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

Optimal. Leaf size=318 \[ \frac{a x^{2 n+1} (e x)^m \left (A \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )+a B c (2 a d+3 b c)\right )}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left (A b \left (3 a^2 d^2+6 a b c d+b^2 c^2\right )+a B \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )\right )}{m+3 n+1}+\frac{b x^{4 n+1} (e x)^m \left (3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right )}{m+4 n+1}+\frac{a^2 c x^{n+1} (e x)^m (2 a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d x^{5 n+1} (e x)^m (3 a B d+A b d+2 b B c)}{m+5 n+1}+\frac{b^3 B d^2 x^{6 n+1} (e x)^m}{m+6 n+1} \]

[Out]

(a^2*c*(3*A*b*c + a*B*c + 2*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (a*(a*B*c*(3*b*c + 2*a*d) + A*(3*b^2*c^2 +
6*a*b*c*d + a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((a*B*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2) + A*b*(b^2
*c^2 + 6*a*b*c*d + 3*a^2*d^2))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b*(3*a^2*B*d^2 + 3*a*b*d*(2*B*c + A*d) +
b^2*c*(B*c + 2*A*d))*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b^2*d*(2*b*B*c + A*b*d + 3*a*B*d)*x^(1 + 5*n)*(e*x)
^m)/(1 + m + 5*n) + (b^3*B*d^2*x^(1 + 6*n)*(e*x)^m)/(1 + m + 6*n) + (a^3*A*c^2*(e*x)^(1 + m))/(e*(1 + m))

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Rubi [A]  time = 0.411183, antiderivative size = 318, normalized size of antiderivative = 1., number of steps used = 14, number of rules used = 3, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.097, Rules used = {570, 20, 30} \[ \frac{a x^{2 n+1} (e x)^m \left (A \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )+a B c (2 a d+3 b c)\right )}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left (A b \left (3 a^2 d^2+6 a b c d+b^2 c^2\right )+a B \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )\right )}{m+3 n+1}+\frac{b x^{4 n+1} (e x)^m \left (3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right )}{m+4 n+1}+\frac{a^2 c x^{n+1} (e x)^m (2 a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d x^{5 n+1} (e x)^m (3 a B d+A b d+2 b B c)}{m+5 n+1}+\frac{b^3 B d^2 x^{6 n+1} (e x)^m}{m+6 n+1} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(a^2*c*(3*A*b*c + a*B*c + 2*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (a*(a*B*c*(3*b*c + 2*a*d) + A*(3*b^2*c^2 +
6*a*b*c*d + a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((a*B*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2) + A*b*(b^2
*c^2 + 6*a*b*c*d + 3*a^2*d^2))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b*(3*a^2*B*d^2 + 3*a*b*d*(2*B*c + A*d) +
b^2*c*(B*c + 2*A*d))*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b^2*d*(2*b*B*c + A*b*d + 3*a*B*d)*x^(1 + 5*n)*(e*x)
^m)/(1 + m + 5*n) + (b^3*B*d^2*x^(1 + 6*n)*(e*x)^m)/(1 + m + 6*n) + (a^3*A*c^2*(e*x)^(1 + m))/(e*(1 + 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]

Rule 20

Int[(u_.)*((a_.)*(v_))^(m_)*((b_.)*(v_))^(n_), x_Symbol] :> Dist[(b^IntPart[n]*(b*v)^FracPart[n])/(a^IntPart[n
]*(a*v)^FracPart[n]), Int[u*(a*v)^(m + n), x], x] /; FreeQ[{a, b, m, n}, x] &&  !IntegerQ[m] &&  !IntegerQ[n]
&&  !IntegerQ[m + n]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

