*m^2 + 39*b^3*B*c^3*d^3*e^3*m^2 + 2*A*b^2*c^4*d^3*e^3*m^2 - 156*a*b*B*c^4*d^3*e^3*m^2 - 8*a*A*c^5*d
^3*e^3*m^2 - 21*b^4*B*c^2*d^2*e^4*m^2 - 3*A*b^3*c^3*d^2*e^4*m^2 + 54*a*b^2*B*c^3*d^2*e^4*m^2 + 12*a*A*b*c^4*d^
2*e^4*m^2 + 120*a^2*B*c^4*d^2*e^4*m^2 - 11*b^5*B*c*d*e^5*m^2 + 27*A*b^4*c^2*d*e^5*m^2 + 125*a*b^3*B*c^2*d*e^5*
m^2 - 210*a*A*b^2*c^3*d*e^5*m^2 - 324*a^2*b*B*c^3*d*e^5*m^2 + 408*a^2*A*c^4*d*e^5*m^2 + 9*b^6*B*e^6*m^2 - 13*A
*b^5*c*e^6*m^2 - 84*a*b^4*B*c*e^6*m^2 + 103*a*A*b^3*c^2*e^6*m^2 + 222*a^2*b^2*B*c^2*e^6*m^2 - 204*a^2*A*b*c^3*
e^6*m^2 - 120*a^3*B*c^3*e^6*m^2 - b^3*B*c^3*d^3*e^3*m^3 + 2*A*b^2*c^4*d^3*e^3*m^3 + 4*a*b*B*c^4*d^3*e^3*m^3 -
8*a*A*c^5*d^3*e^3*m^3 + 3*b^4*B*c^2*d^2*e^4*m^3 - 3*A*b^3*c^3*d^2*e^4*m^3 - 18*a*b^2*B*c^3*d^2*e^4*m^3 + 12*a*
A*b*c^4*d^2*e^4*m^3 + 24*a^2*B*c^4*d^2*e^4*m^3 - 3*b^5*B*c*d*e^5*m^3 + 3*A*b^4*c^2*d*e^5*m^3 + 21*a*b^3*B*c^2*
d*e^5*m^3 - 18*a*A*b^2*c^3*d*e^5*m^3 - 36*a^2*b*B*c^3*d*e^5*m^3 + 24*a^2*A*c^4*d*e^5*m^3 + b^6*B*e^6*m^3 - A*b
^5*c*e^6*m^3 - 8*a*b^4*B*c*e^6*m^3 + 7*a*A*b^3*c^2*e^6*m^3 + 18*a^2*b^2*B*c^2*e^6*m^3 - 12*a^2*A*b*c^3*e^6*m^3
- 8*a^3*B*c^3*e^6*m^3)*(d + e*x)^(2 + m))/(e^2*(2 + m)))/(c*e^2*(3 + m)*(4 + m))))/(c*e^2*(5 + m)*(6 + m))))/
(c*e^2*(7 + m)*(8 + m))

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Maple [B]  time = 0.023, size = 8232, normalized size = 13.9 \begin{align*} \text{output too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x)

[Out]

result too large to display

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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((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [B]  time = 2.519, size = 13140, normalized size = 22.12 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm="fricas")

[Out]

(A*a^3*d*e^7*m^7 - 5040*B*c^3*d^8 + 40320*A*a^3*d*e^7 + 5760*(3*B*b*c^2 + A*c^3)*d^7*e - 20160*(B*b^2*c + (B*a
+ A*b)*c^2)*d^6*e^2 + 8064*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 10080*(3*B*a*b^2 + A*b^3 + 3
*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 40320*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 20160*(B*a^3 + 3*A*a^2*b)*d^2*e^
6 + (B*c^3*e^8*m^7 + 28*B*c^3*e^8*m^6 + 322*B*c^3*e^8*m^5 + 1960*B*c^3*e^8*m^4 + 6769*B*c^3*e^8*m^3 + 13132*B*
c^3*e^8*m^2 + 13068*B*c^3*e^8*m + 5040*B*c^3*e^8)*x^8 + (5760*(3*B*b*c^2 + A*c^3)*e^8 + (B*c^3*d*e^7 + (3*B*b*
c^2 + A*c^3)*e^8)*m^7 + (21*B*c^3*d*e^7 + 29*(3*B*b*c^2 + A*c^3)*e^8)*m^6 + 7*(25*B*c^3*d*e^7 + 49*(3*B*b*c^2
+ A*c^3)*e^8)*m^5 + 35*(21*B*c^3*d*e^7 + 61*(3*B*b*c^2 + A*c^3)*e^8)*m^4 + 56*(29*B*c^3*d*e^7 + 134*(3*B*b*c^2
+ A*c^3)*e^8)*m^3 + 28*(63*B*c^3*d*e^7 + 527*(3*B*b*c^2 + A*c^3)*e^8)*m^2 + 144*(5*B*c^3*d*e^7 + 103*(3*B*b*c
^2 + A*c^3)*e^8)*m)*x^7 + (35*A*a^3*d*e^7 - (B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^6 + (20160*(B*b^2*c + (B*a + A*b)*c
^2)*e^8 + ((3*B*b*c^2 + A*c^3)*d*e^7 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^7 - (7*B*c^3*d^2*e^6 - 23*(3*B*b*c
^2 + A*c^3)*d*e^7 - 90*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^6 - (105*B*c^3*d^2*e^6 - 205*(3*B*b*c^2 + A*c^3)*d*e
^7 - 1098*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^5 - 5*(119*B*c^3*d^2*e^6 - 181*(3*B*b*c^2 + A*c^3)*d*e^7 - 1404*(
B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^4 - (1575*B*c^3*d^2*e^6 - 2074*(3*B*b*c^2 + A*c^3)*d*e^7 - 25227*(B*b^2*c +
(B*a + A*b)*c^2)*e^8)*m^3 - 2*(959*B*c^3*d^2*e^6 - 1156*(3*B*b*c^2 + A*c^3)*d*e^7 - 25245*(B*b^2*c + (B*a + A*
b)*c^2)*e^8)*m^2 - 24*(35*B*c^3*d^2*e^6 - 40*(3*B*b*c^2 + A*c^3)*d*e^7 - 2143*(B*b^2*c + (B*a + A*b)*c^2)*e^8)
*m)*x^6 + (511*A*a^3*d*e^7 + 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 33*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^5 + (
8064*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8 + (3*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + (B*b^3 + 3*A*a*c
^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^7 - (6*(3*B*b*c^2 + A*c^3)*d^2*e^6 - 75*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 -
31*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^6 + (42*B*c^3*d^3*e^5 - 108*(3*B*b*c^2 + A*c^3)*d^2*e^6
+ 723*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 391*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^5 + (420*B*c
^3*d^3*e^5 - 690*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 3405*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 2581*(B*b^3 + 3*A*a*c^
2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^4 + 2*(735*B*c^3*d^3*e^5 - 990*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 4101*(B*b^2*c +
(B*a + A*b)*c^2)*d*e^7 + 4772*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^3 + 4*(525*B*c^3*d^3*e^5 - 6