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

Mathematica [A]  time = 1.10686, size = 273, normalized size = 0.86 \[ x (e x)^m \left (\frac{a x^{2 n} \left (A \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )+a B c (2 a d+3 b c)\right )}{m+2 n+1}+\frac{x^{3 n} \left (A b \left (3 a^2 d^2+6 a b c d+b^2 c^2\right )+a B \left (a^2 d^2+6 a b c d+3 b^2 c^2\right )\right )}{m+3 n+1}+\frac{b x^{4 n} \left (3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right )}{m+4 n+1}+\frac{a^2 c x^n (2 a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c^2}{m+1}+\frac{b^2 d x^{5 n} (3 a B d+A b d+2 b B c)}{m+5 n+1}+\frac{b^3 B d^2 x^{6 n}}{m+6 n+1}\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

x*(e*x)^m*((a^3*A*c^2)/(1 + m) + (a^2*c*(3*A*b*c + a*B*c + 2*a*A*d)*x^n)/(1 + m + n) + (a*(a*B*c*(3*b*c + 2*a*
d) + A*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2))*x^(2*n))/(1 + m + 2*n) + ((a*B*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2) + A
*b*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2))*x^(3*n))/(1 + m + 3*n) + (b*(3*a^2*B*d^2 + 3*a*b*d*(2*B*c + A*d) + b^2*c
*(B*c + 2*A*d))*x^(4*n))/(1 + m + 4*n) + (b^2*d*(2*b*B*c + A*b*d + 3*a*B*d)*x^(5*n))/(1 + m + 5*n) + (b^3*B*d^
2*x^(6*n))/(1 + m + 6*n))

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Maple [C]  time = 0.175, size = 11389, normalized size = 35.8 \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*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,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((e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [B]  time = 1.79572, size = 14151, normalized size = 44.5 \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*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,x, algorithm="fricas")

[Out]