36*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 2370*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 4891*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b
+ A*b^2)*c)*e^8)*m^2 + 144*(7*B*c^3*d^3*e^5 - 8*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 28*(B*b^2*c + (B*a + A*b)*c^2)*
d*e^7 + 141*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m)*x^5 + (4025*A*a^3*d*e^7 - 6*(3*B*a*b^2 + A*b^3
+ 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 445*(B*a^3 + 3*A*a^2*b)*d^2*e^
6)*m^4 + (10080*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8 + ((B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)
*d*e^7 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^7 - (15*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 27*(
B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 32*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^6 + (
30*(3*B*b*c^2 + A*c^3)*d^3*e^5 - 315*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 + 283*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b
+ A*b^2)*c)*d*e^7 + 418*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^5 - (210*B*c^3*d^4*e^4 - 420*(3*B*
b*c^2 + A*c^3)*d^3*e^5 + 2355*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 1449*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b
^2)*c)*d*e^7 - 2864*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^4 - (1260*B*c^3*d^4*e^4 - 1770*(3*B*b*c
^2 + A*c^3)*d^3*e^5 + 7605*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 3748*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)
*c)*d*e^7 - 10993*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^3 - 2*(1155*B*c^3*d^4*e^4 - 1410*(3*B*b*c
^2 + A*c^3)*d^3*e^5 + 5295*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 2286*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)
*c)*d*e^7 - 11656*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^2 - 36*(35*B*c^3*d^4*e^4 - 40*(3*B*b*c^2
+ A*c^3)*d^3*e^5 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*
e^7 - 691*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m)*x^4 + (18424*A*a^3*d*e^7 + 24*(B*b^3 + 3*A*a*c^2
+ 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 156*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 2130*(B*a^2*b +
A*a*b^2 + A*a^2*c)*d^3*e^5 - 3135*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^3 + (40320*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8
+ ((3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^7 - (4*(B*b^3 +
3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 - 29*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 - 99*(B*a^2*
b + A*a*b^2 + A*a^2*c)*e^8)*m^6 + (60*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 96*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b
+ A*b^2)*c)*d^2*e^6 + 331*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 1341*(B*a^2*b + A*a*b^2 + A*a^2
*c)*e^8)*m^5 - (120*(3*B*b*c^2 + A*c^3)*d^4*e^4 - 1080*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 + 844*(B*b^3 + 3*A*
a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 - 1871*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 - 9585*(B*a^2*
b + A*a*b^2 + A*a^2*c)*e^8)*m^4 + 4*(210*B*c^3*d^5*e^3 - 330*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 1545*(B*b^2*c + (B*
a + A*b)*c^2)*d^3*e^5 - 816*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 1345*(3*B*a*b^2 + A*b^3 + 3*
(B*a^2 + 2*A*a*b)*c)*d*e^7 + 9648*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^3 + 4*(630*B*c^3*d^5*e^3 - 780*(3*B*b*c
^2 + A*c^3)*d^4*e^4 + 2970*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 1300*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)
*c)*d^2*e^6 + 1793*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 21519*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8
)*m^2 + 48*(35*B*c^3*d^5*e^3 - 40*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 56*(
B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 70*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 20
03*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m)*x^3 + 2*(24430*A*a^3*d*e^7 - 180*(B*b^2*c + (B*a + A*b)*c^2)*d^6*e^2
+ 252*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 753*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^
4*e^4 + 6210*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 6077*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^2 + (20160*(B*a^3 + 3
*A*a^2*b)*e^8 + (3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 + (B*a^3 + 3*A*a^2*b)*e^8)*m^7 - (3*(3*B*a*b^2 + A*b^3
+ 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 93*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 34*(B*a^3 + 3*A*a^2*b)*e^8)*m^6 +
(12*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 - 81*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e