((B*b^3*d^2*m^6 + 6*B*b^3*d^2*m^5 + 15*B*b^3*d^2*m^4 + 20*B*b^3*d^2*m^3 + 15*B*b^3*d^2*m^2 + 6*B*b^3*d^2*m + B
*b^3*d^2 + 120*(B*b^3*d^2*m + B*b^3*d^2)*n^5 + 274*(B*b^3*d^2*m^2 + 2*B*b^3*d^2*m + B*b^3*d^2)*n^4 + 225*(B*b^
3*d^2*m^3 + 3*B*b^3*d^2*m^2 + 3*B*b^3*d^2*m + B*b^3*d^2)*n^3 + 85*(B*b^3*d^2*m^4 + 4*B*b^3*d^2*m^3 + 6*B*b^3*d
^2*m^2 + 4*B*b^3*d^2*m + B*b^3*d^2)*n^2 + 15*(B*b^3*d^2*m^5 + 5*B*b^3*d^2*m^4 + 10*B*b^3*d^2*m^3 + 10*B*b^3*d^
2*m^2 + 5*B*b^3*d^2*m + B*b^3*d^2)*n)*x*x^(6*n)*e^(m*log(e) + m*log(x)) + ((2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*
d^2)*m^6 + 2*B*b^3*c*d + 6*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^5 + 144*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3
)*d^2 + (2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m)*n^5 + 15*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^4 + 324*
(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2 + (2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^2 + 2*(2*B*b^3*c*d + (3*B*a
*b^2 + A*b^3)*d^2)*m)*n^4 + 20*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^3 + 260*(2*B*b^3*c*d + (2*B*b^3*c*d +
(3*B*a*b^2 + A*b^3)*d^2)*m^3 + (3*B*a*b^2 + A*b^3)*d^2 + 3*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^2 + 3*(2
*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m)*n^3 + (3*B*a*b^2 + A*b^3)*d^2 + 15*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)
*d^2)*m^2 + 95*(2*B*b^3*c*d + (2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^4 + 4*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^
3)*d^2)*m^3 + (3*B*a*b^2 + A*b^3)*d^2 + 6*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^2 + 4*(2*B*b^3*c*d + (3*B*
a*b^2 + A*b^3)*d^2)*m)*n^2 + 6*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m + 16*(2*B*b^3*c*d + (2*B*b^3*c*d + (3
*B*a*b^2 + A*b^3)*d^2)*m^5 + 5*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^4 + 10*(2*B*b^3*c*d + (3*B*a*b^2 + A*
b^3)*d^2)*m^3 + (3*B*a*b^2 + A*b^3)*d^2 + 10*(2*B*b^3*c*d + (3*B*a*b^2 + A*b^3)*d^2)*m^2 + 5*(2*B*b^3*c*d + (3
*B*a*b^2 + A*b^3)*d^2)*m)*n)*x*x^(5*n)*e^(m*log(e) + m*log(x)) + ((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 + B*b^3*c^2 + 6*(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 + 180*(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 + (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)*n^5 + 15*(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 + 396*(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 + (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 + 2*(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)*n^4 + 20*(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 + 307*(B*b^3*c
^2 + (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 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(
B*a^2*b + A*a*b^2)*d^2 + 3*(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 + 3*(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)*n^3 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b +
A*a*b^2)*d^2 + 15*(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 + 107*(B*b^3*c^2 +
(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 + 4*(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 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2 + 6*(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 + 4*(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)*n^2 + 6*(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 + 17*(B
*b^3*c^2 + (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 + 5*(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 + 10*(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 + 2*(3*B*a*b^2 + A*b^3)*c*d + 3*(B*a^2*b + A*a*b^2)*d^2 + 10*(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 + 5*(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)*n)*x*x^(4*n)*e^(m*log(e) + m*log(x)) + (((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 + 6*((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 + 24
0*((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 + ((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)*n^5 + 15*((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 + 508*((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 + ((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 + 2*((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)*n^4 + 20*((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 + 372*(((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 + (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 + 3*((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 + 3*((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)*n^3 + (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 + 15*((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 + 121*(((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 + 4*((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 + (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 + 6*((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 + 4*((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)*n^2 + 6*((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 + 18*(((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 + 5*((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 + 10*((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 + (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 + 10*((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 +
5*((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)*n)*x*x^(3*n)*e^(m*log(e)
+ m*log(x)) + ((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 + A*a^3*d^2 + 6*(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 + 360*(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 + (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)*n^5 + 15
*(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 + 702*(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 + (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
+ 2*(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)*n^4 + 20*(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 + 461*(A*a^3*d^2 + (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 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d + 3*(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 + 3*(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)*n^3 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d + 15*(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 + 137*(A*a^3*d^2 + (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 + 4*(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 + 3*(B*a^2*b
+ A*a*b^2)*c^2 + 2*(B*a^3 + 3*A*a^2*b)*c*d + 6*(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 + 4*(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)*n^2 + 6*(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 + 19*(A*a^3*d^2 + (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 + 5*(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 +
10*(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 + 3*(B*a^2*b + A*a*b^2)*c^2 + 2*(B
*a^3 + 3*A*a^2*b)*c*d + 10*(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 + 5*(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)*n)*x*x^(2*n)*e^(m*log(e) + m*log(x)) + ((2*A*a
^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^6 + 2*A*a^3*c*d + 6*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^5 + 720*(2*A
*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2 + (2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*n^5 + 15*(2*A*a^3*c*d + (B*a^3
+ 3*A*a^2*b)*c^2)*m^4 + 1044*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2 + (2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)
*m^2 + 2*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*n^4 + 20*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^3 + 580
*(2*A*a^3*c*d + (2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^3 + (B*a^3 + 3*A*a^2*b)*c^2 + 3*(2*A*a^3*c*d + (B*a^
3 + 3*A*a^2*b)*c^2)*m^2 + 3*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*n^3 + (B*a^3 + 3*A*a^2*b)*c^2 + 15*(2*A
*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^2 + 155*(2*A*a^3*c*d + (2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^4 + 4*(
2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^3 + (B*a^3 + 3*A*a^2*b)*c^2 + 6*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^
2)*m^2 + 4*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*n^2 + 6*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m + 20*(
2*A*a^3*c*d + (2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^5 + 5*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^4 + 10
*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m^3 + (B*a^3 + 3*A*a^2*b)*c^2 + 10*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)
*c^2)*m^2 + 5*(2*A*a^3*c*d + (B*a^3 + 3*A*a^2*b)*c^2)*m)*n)*x*x^n*e^(m*log(e) + m*log(x)) + (A*a^3*c^2*m^6 + 7
20*A*a^3*c^2*n^6 + 6*A*a^3*c^2*m^5 + 15*A*a^3*c^2*m^4 + 20*A*a^3*c^2*m^3 + 15*A*a^3*c^2*m^2 + 6*A*a^3*c^2*m +
A*a^3*c^2 + 1764*(A*a^3*c^2*m + A*a^3*c^2)*n^5 + 1624*(A*a^3*c^2*m^2 + 2*A*a^3*c^2*m + A*a^3*c^2)*n^4 + 735*(A
*a^3*c^2*m^3 + 3*A*a^3*c^2*m^2 + 3*A*a^3*c^2*m + A*a^3*c^2)*n^3 + 175*(A*a^3*c^2*m^4 + 4*A*a^3*c^2*m^3 + 6*A*a
^3*c^2*m^2 + 4*A*a^3*c^2*m + A*a^3*c^2)*n^2 + 21*(A*a^3*c^2*m^5 + 5*A*a^3*c^2*m^4 + 10*A*a^3*c^2*m^3 + 10*A*a^
3*c^2*m^2 + 5*A*a^3*c^2*m + A*a^3*c^2)*n)*x*e^(m*log(e) + m*log(x)))/(m^7 + 720*(m + 1)*n^6 + 7*m^6 + 1764*(m^
2 + 2*m + 1)*n^5 + 21*m^5 + 1624*(m^3 + 3*m^2 + 3*m + 1)*n^4 + 35*m^4 + 735*(m^4 + 4*m^3 + 6*m^2 + 4*m + 1)*n^
3 + 35*m^3 + 175*(m^5 + 5*m^4 + 10*m^3 + 10*m^2 + 5*m + 1)*n^2 + 21*m^2 + 21*(m^6 + 6*m^5 + 15*m^4 + 20*m^3 +
15*m^2 + 6*m + 1)*n + 7*m + 1)