^6 + 1155*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 + 478*(B*a^3 + 3*A*a^2*b)*e^8)*m^5 - (180*(B*b^2*c + (B*a + A*b)
*c^2)*d^4*e^4 - 264*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 831*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 +
2*A*a*b)*c)*d^2*e^6 - 7275*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 3580*(B*a^3 + 3*A*a^2*b)*e^8)*m^4 + (360*(3*B
*b*c^2 + A*c^3)*d^5*e^3 - 2880*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 + 2004*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*
b^2)*c)*d^3*e^5 - 3951*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 + 24042*(B*a^2*b + A*a*b^2 + A*a^2*
c)*d*e^7 + 15289*(B*a^3 + 3*A*a^2*b)*e^8)*m^3 - 2*(1260*B*c^3*d^6*e^2 - 1620*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 639
0*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 - 2892*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 4119*(3*B*a
*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 18996*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 18353*(B*a^3 + 3*A
*a^2*b)*e^8)*m^2 - 72*(35*B*c^3*d^6*e^2 - 40*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^4
*e^4 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 70*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)
*d^2*e^6 - 280*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 621*(B*a^3 + 3*A*a^2*b)*e^8)*m)*x^2 + 12*(5772*A*a^3*d*e^
7 + 60*(3*B*b*c^2 + A*c^3)*d^7*e - 450*(B*b^2*c + (B*a + A*b)*c^2)*d^6*e^2 + 292*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a
*b + A*b^2)*c)*d^5*e^3 - 533*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 2972*(B*a^2*b + A*a*b^2 + A
*a^2*c)*d^3*e^5 - 2046*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m + (40320*A*a^3*e^8 + (A*a^3*e^8 + (B*a^3 + 3*A*a^2*b)*d*
e^7)*m^7 + (35*A*a^3*e^8 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 33*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^6 + (511*
A*a^3*e^8 + 6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6
+ 445*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^5 + (4025*A*a^3*e^8 - 24*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^
4 + 156*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 2130*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 313
5*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^4 + 2*(9212*A*a^3*e^8 + 180*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 252*(B*b^3 +
3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 753*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 6210*(B
*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 6077*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^3 + 4*(12215*A*a^3*e^8 - 180*(3*B*b*c^
2 + A*c^3)*d^6*e^2 + 1350*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 876*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c
)*d^4*e^4 + 1599*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 8916*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*
e^6 + 6138*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^2 + 144*(35*B*c^3*d^7*e + 481*A*a^3*e^8 - 40*(3*B*b*c^2 + A*c^3)*d^6*e
^2 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 70*(3*
B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 280*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 140*(B*a^3 + 3*
A*a^2*b)*d*e^7)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e
^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)

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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((B*x+A)*(e*x+d)**m*(c*x**2+b*x+a)**3,x)

[Out]

Timed out

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Giac [B]  time = 1.82613, size = 19408, normalized size = 32.67 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm="giac")

[Out]

((x*e + d)^m*B*c^3*m^7*x^8*e^8 + (x*e + d)^m*B*c^3*d*m^7*x^7*e^7 + 3*(x*e + d)^m*B*b*c^2*m^7*x^7*e^8 + (x*e +
d)^m*A*c^3*m^7*x^7*e^8 + 28*(x*e + d)^m*B*c^3*m^6*x^8*e^8 + 3*(x*e + d)^m*B*b*c^2*d*m^7*x^6*e^7 + (x*e + d)^m*
A*c^3*d*m^7*x^6*e^7 + 21*(x*e + d)^m*B*c^3*d*m^6*x^7*e^7 - 7*(x*e + d)^m*B*c^3*d^2*m^6*x^6*e^6 + 3*(x*e + d)^m
*B*b^2*c*m^7*x^6*e^8 + 3*(x*e + d)^m*B*a*c^2*m^7*x^6*e^8 + 3*(x*e + d)^m*A*b*c^2*m^7*x^6*e^8 + 87*(x*e + d)^m*
B*b*c^2*m^6*x^7*e^8 + 29*(x*e + d)^m*A*c^3*m^6*x^7*e^8 + 322*(x*e + d)^m*B*c^3*m^5*x^8*e^8 + 3*(x*e + d)^m*B*b
^2*c*d*m^7*x^5*e^7 + 3*(x*e + d)^m*B*a*c^2*d*m^7*x^5*e^7 + 3*(x*e + d)^m*A*b*c^2*d*m^7*x^5*e^7 + 69*(x*e + d)^
m*B*b*c^2*d*m^6*x^6*e^7 + 23*(x*e + d)^m*A*c^3*d*m^6*x^6*e^7 + 175*(x*e + d)^m*B*c^3*d*m^5*x^7*e^7 - 18*(x*e +
d)^m*B*b*c^2*d^2*m^6*x^5*e^6 - 6*(x*e + d)^m*A*c^3*d^2*m^6*x^5*e^6 - 105*(x*e + d)^m*B*c^3*d^2*m^5*x^6*e^6 +
42*(x*e + d)^m*B*c^3*d^3*m^5*x^5*e^5 + (x*e + d)^m*B*b^3*m^7*x^5*e^8 + 6*(x*e + d)^m*B*a*b*c*m^7*x^5*e^8 + 3*(
x*e + d)^m*A*b^2*c*m^7*x^5*e^8 + 3*(x*e + d)^m*A*a*c^2*m^7*x^5*e^8 + 90*(x*e + d)^m*B*b^2*c*m^6*x^6*e^8 + 90*(
x*e + d)^m*B*a*c^2*m^6*x^6*e^8 + 90*(x*e + d)^m*A*b*c^2*m^6*x^6*e^8 + 1029*(x*e + d)^m*B*b*c^2*m^5*x^7*e^8 + 3
43*(x*e + d)^m*A*c^3*m^5*x^7*e^8 + 1960*(x*e + d)^m*B*c^3*m^4*x^8*e^8 + (x*e + d)^m*B*b^3*d*m^7*x^4*e^7 + 6*(x
*e + d)^m*B*a*b*c*d*m^7*x^4*e^7 + 3*(x*e + d)^m*A*b^2*c*d*m^7*x^4*e^7 + 3*(x*e + d)^m*A*a*c^2*d*m^7*x^4*e^7 +
75*(x*e + d)^m*B*b^2*c*d*m^6*x^5*e^7 + 75*(x*e + d)^m*B*a*c^2*d*m^6*x^5*e^7 + 75*(x*e + d)^m*A*b*c^2*d*m^6*x^5
*e^7 + 615*(x*e + d)^m*B*b*c^2*d*m^5*x^6*e^7 + 205*(x*e + d)^m*A*c^3*d*m^5*x^6*e^7 + 735*(x*e + d)^m*B*c^3*d*m
^4*x^7*e^7 - 15*(x*e + d)^m*B*b^2*c*d^2*m^6*x^4*e^6 - 15*(x*e + d)^m*B*a*c^2*d^2*m^6*x^4*e^6 - 15*(x*e + d)^m*
A*b*c^2*d^2*m^6*x^4*e^6 - 324*(x*e + d)^m*B*b*c^2*d^2*m^5*x^5*e^6 - 108*(x*e + d)^m*A*c^3*d^2*m^5*x^5*e^6 - 59
5*(x*e + d)^m*B*c^3*d^2*m^4*x^6*e^6 + 90*(x*e + d)^m*B*b*c^2*d^3*m^5*x^4*e^5 + 30*(x*e + d)^m*A*c^3*d^3*m^5*x^
4*e^5 + 420*(x*e + d)^m*B*c^3*d^3*m^4*x^5*e^5 - 210*(x*e + d)^m*B*c^3*d^4*m^4*x^4*e^4 + 3*(x*e + d)^m*B*a*b^2*
m^7*x^4*e^8 + (x*e + d)^m*A*b^3*m^7*x^4*e^8 + 3*(x*e + d)^m*B*a^2*c*m^7*x^4*e^8 + 6*(x*e + d)^m*A*a*b*c*m^7*x^
4*e^8 + 31*(x*e + d)^m*B*b^3*m^6*x^5*e^8 + 186*(x*e + d)^m*B*a*b*c*m^6*x^5*e^8 + 93*(x*e + d)^m*A*b^2*c*m^6*x^
5*e^8 + 93*(x*e + d)^m*A*a*c^2*m^6*x^5*e^8 + 1098*(x*e + d)^m*B*b^2*c*m^5*x^6*e^8 + 1098*(x*e + d)^m*B*a*c^2*m
^5*x^6*e^8 + 1098*(x*e + d)^m*A*b*c^2*m^5*x^6*e^8 + 6405*(x*e + d)^m*B*b*c^2*m^4*x^7*e^8 + 2135*(x*e + d)^m*A*
c^3*m^4*x^7*e^8 + 6769*(x*e + d)^m*B*c^3*m^3*x^8*e^8 + 3*(x*e + d)^m*B*a*b^2*d*m^7*x^3*e^7 + (x*e + d)^m*A*b^3
*d*m^7*x^3*e^7 + 3*(x*e + d)^m*B*a^2*c*d*m^7*x^3*e^7 + 6*(x*e + d)^m*A*a*b*c*d*m^7*x^3*e^7 + 27*(x*e + d)^m*B*
b^3*d*m^6*x^4*e^7 + 162*(x*e + d)^m*B*a*b*c*d*m^6*x^4*e^7 + 81*(x*e + d)^m*A*b^2*c*d*m^6*x^4*e^7 + 81*(x*e + d
)^m*A*a*c^2*d*m^6*x^4*e^7 + 723*(x*e + d)^m*B*b^2*c*d*m^5*x^5*e^7 + 723*(x*e + d)^m*B*a*c^2*d*m^5*x^5*e^7 + 72
3*(x*e + d)^m*A*b*c^2*d*m^5*x^5*e^7 + 2715*(x*e + d)^m*B*b*c^2*d*m^4*x^6*e^7 + 905*(x*e + d)^m*A*c^3*d*m^4*x^6
*e^7 + 1624*(x*e + d)^m*B*c^3*d*m^3*x^7*e^7 - 4*(x*e + d)^m*B*b^3*d^2*m^6*x^3*e^6 - 24*(x*e + d)^m*B*a*b*c*d^2
*m^6*x^3*e^6 - 12*(x*e + d)^m*A*b^2*c*d^2*m^6*x^3*e^6 - 12*(x*e + d)^m*A*a*c^2*d^2*m^6*x^3*e^6 - 315*(x*e + d)
^m*B*b^2*c*d^2*m^5*x^4*e^6 - 315*(x*e + d)^m*B*a*c^2*d^2*m^5*x^4*e^6 - 315*(x*e + d)^m*A*b*c^2*d^2*m^5*x^4*e^6
- 2070*(x*e + d)^m*B*b*c^2*d^2*m^4*x^5*e^6 - 690*(x*e + d)^m*A*c^3*d^2*m^4*x^5*e^6 - 1575*(x*e + d)^m*B*c^3*d
^2*m^3*x^6*e^6 + 60*(x*e + d)^m*B*b^2*c*d^3*m^5*x^3*e^5 + 60*(x*e + d)^m*B*a*c^2*d^3*m^5*x^3*e^5 + 60*(x*e + d
)^m*A*b*c^2*d^3*m^5*x^3*e^5 + 1260*(x*e + d)^m*B*b*c^2*d^3*m^4*x^4*e^5 + 420*(x*e + d)^m*A*c^3*d^3*m^4*x^4*e^5
+ 1470*(x*e + d)^m*B*c^3*d^3*m^3*x^5*e^5 - 360*(x*e + d)^m*B*b*c^2*d^4*m^4*x^3*e^4 - 120*(x*e + d)^m*A*c^3*d^
4*m^4*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m^3*x^4*e^4 + 840*(x*e + d)^m*B*c^3*d^5*m^3*x^3*e^3 + 3*(x*e + d)^m
*B*a^2*b*m^7*x^3*e^8 + 3*(x*e + d)^m*A*a*b^2*m^7*x^3*e^8 + 3*(x*e + d)^m*A*a^2*c*m^7*x^3*e^8 + 96*(x*e + d)^m*
B*a*b^2*m^6*x^4*e^8 + 32*(x*e + d)^m*A*b^3*m^6*x^4*e^8 + 96*(x*e + d)^m*B*a^2*c*m^6*x^4*e^8 + 192*(x*e + d)^m*
A*a*b*c*m^6*x^4*e^8 + 391*(x*e + d)^m*B*b^3*m^5*x^5*e^8 + 2346*(x*e + d)^m*B*a*b*c*m^5*x^5*e^8 + 1173*(x*e + d
)^m*A*b^2*c*m^5*x^5*e^8 + 1173*(x*e + d)^m*A*a*c^2*m^5*x^5*e^8 + 7020*(x*e + d)^m*B*b^2*c*m^4*x^6*e^8 + 7020*(
x*e + d)^m*B*a*c^2*m^4*x^6*e^8 + 7020*(x*e + d)^m*A*b*c^2*m^4*x^6*e^8 + 22512*(x*e + d)^m*B*b*c^2*m^3*x^7*e^8
+ 7504*(x*e + d)^m*A*c^3*m^3*x^7*e^8 + 13132*(x*e + d)^m*B*c^3*m^2*x^8*e^8 + 3*(x*e + d)^m*B*a^2*b*d*m^7*x^2*e
^7 + 3*(x*e + d)^m*A*a*b^2*d*m^7*x^2*e^7 + 3*(x*e + d)^m*A*a^2*c*d*m^7*x^2*e^7 + 87*(x*e + d)^m*B*a*b^2*d*m^6*
x^3*e^7 + 29*(x*e + d)^m*A*b^3*d*m^6*x^3*e^7 + 87*(x*e + d)^m*B*a^2*c*d*m^6*x^3*e^7 + 174*(x*e + d)^m*A*a*b*c*
d*m^6*x^3*e^7 + 283*(x*e + d)^m*B*b^3*d*m^5*x^4*e^7 + 1698*(x*e + d)^m*B*a*b*c*d*m^5*x^4*e^7 + 849*(x*e + d)^m
*A*b^2*c*d*m^5*x^4*e^7 + 849*(x*e + d)^m*A*a*c^2*d*m^5*x^4*e^7 + 3405*(x*e + d)^m*B*b^2*c*d*m^4*x^5*e^7 + 3405
*(x*e + d)^m*B*a*c^2*d*m^4*x^5*e^7 + 3405*(x*e + d)^m*A*b*c^2*d*m^4*x^5*e^7 + 6222*(x*e + d)^m*B*b*c^2*d*m^3*x
^6*e^7 + 2074*(x*e + d)^m*A*c^3*d*m^3*x^6*e^7 + 1764*(x*e + d)^m*B*c^3*d*m^2*x^7*e^7 - 9*(x*e + d)^m*B*a*b^2*d
^2*m^6*x^2*e^6 - 3*(x*e + d)^m*A*b^3*d^2*m^6*x^2*e^6 - 9*(x*e + d)^m*B*a^2*c*d^2*m^6*x^2*e^6 - 18*(x*e + d)^m*
A*a*b*c*d^2*m^6*x^2*e^6 - 96*(x*e + d)^m*B*b^3*d^2*m^5*x^3*e^6 - 576*(x*e + d)^m*B*a*b*c*d^2*m^5*x^3*e^6 - 288
*(x*e + d)^m*A*b^2*c*d^2*m^5*x^3*e^6 - 288*(x*e + d)^m*A*a*c^2*d^2*m^5*x^3*e^6 - 2355*(x*e + d)^m*B*b^2*c*d^2*