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

[Out]

Timed out

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Giac [B]  time = 1.43246, size = 20733, normalized size = 65.2 \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*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,x, algorithm="giac")

[Out]

(B*b^3*d^2*m^6*x*x^m*x^(6*n)*e^m + 15*B*b^3*d^2*m^5*n*x*x^m*x^(6*n)*e^m + 85*B*b^3*d^2*m^4*n^2*x*x^m*x^(6*n)*e
^m + 225*B*b^3*d^2*m^3*n^3*x*x^m*x^(6*n)*e^m + 274*B*b^3*d^2*m^2*n^4*x*x^m*x^(6*n)*e^m + 120*B*b^3*d^2*m*n^5*x
*x^m*x^(6*n)*e^m + 2*B*b^3*c*d*m^6*x*x^m*x^(5*n)*e^m + 3*B*a*b^2*d^2*m^6*x*x^m*x^(5*n)*e^m + A*b^3*d^2*m^6*x*x
^m*x^(5*n)*e^m + 32*B*b^3*c*d*m^5*n*x*x^m*x^(5*n)*e^m + 48*B*a*b^2*d^2*m^5*n*x*x^m*x^(5*n)*e^m + 16*A*b^3*d^2*
m^5*n*x*x^m*x^(5*n)*e^m + 190*B*b^3*c*d*m^4*n^2*x*x^m*x^(5*n)*e^m + 285*B*a*b^2*d^2*m^4*n^2*x*x^m*x^(5*n)*e^m
+ 95*A*b^3*d^2*m^4*n^2*x*x^m*x^(5*n)*e^m + 520*B*b^3*c*d*m^3*n^3*x*x^m*x^(5*n)*e^m + 780*B*a*b^2*d^2*m^3*n^3*x
*x^m*x^(5*n)*e^m + 260*A*b^3*d^2*m^3*n^3*x*x^m*x^(5*n)*e^m + 648*B*b^3*c*d*m^2*n^4*x*x^m*x^(5*n)*e^m + 972*B*a
*b^2*d^2*m^2*n^4*x*x^m*x^(5*n)*e^m + 324*A*b^3*d^2*m^2*n^4*x*x^m*x^(5*n)*e^m + 288*B*b^3*c*d*m*n^5*x*x^m*x^(5*
n)*e^m + 432*B*a*b^2*d^2*m*n^5*x*x^m*x^(5*n)*e^m + 144*A*b^3*d^2*m*n^5*x*x^m*x^(5*n)*e^m + B*b^3*c^2*m^6*x*x^m
*x^(4*n)*e^m + 6*B*a*b^2*c*d*m^6*x*x^m*x^(4*n)*e^m + 2*A*b^3*c*d*m^6*x*x^m*x^(4*n)*e^m + 3*B*a^2*b*d^2*m^6*x*x
^m*x^(4*n)*e^m + 3*A*a*b^2*d^2*m^6*x*x^m*x^(4*n)*e^m + 17*B*b^3*c^2*m^5*n*x*x^m*x^(4*n)*e^m + 102*B*a*b^2*c*d*
m^5*n*x*x^m*x^(4*n)*e^m + 34*A*b^3*c*d*m^5*n*x*x^m*x^(4*n)*e^m + 51*B*a^2*b*d^2*m^5*n*x*x^m*x^(4*n)*e^m + 51*A
*a*b^2*d^2*m^5*n*x*x^m*x^(4*n)*e^m + 107*B*b^3*c^2*m^4*n^2*x*x^m*x^(4*n)*e^m + 642*B*a*b^2*c*d*m^4*n^2*x*x^m*x
^(4*n)*e^m + 214*A*b^3*c*d*m^4*n^2*x*x^m*x^(4*n)*e^m + 321*B*a^2*b*d^2*m^4*n^2*x*x^m*x^(4*n)*e^m + 321*A*a*b^2