m^4*x^4*e^6 - 2355*(x*e + d)^m*B*a*c^2*d^2*m^4*x^4*e^6 - 2355*(x*e + d)^m*A*b*c^2*d^2*m^4*x^4*e^6 - 5940*(x*e
+ d)^m*B*b*c^2*d^2*m^3*x^5*e^6 - 1980*(x*e + d)^m*A*c^3*d^2*m^3*x^5*e^6 - 1918*(x*e + d)^m*B*c^3*d^2*m^2*x^6*e
^6 + 12*(x*e + d)^m*B*b^3*d^3*m^5*x^2*e^5 + 72*(x*e + d)^m*B*a*b*c*d^3*m^5*x^2*e^5 + 36*(x*e + d)^m*A*b^2*c*d^
3*m^5*x^2*e^5 + 36*(x*e + d)^m*A*a*c^2*d^3*m^5*x^2*e^5 + 1080*(x*e + d)^m*B*b^2*c*d^3*m^4*x^3*e^5 + 1080*(x*e
+ d)^m*B*a*c^2*d^3*m^4*x^3*e^5 + 1080*(x*e + d)^m*A*b*c^2*d^3*m^4*x^3*e^5 + 5310*(x*e + d)^m*B*b*c^2*d^3*m^3*x
^4*e^5 + 1770*(x*e + d)^m*A*c^3*d^3*m^3*x^4*e^5 + 2100*(x*e + d)^m*B*c^3*d^3*m^2*x^5*e^5 - 180*(x*e + d)^m*B*b
^2*c*d^4*m^4*x^2*e^4 - 180*(x*e + d)^m*B*a*c^2*d^4*m^4*x^2*e^4 - 180*(x*e + d)^m*A*b*c^2*d^4*m^4*x^2*e^4 - 396
0*(x*e + d)^m*B*b*c^2*d^4*m^3*x^3*e^4 - 1320*(x*e + d)^m*A*c^3*d^4*m^3*x^3*e^4 - 2310*(x*e + d)^m*B*c^3*d^4*m^
2*x^4*e^4 + 1080*(x*e + d)^m*B*b*c^2*d^5*m^3*x^2*e^3 + 360*(x*e + d)^m*A*c^3*d^5*m^3*x^2*e^3 + 2520*(x*e + d)^
m*B*c^3*d^5*m^2*x^3*e^3 - 2520*(x*e + d)^m*B*c^3*d^6*m^2*x^2*e^2 + (x*e + d)^m*B*a^3*m^7*x^2*e^8 + 3*(x*e + d)
^m*A*a^2*b*m^7*x^2*e^8 + 99*(x*e + d)^m*B*a^2*b*m^6*x^3*e^8 + 99*(x*e + d)^m*A*a*b^2*m^6*x^3*e^8 + 99*(x*e + d
)^m*A*a^2*c*m^6*x^3*e^8 + 1254*(x*e + d)^m*B*a*b^2*m^5*x^4*e^8 + 418*(x*e + d)^m*A*b^3*m^5*x^4*e^8 + 1254*(x*e
+ d)^m*B*a^2*c*m^5*x^4*e^8 + 2508*(x*e + d)^m*A*a*b*c*m^5*x^4*e^8 + 2581*(x*e + d)^m*B*b^3*m^4*x^5*e^8 + 1548
6*(x*e + d)^m*B*a*b*c*m^4*x^5*e^8 + 7743*(x*e + d)^m*A*b^2*c*m^4*x^5*e^8 + 7743*(x*e + d)^m*A*a*c^2*m^4*x^5*e^
8 + 25227*(x*e + d)^m*B*b^2*c*m^3*x^6*e^8 + 25227*(x*e + d)^m*B*a*c^2*m^3*x^6*e^8 + 25227*(x*e + d)^m*A*b*c^2*
m^3*x^6*e^8 + 44268*(x*e + d)^m*B*b*c^2*m^2*x^7*e^8 + 14756*(x*e + d)^m*A*c^3*m^2*x^7*e^8 + 13068*(x*e + d)^m*
B*c^3*m*x^8*e^8 + (x*e + d)^m*B*a^3*d*m^7*x*e^7 + 3*(x*e + d)^m*A*a^2*b*d*m^7*x*e^7 + 93*(x*e + d)^m*B*a^2*b*d
*m^6*x^2*e^7 + 93*(x*e + d)^m*A*a*b^2*d*m^6*x^2*e^7 + 93*(x*e + d)^m*A*a^2*c*d*m^6*x^2*e^7 + 993*(x*e + d)^m*B
*a*b^2*d*m^5*x^3*e^7 + 331*(x*e + d)^m*A*b^3*d*m^5*x^3*e^7 + 993*(x*e + d)^m*B*a^2*c*d*m^5*x^3*e^7 + 1986*(x*e
+ d)^m*A*a*b*c*d*m^5*x^3*e^7 + 1449*(x*e + d)^m*B*b^3*d*m^4*x^4*e^7 + 8694*(x*e + d)^m*B*a*b*c*d*m^4*x^4*e^7
+ 4347*(x*e + d)^m*A*b^2*c*d*m^4*x^4*e^7 + 4347*(x*e + d)^m*A*a*c^2*d*m^4*x^4*e^7 + 8202*(x*e + d)^m*B*b^2*c*d
*m^3*x^5*e^7 + 8202*(x*e + d)^m*B*a*c^2*d*m^3*x^5*e^7 + 8202*(x*e + d)^m*A*b*c^2*d*m^3*x^5*e^7 + 6936*(x*e + d
)^m*B*b*c^2*d*m^2*x^6*e^7 + 2312*(x*e + d)^m*A*c^3*d*m^2*x^6*e^7 + 720*(x*e + d)^m*B*c^3*d*m*x^7*e^7 - 6*(x*e
+ d)^m*B*a^2*b*d^2*m^6*x*e^6 - 6*(x*e + d)^m*A*a*b^2*d^2*m^6*x*e^6 - 6*(x*e + d)^m*A*a^2*c*d^2*m^6*x*e^6 - 243
*(x*e + d)^m*B*a*b^2*d^2*m^5*x^2*e^6 - 81*(x*e + d)^m*A*b^3*d^2*m^5*x^2*e^6 - 243*(x*e + d)^m*B*a^2*c*d^2*m^5*
x^2*e^6 - 486*(x*e + d)^m*A*a*b*c*d^2*m^5*x^2*e^6 - 844*(x*e + d)^m*B*b^3*d^2*m^4*x^3*e^6 - 5064*(x*e + d)^m*B
*a*b*c*d^2*m^4*x^3*e^6 - 2532*(x*e + d)^m*A*b^2*c*d^2*m^4*x^3*e^6 - 2532*(x*e + d)^m*A*a*c^2*d^2*m^4*x^3*e^6 -
7605*(x*e + d)^m*B*b^2*c*d^2*m^3*x^4*e^6 - 7605*(x*e + d)^m*B*a*c^2*d^2*m^3*x^4*e^6 - 7605*(x*e + d)^m*A*b*c^
2*d^2*m^3*x^4*e^6 - 7632*(x*e + d)^m*B*b*c^2*d^2*m^2*x^5*e^6 - 2544*(x*e + d)^m*A*c^3*d^2*m^2*x^5*e^6 - 840*(x
*e + d)^m*B*c^3*d^2*m*x^6*e^6 + 18*(x*e + d)^m*B*a*b^2*d^3*m^5*x*e^5 + 6*(x*e + d)^m*A*b^3*d^3*m^5*x*e^5 + 18*
(x*e + d)^m*B*a^2*c*d^3*m^5*x*e^5 + 36*(x*e + d)^m*A*a*b*c*d^3*m^5*x*e^5 + 264*(x*e + d)^m*B*b^3*d^3*m^4*x^2*e
^5 + 1584*(x*e + d)^m*B*a*b*c*d^3*m^4*x^2*e^5 + 792*(x*e + d)^m*A*b^2*c*d^3*m^4*x^2*e^5 + 792*(x*e + d)^m*A*a*
c^2*d^3*m^4*x^2*e^5 + 6180*(x*e + d)^m*B*b^2*c*d^3*m^3*x^3*e^5 + 6180*(x*e + d)^m*B*a*c^2*d^3*m^3*x^3*e^5 + 61
80*(x*e + d)^m*A*b*c^2*d^3*m^3*x^3*e^5 + 8460*(x*e + d)^m*B*b*c^2*d^3*m^2*x^4*e^5 + 2820*(x*e + d)^m*A*c^3*d^3
*m^2*x^4*e^5 + 1008*(x*e + d)^m*B*c^3*d^3*m*x^5*e^5 - 24*(x*e + d)^m*B*b^3*d^4*m^4*x*e^4 - 144*(x*e + d)^m*B*a
*b*c*d^4*m^4*x*e^4 - 72*(x*e + d)^m*A*b^2*c*d^4*m^4*x*e^4 - 72*(x*e + d)^m*A*a*c^2*d^4*m^4*x*e^4 - 2880*(x*e +
d)^m*B*b^2*c*d^4*m^3*x^2*e^4 - 2880*(x*e + d)^m*B*a*c^2*d^4*m^3*x^2*e^4 - 2880*(x*e + d)^m*A*b*c^2*d^4*m^3*x^
2*e^4 - 9360*(x*e + d)^m*B*b*c^2*d^4*m^2*x^3*e^4 - 3120*(x*e + d)^m*A*c^3*d^4*m^2*x^3*e^4 - 1260*(x*e + d)^m*B
*c^3*d^4*m*x^4*e^4 + 360*(x*e + d)^m*B*b^2*c*d^5*m^3*x*e^3 + 360*(x*e + d)^m*B*a*c^2*d^5*m^3*x*e^3 + 360*(x*e
+ d)^m*A*b*c^2*d^5*m^3*x*e^3 + 9720*(x*e + d)^m*B*b*c^2*d^5*m^2*x^2*e^3 + 3240*(x*e + d)^m*A*c^3*d^5*m^2*x^2*e
^3 + 1680*(x*e + d)^m*B*c^3*d^5*m*x^3*e^3 - 2160*(x*e + d)^m*B*b*c^2*d^6*m^2*x*e^2 - 720*(x*e + d)^m*A*c^3*d^6
*m^2*x*e^2 - 2520*(x*e + d)^m*B*c^3*d^6*m*x^2*e^2 + 5040*(x*e + d)^m*B*c^3*d^7*m*x*e + (x*e + d)^m*A*a^3*m^7*x
*e^8 + 34*(x*e + d)^m*B*a^3*m^6*x^2*e^8 + 102*(x*e + d)^m*A*a^2*b*m^6*x^2*e^8 + 1341*(x*e + d)^m*B*a^2*b*m^5*x
^3*e^8 + 1341*(x*e + d)^m*A*a*b^2*m^5*x^3*e^8 + 1341*(x*e + d)^m*A*a^2*c*m^5*x^3*e^8 + 8592*(x*e + d)^m*B*a*b^
2*m^4*x^4*e^8 + 2864*(x*e + d)^m*A*b^3*m^4*x^4*e^8 + 8592*(x*e + d)^m*B*a^2*c*m^4*x^4*e^8 + 17184*(x*e + d)^m*
A*a*b*c*m^4*x^4*e^8 + 9544*(x*e + d)^m*B*b^3*m^3*x^5*e^8 + 57264*(x*e + d)^m*B*a*b*c*m^3*x^5*e^8 + 28632*(x*e
+ d)^m*A*b^2*c*m^3*x^5*e^8 + 28632*(x*e + d)^m*A*a*c^2*m^3*x^5*e^8 + 50490*(x*e + d)^m*B*b^2*c*m^2*x^6*e^8 + 5
0490*(x*e + d)^m*B*a*c^2*m^2*x^6*e^8 + 50490*(x*e + d)^m*A*b*c^2*m^2*x^6*e^8 + 44496*(x*e + d)^m*B*b*c^2*m*x^7
*e^8 + 14832*(x*e + d)^m*A*c^3*m*x^7*e^8 + 5040*(x*e + d)^m*B*c^3*x^8*e^8 + (x*e + d)^m*A*a^3*d*m^7*e^7 + 33*(
x*e + d)^m*B*a^3*d*m^6*x*e^7 + 99*(x*e + d)^m*A*a^2*b*d*m^6*x*e^7 + 1155*(x*e + d)^m*B*a^2*b*d*m^5*x^2*e^7 + 1
155*(x*e + d)^m*A*a*b^2*d*m^5*x^2*e^7 + 1155*(x*e + d)^m*A*a^2*c*d*m^5*x^2*e^7 + 5613*(x*e + d)^m*B*a*b^2*d*m^
4*x^3*e^7 + 1871*(x*e + d)^m*A*b^3*d*m^4*x^3*e^7 + 5613*(x*e + d)^m*B*a^2*c*d*m^4*x^3*e^7 + 11226*(x*e + d)^m*
A*a*b*c*d*m^4*x^3*e^7 + 3748*(x*e + d)^m*B*b^3*d*m^3*x^4*e^7 + 22488*(x*e + d)^m*B*a*b*c*d*m^3*x^4*e^7 + 11244
*(x*e + d)^m*A*b^2*c*d*m^3*x^4*e^7 + 11244*(x*e + d)^m*A*a*c^2*d*m^3*x^4*e^7 + 9480*(x*e + d)^m*B*b^2*c*d*m^2*
x^5*e^7 + 9480*(x*e + d)^m*B*a*c^2*d*m^2*x^5*e^7 + 9480*(x*e + d)^m*A*b*c^2*d*m^2*x^5*e^7 + 2880*(x*e + d)^m*B
*b*c^2*d*m*x^6*e^7 + 960*(x*e + d)^m*A*c^3*d*m*x^6*e^7 - (x*e + d)^m*B*a^3*d^2*m^6*e^6 - 3*(x*e + d)^m*A*a^2*b
*d^2*m^6*e^6 - 180*(x*e + d)^m*B*a^2*b*d^2*m^5*x*e^6 - 180*(x*e + d)^m*A*a*b^2*d^2*m^5*x*e^6 - 180*(x*e + d)^m
*A*a^2*c*d^2*m^5*x*e^6 - 2493*(x*e + d)^m*B*a*b^2*d^2*m^4*x^2*e^6 - 831*(x*e + d)^m*A*b^3*d^2*m^4*x^2*e^6 - 24
93*(x*e + d)^m*B*a^2*c*d^2*m^4*x^2*e^6 - 4986*(x*e + d)^m*A*a*b*c*d^2*m^4*x^2*e^6 - 3264*(x*e + d)^m*B*b^3*d^2
*m^3*x^3*e^6 - 19584*(x*e + d)^m*B*a*b*c*d^2*m^3*x^3*e^6 - 9792*(x*e + d)^m*A*b^2*c*d^2*m^3*x^3*e^6 - 9792*(x*
e + d)^m*A*a*c^2*d^2*m^3*x^3*e^6 - 10590*(x*e + d)^m*B*b^2*c*d^2*m^2*x^4*e^6 - 10590*(x*e + d)^m*B*a*c^2*d^2*m
^2*x^4*e^6 - 10590*(x*e + d)^m*A*b*c^2*d^2*m^2*x^4*e^6 - 3456*(x*e + d)^m*B*b*c^2*d^2*m*x^5*e^6 - 1152*(x*e +
d)^m*A*c^3*d^2*m*x^5*e^6 + 6*(x*e + d)^m*B*a^2*b*d^3*m^5*e^5 + 6*(x*e + d)^m*A*a*b^2*d^3*m^5*e^5 + 6*(x*e + d)
^m*A*a^2*c*d^3*m^5*e^5 + 468*(x*e + d)^m*B*a*b^2*d^3*m^4*x*e^5 + 156*(x*e + d)^m*A*b^3*d^3*m^4*x*e^5 + 468*(x*
e + d)^m*B*a^2*c*d^3*m^4*x*e^5 + 936*(x*e + d)^m*A*a*b*c*d^3*m^4*x*e^5 + 2004*(x*e + d)^m*B*b^3*d^3*m^3*x^2*e^
5 + 12024*(x*e + d)^m*B*a*b*c*d^3*m^3*x^2*e^5 + 6012*(x*e + d)^m*A*b^2*c*d^3*m^3*x^2*e^5 + 6012*(x*e + d)^m*A*
a*c^2*d^3*m^3*x^2*e^5 + 11880*(x*e + d)^m*B*b^2*c*d^3*m^2*x^3*e^5 + 11880*(x*e + d)^m*B*a*c^2*d^3*m^2*x^3*e^5
+ 11880*(x*e + d)^m*A*b*c^2*d^3*m^2*x^3*e^5 + 4320*(x*e + d)^m*B*b*c^2*d^3*m*x^4*e^5 + 1440*(x*e + d)^m*A*c^3*
d^3*m*x^4*e^5 - 18*(x*e + d)^m*B*a*b^2*d^4*m^4*e^4 - 6*(x*e + d)^m*A*b^3*d^4*m^4*e^4 - 18*(x*e + d)^m*B*a^2*c*
d^4*m^4*e^4 - 36*(x*e + d)^m*A*a*b*c*d^4*m^4*e^4 - 504*(x*e + d)^m*B*b^3*d^4*m^3*x*e^4 - 3024*(x*e + d)^m*B*a*
b*c*d^4*m^3*x*e^4 - 1512*(x*e + d)^m*A*b^2*c*d^4*m^3*x*e^4 - 1512*(x*e + d)^m*A*a*c^2*d^4*m^3*x*e^4 - 12780*(x
*e + d)^m*B*b^2*c*d^4*m^2*x^2*e^4 - 12780*(x*e + d)^m*B*a*c^2*d^4*m^2*x^2*e^4 - 12780*(x*e + d)^m*A*b*c^2*d^4*
m^2*x^2*e^4 - 5760*(x*e + d)^m*B*b*c^2*d^4*m*x^3*e^4 - 1920*(x*e + d)^m*A*c^3*d^4*m*x^3*e^4 + 24*(x*e + d)^m*B
*b^3*d^5*m^3*e^3 + 144*(x*e + d)^m*B*a*b*c*d^5*m^3*e^3 + 72*(x*e + d)^m*A*b^2*c*d^5*m^3*e^3 + 72*(x*e + d)^m*A
*a*c^2*d^5*m^3*e^3 + 5400*(x*e + d)^m*B*b^2*c*d^5*m^2*x*e^3 + 5400*(x*e + d)^m*B*a*c^2*d^5*m^2*x*e^3 + 5400*(x
*e + d)^m*A*b*c^2*d^5*m^2*x*e^3 + 8640*(x*e + d)^m*B*b*c^2*d^5*m*x^2*e^3 + 2880*(x*e + d)^m*A*c^3*d^5*m*x^2*e^
3 - 360*(x*e + d)^m*B*b^2*c*d^6*m^2*e^2 - 360*(x*e + d)^m*B*a*c^2*d^6*m^2*e^2 - 360*(x*e + d)^m*A*b*c^2*d^6*m^
2*e^2 - 17280*(x*e + d)^m*B*b*c^2*d^6*m*x*e^2 - 5760*(x*e + d)^m*A*c^3*d^6*m*x*e^2 + 2160*(x*e + d)^m*B*b*c^2*
d^7*m*e + 720*(x*e + d)^m*A*c^3*d^7*m*e - 5040*(x*e + d)^m*B*c^3*d^8 + 35*(x*e + d)^m*A*a^3*m^6*x*e^8 + 478*(x
*e + d)^m*B*a^3*m^5*x^2*e^8 + 1434*(x*e + d)^m*A*a^2*b*m^5*x^2*e^8 + 9585*(x*e + d)^m*B*a^2*b*m^4*x^3*e^8 + 95
85*(x*e + d)^m*A*a*b^2*m^4*x^3*e^8 + 9585*(x*e + d)^m*A*a^2*c*m^4*x^3*e^8 + 32979*(x*e + d)^m*B*a*b^2*m^3*x^4*
e^8 + 10993*(x*e + d)^m*A*b^3*m^3*x^4*e^8 + 32979*(x*e + d)^m*B*a^2*c*m^3*x^4*e^8 + 65958*(x*e + d)^m*A*a*b*c*
m^3*x^4*e^8 + 19564*(x*e + d)^m*B*b^3*m^2*x^5*e^8 + 117384*(x*e + d)^m*B*a*b*c*m^2*x^5*e^8 + 58692*(x*e + d)^m
*A*b^2*c*m^2*x^5*e^8 + 58692*(x*e + d)^m*A*a*c^2*m^2*x^5*e^8 + 51432*(x*e + d)^m*B*b^2*c*m*x^6*e^8 + 51432*(x*
e + d)^m*B*a*c^2*m*x^6*e^8 + 51432*(x*e + d)^m*A*b*c^2*m*x^6*e^8 + 17280*(x*e + d)^m*B*b*c^2*x^7*e^8 + 5760*(x