*d^2*m^4*n^2*x*x^m*x^(4*n)*e^m + 307*B*b^3*c^2*m^3*n^3*x*x^m*x^(4*n)*e^m + 1842*B*a*b^2*c*d*m^3*n^3*x*x^m*x^(4
*n)*e^m + 614*A*b^3*c*d*m^3*n^3*x*x^m*x^(4*n)*e^m + 921*B*a^2*b*d^2*m^3*n^3*x*x^m*x^(4*n)*e^m + 921*A*a*b^2*d^
2*m^3*n^3*x*x^m*x^(4*n)*e^m + 396*B*b^3*c^2*m^2*n^4*x*x^m*x^(4*n)*e^m + 2376*B*a*b^2*c*d*m^2*n^4*x*x^m*x^(4*n)
*e^m + 792*A*b^3*c*d*m^2*n^4*x*x^m*x^(4*n)*e^m + 1188*B*a^2*b*d^2*m^2*n^4*x*x^m*x^(4*n)*e^m + 1188*A*a*b^2*d^2
*m^2*n^4*x*x^m*x^(4*n)*e^m + 180*B*b^3*c^2*m*n^5*x*x^m*x^(4*n)*e^m + 1080*B*a*b^2*c*d*m*n^5*x*x^m*x^(4*n)*e^m
+ 360*A*b^3*c*d*m*n^5*x*x^m*x^(4*n)*e^m + 540*B*a^2*b*d^2*m*n^5*x*x^m*x^(4*n)*e^m + 540*A*a*b^2*d^2*m*n^5*x*x^
m*x^(4*n)*e^m + 3*B*a*b^2*c^2*m^6*x*x^m*x^(3*n)*e^m + A*b^3*c^2*m^6*x*x^m*x^(3*n)*e^m + 6*B*a^2*b*c*d*m^6*x*x^
m*x^(3*n)*e^m + 6*A*a*b^2*c*d*m^6*x*x^m*x^(3*n)*e^m + B*a^3*d^2*m^6*x*x^m*x^(3*n)*e^m + 3*A*a^2*b*d^2*m^6*x*x^
m*x^(3*n)*e^m + 54*B*a*b^2*c^2*m^5*n*x*x^m*x^(3*n)*e^m + 18*A*b^3*c^2*m^5*n*x*x^m*x^(3*n)*e^m + 108*B*a^2*b*c*
d*m^5*n*x*x^m*x^(3*n)*e^m + 108*A*a*b^2*c*d*m^5*n*x*x^m*x^(3*n)*e^m + 18*B*a^3*d^2*m^5*n*x*x^m*x^(3*n)*e^m + 5
4*A*a^2*b*d^2*m^5*n*x*x^m*x^(3*n)*e^m + 363*B*a*b^2*c^2*m^4*n^2*x*x^m*x^(3*n)*e^m + 121*A*b^3*c^2*m^4*n^2*x*x^
m*x^(3*n)*e^m + 726*B*a^2*b*c*d*m^4*n^2*x*x^m*x^(3*n)*e^m + 726*A*a*b^2*c*d*m^4*n^2*x*x^m*x^(3*n)*e^m + 121*B*
a^3*d^2*m^4*n^2*x*x^m*x^(3*n)*e^m + 363*A*a^2*b*d^2*m^4*n^2*x*x^m*x^(3*n)*e^m + 1116*B*a*b^2*c^2*m^3*n^3*x*x^m
*x^(3*n)*e^m + 372*A*b^3*c^2*m^3*n^3*x*x^m*x^(3*n)*e^m + 2232*B*a^2*b*c*d*m^3*n^3*x*x^m*x^(3*n)*e^m + 2232*A*a
*b^2*c*d*m^3*n^3*x*x^m*x^(3*n)*e^m + 372*B*a^3*d^2*m^3*n^3*x*x^m*x^(3*n)*e^m + 1116*A*a^2*b*d^2*m^3*n^3*x*x^m*
x^(3*n)*e^m + 1524*B*a*b^2*c^2*m^2*n^4*x*x^m*x^(3*n)*e^m + 508*A*b^3*c^2*m^2*n^4*x*x^m*x^(3*n)*e^m + 3048*B*a^
2*b*c*d*m^2*n^4*x*x^m*x^(3*n)*e^m + 3048*A*a*b^2*c*d*m^2*n^4*x*x^m*x^(3*n)*e^m + 508*B*a^3*d^2*m^2*n^4*x*x^m*x