*e + d)^m*A*c^3*x^7*e^8 + 35*(x*e + d)^m*A*a^3*d*m^6*e^7 + 445*(x*e + d)^m*B*a^3*d*m^5*x*e^7 + 1335*(x*e + d)^
m*A*a^2*b*d*m^5*x*e^7 + 7275*(x*e + d)^m*B*a^2*b*d*m^4*x^2*e^7 + 7275*(x*e + d)^m*A*a*b^2*d*m^4*x^2*e^7 + 7275
*(x*e + d)^m*A*a^2*c*d*m^4*x^2*e^7 + 16140*(x*e + d)^m*B*a*b^2*d*m^3*x^3*e^7 + 5380*(x*e + d)^m*A*b^3*d*m^3*x^
3*e^7 + 16140*(x*e + d)^m*B*a^2*c*d*m^3*x^3*e^7 + 32280*(x*e + d)^m*A*a*b*c*d*m^3*x^3*e^7 + 4572*(x*e + d)^m*B
*b^3*d*m^2*x^4*e^7 + 27432*(x*e + d)^m*B*a*b*c*d*m^2*x^4*e^7 + 13716*(x*e + d)^m*A*b^2*c*d*m^2*x^4*e^7 + 13716
*(x*e + d)^m*A*a*c^2*d*m^2*x^4*e^7 + 4032*(x*e + d)^m*B*b^2*c*d*m*x^5*e^7 + 4032*(x*e + d)^m*B*a*c^2*d*m*x^5*e
^7 + 4032*(x*e + d)^m*A*b*c^2*d*m*x^5*e^7 - 33*(x*e + d)^m*B*a^3*d^2*m^5*e^6 - 99*(x*e + d)^m*A*a^2*b*d^2*m^5*
e^6 - 2130*(x*e + d)^m*B*a^2*b*d^2*m^4*x*e^6 - 2130*(x*e + d)^m*A*a*b^2*d^2*m^4*x*e^6 - 2130*(x*e + d)^m*A*a^2
*c*d^2*m^4*x*e^6 - 11853*(x*e + d)^m*B*a*b^2*d^2*m^3*x^2*e^6 - 3951*(x*e + d)^m*A*b^3*d^2*m^3*x^2*e^6 - 11853*
(x*e + d)^m*B*a^2*c*d^2*m^3*x^2*e^6 - 23706*(x*e + d)^m*A*a*b*c*d^2*m^3*x^2*e^6 - 5200*(x*e + d)^m*B*b^3*d^2*m
^2*x^3*e^6 - 31200*(x*e + d)^m*B*a*b*c*d^2*m^2*x^3*e^6 - 15600*(x*e + d)^m*A*b^2*c*d^2*m^2*x^3*e^6 - 15600*(x*
e + d)^m*A*a*c^2*d^2*m^2*x^3*e^6 - 5040*(x*e + d)^m*B*b^2*c*d^2*m*x^4*e^6 - 5040*(x*e + d)^m*B*a*c^2*d^2*m*x^4
*e^6 - 5040*(x*e + d)^m*A*b*c^2*d^2*m*x^4*e^6 + 180*(x*e + d)^m*B*a^2*b*d^3*m^4*e^5 + 180*(x*e + d)^m*A*a*b^2*
d^3*m^4*e^5 + 180*(x*e + d)^m*A*a^2*c*d^3*m^4*e^5 + 4518*(x*e + d)^m*B*a*b^2*d^3*m^3*x*e^5 + 1506*(x*e + d)^m*
A*b^3*d^3*m^3*x*e^5 + 4518*(x*e + d)^m*B*a^2*c*d^3*m^3*x*e^5 + 9036*(x*e + d)^m*A*a*b*c*d^3*m^3*x*e^5 + 5784*(
x*e + d)^m*B*b^3*d^3*m^2*x^2*e^5 + 34704*(x*e + d)^m*B*a*b*c*d^3*m^2*x^2*e^5 + 17352*(x*e + d)^m*A*b^2*c*d^3*m
^2*x^2*e^5 + 17352*(x*e + d)^m*A*a*c^2*d^3*m^2*x^2*e^5 + 6720*(x*e + d)^m*B*b^2*c*d^3*m*x^3*e^5 + 6720*(x*e +
d)^m*B*a*c^2*d^3*m*x^3*e^5 + 6720*(x*e + d)^m*A*b*c^2*d^3*m*x^3*e^5 - 468*(x*e + d)^m*B*a*b^2*d^4*m^3*e^4 - 15
6*(x*e + d)^m*A*b^3*d^4*m^3*e^4 - 468*(x*e + d)^m*B*a^2*c*d^4*m^3*e^4 - 936*(x*e + d)^m*A*a*b*c*d^4*m^3*e^4 -
3504*(x*e + d)^m*B*b^3*d^4*m^2*x*e^4 - 21024*(x*e + d)^m*B*a*b*c*d^4*m^2*x*e^4 - 10512*(x*e + d)^m*A*b^2*c*d^4
*m^2*x*e^4 - 10512*(x*e + d)^m*A*a*c^2*d^4*m^2*x*e^4 - 10080*(x*e + d)^m*B*b^2*c*d^4*m*x^2*e^4 - 10080*(x*e +
d)^m*B*a*c^2*d^4*m*x^2*e^4 - 10080*(x*e + d)^m*A*b*c^2*d^4*m*x^2*e^4 + 504*(x*e + d)^m*B*b^3*d^5*m^2*e^3 + 302
4*(x*e + d)^m*B*a*b*c*d^5*m^2*e^3 + 1512*(x*e + d)^m*A*b^2*c*d^5*m^2*e^3 + 1512*(x*e + d)^m*A*a*c^2*d^5*m^2*e^
3 + 20160*(x*e + d)^m*B*b^2*c*d^5*m*x*e^3 + 20160*(x*e + d)^m*B*a*c^2*d^5*m*x*e^3 + 20160*(x*e + d)^m*A*b*c^2*
d^5*m*x*e^3 - 5400*(x*e + d)^m*B*b^2*c*d^6*m*e^2 - 5400*(x*e + d)^m*B*a*c^2*d^6*m*e^2 - 5400*(x*e + d)^m*A*b*c
^2*d^6*m*e^2 + 17280*(x*e + d)^m*B*b*c^2*d^7*e + 5760*(x*e + d)^m*A*c^3*d^7*e + 511*(x*e + d)^m*A*a^3*m^5*x*e^
8 + 3580*(x*e + d)^m*B*a^3*m^4*x^2*e^8 + 10740*(x*e + d)^m*A*a^2*b*m^4*x^2*e^8 + 38592*(x*e + d)^m*B*a^2*b*m^3
*x^3*e^8 + 38592*(x*e + d)^m*A*a*b^2*m^3*x^3*e^8 + 38592*(x*e + d)^m*A*a^2*c*m^3*x^3*e^8 + 69936*(x*e + d)^m*B
*a*b^2*m^2*x^4*e^8 + 23312*(x*e + d)^m*A*b^3*m^2*x^4*e^8 + 69936*(x*e + d)^m*B*a^2*c*m^2*x^4*e^8 + 139872*(x*e
+ d)^m*A*a*b*c*m^2*x^4*e^8 + 20304*(x*e + d)^m*B*b^3*m*x^5*e^8 + 121824*(x*e + d)^m*B*a*b*c*m*x^5*e^8 + 60912
*(x*e + d)^m*A*b^2*c*m*x^5*e^8 + 60912*(x*e + d)^m*A*a*c^2*m*x^5*e^8 + 20160*(x*e + d)^m*B*b^2*c*x^6*e^8 + 201
60*(x*e + d)^m*B*a*c^2*x^6*e^8 + 20160*(x*e + d)^m*A*b*c^2*x^6*e^8 + 511*(x*e + d)^m*A*a^3*d*m^5*e^7 + 3135*(x
*e + d)^m*B*a^3*d*m^4*x*e^7 + 9405*(x*e + d)^m*A*a^2*b*d*m^4*x*e^7 + 24042*(x*e + d)^m*B*a^2*b*d*m^3*x^2*e^7 +
24042*(x*e + d)^m*A*a*b^2*d*m^3*x^2*e^7 + 24042*(x*e + d)^m*A*a^2*c*d*m^3*x^2*e^7 + 21516*(x*e + d)^m*B*a*b^2
*d*m^2*x^3*e^7 + 7172*(x*e + d)^m*A*b^3*d*m^2*x^3*e^7 + 21516*(x*e + d)^m*B*a^2*c*d*m^2*x^3*e^7 + 43032*(x*e +
d)^m*A*a*b*c*d*m^2*x^3*e^7 + 2016*(x*e + d)^m*B*b^3*d*m*x^4*e^7 + 12096*(x*e + d)^m*B*a*b*c*d*m*x^4*e^7 + 604
8*(x*e + d)^m*A*b^2*c*d*m*x^4*e^7 + 6048*(x*e + d)^m*A*a*c^2*d*m*x^4*e^7 - 445*(x*e + d)^m*B*a^3*d^2*m^4*e^6 -
1335*(x*e + d)^m*A*a^2*b*d^2*m^4*e^6 - 12420*(x*e + d)^m*B*a^2*b*d^2*m^3*x*e^6 - 12420*(x*e + d)^m*A*a*b^2*d^
2*m^3*x*e^6 - 12420*(x*e + d)^m*A*a^2*c*d^2*m^3*x*e^6 - 24714*(x*e + d)^m*B*a*b^2*d^2*m^2*x^2*e^6 - 8238*(x*e
+ d)^m*A*b^3*d^2*m^2*x^2*e^6 - 24714*(x*e + d)^m*B*a^2*c*d^2*m^2*x^2*e^6 - 49428*(x*e + d)^m*A*a*b*c*d^2*m^2*x
^2*e^6 - 2688*(x*e + d)^m*B*b^3*d^2*m*x^3*e^6 - 16128*(x*e + d)^m*B*a*b*c*d^2*m*x^3*e^6 - 8064*(x*e + d)^m*A*b
^2*c*d^2*m*x^3*e^6 - 8064*(x*e + d)^m*A*a*c^2*d^2*m*x^3*e^6 + 2130*(x*e + d)^m*B*a^2*b*d^3*m^3*e^5 + 2130*(x*e
+ d)^m*A*a*b^2*d^3*m^3*e^5 + 2130*(x*e + d)^m*A*a^2*c*d^3*m^3*e^5 + 19188*(x*e + d)^m*B*a*b^2*d^3*m^2*x*e^5 +
6396*(x*e + d)^m*A*b^3*d^3*m^2*x*e^5 + 19188*(x*e + d)^m*B*a^2*c*d^3*m^2*x*e^5 + 38376*(x*e + d)^m*A*a*b*c*d^
3*m^2*x*e^5 + 4032*(x*e + d)^m*B*b^3*d^3*m*x^2*e^5 + 24192*(x*e + d)^m*B*a*b*c*d^3*m*x^2*e^5 + 12096*(x*e + d)
^m*A*b^2*c*d^3*m*x^2*e^5 + 12096*(x*e + d)^m*A*a*c^2*d^3*m*x^2*e^5 - 4518*(x*e + d)^m*B*a*b^2*d^4*m^2*e^4 - 15
06*(x*e + d)^m*A*b^3*d^4*m^2*e^4 - 4518*(x*e + d)^m*B*a^2*c*d^4*m^2*e^4 - 9036*(x*e + d)^m*A*a*b*c*d^4*m^2*e^4
- 8064*(x*e + d)^m*B*b^3*d^4*m*x*e^4 - 48384*(x*e + d)^m*B*a*b*c*d^4*m*x*e^4 - 24192*(x*e + d)^m*A*b^2*c*d^4*
m*x*e^4 - 24192*(x*e + d)^m*A*a*c^2*d^4*m*x*e^4 + 3504*(x*e + d)^m*B*b^3*d^5*m*e^3 + 21024*(x*e + d)^m*B*a*b*c
*d^5*m*e^3 + 10512*(x*e + d)^m*A*b^2*c*d^5*m*e^3 + 10512*(x*e + d)^m*A*a*c^2*d^5*m*e^3 - 20160*(x*e + d)^m*B*b
^2*c*d^6*e^2 - 20160*(x*e + d)^m*B*a*c^2*d^6*e^2 - 20160*(x*e + d)^m*A*b*c^2*d^6*e^2 + 4025*(x*e + d)^m*A*a^3*
m^4*x*e^8 + 15289*(x*e + d)^m*B*a^3*m^3*x^2*e^8 + 45867*(x*e + d)^m*A*a^2*b*m^3*x^2*e^8 + 86076*(x*e + d)^m*B*
a^2*b*m^2*x^3*e^8 + 86076*(x*e + d)^m*A*a*b^2*m^2*x^3*e^8 + 86076*(x*e + d)^m*A*a^2*c*m^2*x^3*e^8 + 74628*(x*e
+ d)^m*B*a*b^2*m*x^4*e^8 + 24876*(x*e + d)^m*A*b^3*m*x^4*e^8 + 74628*(x*e + d)^m*B*a^2*c*m*x^4*e^8 + 149256*(
x*e + d)^m*A*a*b*c*m*x^4*e^8 + 8064*(x*e + d)^m*B*b^3*x^5*e^8 + 48384*(x*e + d)^m*B*a*b*c*x^5*e^8 + 24192*(x*e
+ d)^m*A*b^2*c*x^5*e^8 + 24192*(x*e + d)^m*A*a*c^2*x^5*e^8 + 4025*(x*e + d)^m*A*a^3*d*m^4*e^7 + 12154*(x*e +
d)^m*B*a^3*d*m^3*x*e^7 + 36462*(x*e + d)^m*A*a^2*b*d*m^3*x*e^7 + 37992*(x*e + d)^m*B*a^2*b*d*m^2*x^2*e^7 + 379
92*(x*e + d)^m*A*a*b^2*d*m^2*x^2*e^7 + 37992*(x*e + d)^m*A*a^2*c*d*m^2*x^2*e^7 + 10080*(x*e + d)^m*B*a*b^2*d*m
*x^3*e^7 + 3360*(x*e + d)^m*A*b^3*d*m*x^3*e^7 + 10080*(x*e + d)^m*B*a^2*c*d*m*x^3*e^7 + 20160*(x*e + d)^m*A*a*
b*c*d*m*x^3*e^7 - 3135*(x*e + d)^m*B*a^3*d^2*m^3*e^6 - 9405*(x*e + d)^m*A*a^2*b*d^2*m^3*e^6 - 35664*(x*e + d)^
m*B*a^2*b*d^2*m^2*x*e^6 - 35664*(x*e + d)^m*A*a*b^2*d^2*m^2*x*e^6 - 35664*(x*e + d)^m*A*a^2*c*d^2*m^2*x*e^6 -
15120*(x*e + d)^m*B*a*b^2*d^2*m*x^2*e^6 - 5040*(x*e + d)^m*A*b^3*d^2*m*x^2*e^6 - 15120*(x*e + d)^m*B*a^2*c*d^2
*m*x^2*e^6 - 30240*(x*e + d)^m*A*a*b*c*d^2*m*x^2*e^6 + 12420*(x*e + d)^m*B*a^2*b*d^3*m^2*e^5 + 12420*(x*e + d)
^m*A*a*b^2*d^3*m^2*e^5 + 12420*(x*e + d)^m*A*a^2*c*d^3*m^2*e^5 + 30240*(x*e + d)^m*B*a*b^2*d^3*m*x*e^5 + 10080
*(x*e + d)^m*A*b^3*d^3*m*x*e^5 + 30240*(x*e + d)^m*B*a^2*c*d^3*m*x*e^5 + 60480*(x*e + d)^m*A*a*b*c*d^3*m*x*e^5
- 19188*(x*e + d)^m*B*a*b^2*d^4*m*e^4 - 6396*(x*e + d)^m*A*b^3*d^4*m*e^4 - 19188*(x*e + d)^m*B*a^2*c*d^4*m*e^
4 - 38376*(x*e + d)^m*A*a*b*c*d^4*m*e^4 + 8064*(x*e + d)^m*B*b^3*d^5*e^3 + 48384*(x*e + d)^m*B*a*b*c*d^5*e^3 +
24192*(x*e + d)^m*A*b^2*c*d^5*e^3 + 24192*(x*e + d)^m*A*a*c^2*d^5*e^3 + 18424*(x*e + d)^m*A*a^3*m^3*x*e^8 + 3
6706*(x*e + d)^m*B*a^3*m^2*x^2*e^8 + 110118*(x*e + d)^m*A*a^2*b*m^2*x^2*e^8 + 96144*(x*e + d)^m*B*a^2*b*m*x^3*
e^8 + 96144*(x*e + d)^m*A*a*b^2*m*x^3*e^8 + 96144*(x*e + d)^m*A*a^2*c*m*x^3*e^8 + 30240*(x*e + d)^m*B*a*b^2*x^
4*e^8 + 10080*(x*e + d)^m*A*b^3*x^4*e^8 + 30240*(x*e + d)^m*B*a^2*c*x^4*e^8 + 60480*(x*e + d)^m*A*a*b*c*x^4*e^
8 + 18424*(x*e + d)^m*A*a^3*d*m^3*e^7 + 24552*(x*e + d)^m*B*a^3*d*m^2*x*e^7 + 73656*(x*e + d)^m*A*a^2*b*d*m^2*
x*e^7 + 20160*(x*e + d)^m*B*a^2*b*d*m*x^2*e^7 + 20160*(x*e + d)^m*A*a*b^2*d*m*x^2*e^7 + 20160*(x*e + d)^m*A*a^
2*c*d*m*x^2*e^7 - 12154*(x*e + d)^m*B*a^3*d^2*m^2*e^6 - 36462*(x*e + d)^m*A*a^2*b*d^2*m^2*e^6 - 40320*(x*e + d
)^m*B*a^2*b*d^2*m*x*e^6 - 40320*(x*e + d)^m*A*a*b^2*d^2*m*x*e^6 - 40320*(x*e + d)^m*A*a^2*c*d^2*m*x*e^6 + 3566
4*(x*e + d)^m*B*a^2*b*d^3*m*e^5 + 35664*(x*e + d)^m*A*a*b^2*d^3*m*e^5 + 35664*(x*e + d)^m*A*a^2*c*d^3*m*e^5 -
30240*(x*e + d)^m*B*a*b^2*d^4*e^4 - 10080*(x*e + d)^m*A*b^3*d^4*e^4 - 30240*(x*e + d)^m*B*a^2*c*d^4*e^4 - 6048
0*(x*e + d)^m*A*a*b*c*d^4*e^4 + 48860*(x*e + d)^m*A*a^3*m^2*x*e^8 + 44712*(x*e + d)^m*B*a^3*m*x^2*e^8 + 134136
*(x*e + d)^m*A*a^2*b*m*x^2*e^8 + 40320*(x*e + d)^m*B*a^2*b*x^3*e^8 + 40320*(x*e + d)^m*A*a*b^2*x^3*e^8 + 40320
*(x*e + d)^m*A*a^2*c*x^3*e^8 + 48860*(x*e + d)^m*A*a^3*d*m^2*e^7 + 20160*(x*e + d)^m*B*a^3*d*m*x*e^7 + 60480*(
x*e + d)^m*A*a^2*b*d*m*x*e^7 - 24552*(x*e + d)^m*B*a^3*d^2*m*e^6 - 73656*(x*e + d)^m*A*a^2*b*d^2*m*e^6 + 40320
*(x*e + d)^m*B*a^2*b*d^3*e^5 + 40320*(x*e + d)^m*A*a*b^2*d^3*e^5 + 40320*(x*e + d)^m*A*a^2*c*d^3*e^5 + 69264*(
x*e + d)^m*A*a^3*m*x*e^8 + 20160*(x*e + d)^m*B*a^3*x^2*e^8 + 60480*(x*e + d)^m*A*a^2*b*x^2*e^8 + 69264*(x*e +
d)^m*A*a^3*d*m*e^7 - 20160*(x*e + d)^m*B*a^3*d^2*e^6 - 60480*(x*e + d)^m*A*a^2*b*d^2*e^6 + 40320*(x*e + d)^m*A
*a^3*x*e^8 + 40320*(x*e + d)^m*A*a^3*d*e^7)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8
+ 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)