^(3*n)*e^m + 1524*A*a^2*b*d^2*m^2*n^4*x*x^m*x^(3*n)*e^m + 720*B*a*b^2*c^2*m*n^5*x*x^m*x^(3*n)*e^m + 240*A*b^3*
c^2*m*n^5*x*x^m*x^(3*n)*e^m + 1440*B*a^2*b*c*d*m*n^5*x*x^m*x^(3*n)*e^m + 1440*A*a*b^2*c*d*m*n^5*x*x^m*x^(3*n)*
e^m + 240*B*a^3*d^2*m*n^5*x*x^m*x^(3*n)*e^m + 720*A*a^2*b*d^2*m*n^5*x*x^m*x^(3*n)*e^m + 3*B*a^2*b*c^2*m^6*x*x^
m*x^(2*n)*e^m + 3*A*a*b^2*c^2*m^6*x*x^m*x^(2*n)*e^m + 2*B*a^3*c*d*m^6*x*x^m*x^(2*n)*e^m + 6*A*a^2*b*c*d*m^6*x*
x^m*x^(2*n)*e^m + A*a^3*d^2*m^6*x*x^m*x^(2*n)*e^m + 57*B*a^2*b*c^2*m^5*n*x*x^m*x^(2*n)*e^m + 57*A*a*b^2*c^2*m^
5*n*x*x^m*x^(2*n)*e^m + 38*B*a^3*c*d*m^5*n*x*x^m*x^(2*n)*e^m + 114*A*a^2*b*c*d*m^5*n*x*x^m*x^(2*n)*e^m + 19*A*
a^3*d^2*m^5*n*x*x^m*x^(2*n)*e^m + 411*B*a^2*b*c^2*m^4*n^2*x*x^m*x^(2*n)*e^m + 411*A*a*b^2*c^2*m^4*n^2*x*x^m*x^
(2*n)*e^m + 274*B*a^3*c*d*m^4*n^2*x*x^m*x^(2*n)*e^m + 822*A*a^2*b*c*d*m^4*n^2*x*x^m*x^(2*n)*e^m + 137*A*a^3*d^
2*m^4*n^2*x*x^m*x^(2*n)*e^m + 1383*B*a^2*b*c^2*m^3*n^3*x*x^m*x^(2*n)*e^m + 1383*A*a*b^2*c^2*m^3*n^3*x*x^m*x^(2
*n)*e^m + 922*B*a^3*c*d*m^3*n^3*x*x^m*x^(2*n)*e^m + 2766*A*a^2*b*c*d*m^3*n^3*x*x^m*x^(2*n)*e^m + 461*A*a^3*d^2
*m^3*n^3*x*x^m*x^(2*n)*e^m + 2106*B*a^2*b*c^2*m^2*n^4*x*x^m*x^(2*n)*e^m + 2106*A*a*b^2*c^2*m^2*n^4*x*x^m*x^(2*
n)*e^m + 1404*B*a^3*c*d*m^2*n^4*x*x^m*x^(2*n)*e^m + 4212*A*a^2*b*c*d*m^2*n^4*x*x^m*x^(2*n)*e^m + 702*A*a^3*d^2
*m^2*n^4*x*x^m*x^(2*n)*e^m + 1080*B*a^2*b*c^2*m*n^5*x*x^m*x^(2*n)*e^m + 1080*A*a*b^2*c^2*m*n^5*x*x^m*x^(2*n)*e
^m + 720*B*a^3*c*d*m*n^5*x*x^m*x^(2*n)*e^m + 2160*A*a^2*b*c*d*m*n^5*x*x^m*x^(2*n)*e^m + 360*A*a^3*d^2*m*n^5*x*
x^m*x^(2*n)*e^m + B*a^3*c^2*m^6*x*x^m*x^n*e^m + 3*A*a^2*b*c^2*m^6*x*x^m*x^n*e^m + 2*A*a^3*c*d*m^6*x*x^m*x^n*e^
m + 20*B*a^3*c^2*m^5*n*x*x^m*x^n*e^m + 60*A*a^2*b*c^2*m^5*n*x*x^m*x^n*e^m + 40*A*a^3*c*d*m^5*n*x*x^m*x^n*e^m +
155*B*a^3*c^2*m^4*n^2*x*x^m*x^n*e^m + 465*A*a^2*b*c^2*m^4*n^2*x*x^m*x^n*e^m + 310*A*a^3*c*d*m^4*n^2*x*x^m*x^n
*e^m + 580*B*a^3*c^2*m^3*n^3*x*x^m*x^n*e^m + 1740*A*a^2*b*c^2*m^3*n^3*x*x^m*x^n*e^m + 1160*A*a^3*c*d*m^3*n^3*x
*x^m*x^n*e^m + 1044*B*a^3*c^2*m^2*n^4*x*x^m*x^n*e^m + 3132*A*a^2*b*c^2*m^2*n^4*x*x^m*x^n*e^m + 2088*A*a^3*c*d*
m^2*n^4*x*x^m*x^n*e^m + 720*B*a^3*c^2*m*n^5*x*x^m*x^n*e^m + 2160*A*a^2*b*c^2*m*n^5*x*x^m*x^n*e^m + 1440*A*a^3*
c*d*m*n^5*x*x^m*x^n*e^m + A*a^3*c^2*m^6*x*x^m*e^m + 21*A*a^3*c^2*m^5*n*x*x^m*e^m + 175*A*a^3*c^2*m^4*n^2*x*x^m
*e^m + 735*A*a^3*c^2*m^3*n^3*x*x^m*e^m + 1624*A*a^3*c^2*m^2*n^4*x*x^m*e^m + 1764*A*a^3*c^2*m*n^5*x*x^m*e^m + 7
20*A*a^3*c^2*n^6*x*x^m*e^m + 6*B*b^3*d^2*m^5*x*x^m*x^(6*n)*e^m + 75*B*b^3*d^2*m^4*n*x*x^m*x^(6*n)*e^m + 340*B*
b^3*d^2*m^3*n^2*x*x^m*x^(6*n)*e^m + 675*B*b^3*d^2*m^2*n^3*x*x^m*x^(6*n)*e^m + 548*B*b^3*d^2*m*n^4*x*x^m*x^(6*n
)*e^m + 120*B*b^3*d^2*n^5*x*x^m*x^(6*n)*e^m + 12*B*b^3*c*d*m^5*x*x^m*x^(5*n)*e^m + 18*B*a*b^2*d^2*m^5*x*x^m*x^
(5*n)*e^m + 6*A*b^3*d^2*m^5*x*x^m*x^(5*n)*e^m + 160*B*b^3*c*d*m^4*n*x*x^m*x^(5*n)*e^m + 240*B*a*b^2*d^2*m^4*n*
x*x^m*x^(5*n)*e^m + 80*A*b^3*d^2*m^4*n*x*x^m*x^(5*n)*e^m + 760*B*b^3*c*d*m^3*n^2*x*x^m*x^(5*n)*e^m + 1140*B*a*
b^2*d^2*m^3*n^2*x*x^m*x^(5*n)*e^m + 380*A*b^3*d^2*m^3*n^2*x*x^m*x^(5*n)*e^m + 1560*B*b^3*c*d*m^2*n^3*x*x^m*x^(
5*n)*e^m + 2340*B*a*b^2*d^2*m^2*n^3*x*x^m*x^(5*n)*e^m + 780*A*b^3*d^2*m^2*n^3*x*x^m*x^(5*n)*e^m + 1296*B*b^3*c
*d*m*n^4*x*x^m*x^(5*n)*e^m + 1944*B*a*b^2*d^2*m*n^4*x*x^m*x^(5*n)*e^m + 648*A*b^3*d^2*m*n^4*x*x^m*x^(5*n)*e^m
+ 288*B*b^3*c*d*n^5*x*x^m*x^(5*n)*e^m + 432*B*a*b^2*d^2*n^5*x*x^m*x^(5*n)*e^m + 144*A*b^3*d^2*n^5*x*x^m*x^(5*n
)*e^m + 6*B*b^3*c^2*m^5*x*x^m*x^(4*n)*e^m + 36*B*a*b^2*c*d*m^5*x*x^m*x^(4*n)*e^m + 12*A*b^3*c*d*m^5*x*x^m*x^(4
*n)*e^m + 18*B*a^2*b*d^2*m^5*x*x^m*x^(4*n)*e^m + 18*A*a*b^2*d^2*m^5*x*x^m*x^(4*n)*e^m + 85*B*b^3*c^2*m^4*n*x*x
^m*x^(4*n)*e^m + 510*B*a*b^2*c*d*m^4*n*x*x^m*x^(4*n)*e^m + 170*A*b^3*c*d*m^4*n*x*x^m*x^(4*n)*e^m + 255*B*a^2*b
*d^2*m^4*n*x*x^m*x^(4*n)*e^m + 255*A*a*b^2*d^2*m^4*n*x*x^m*x^(4*n)*e^m + 428*B*b^3*c^2*m^3*n^2*x*x^m*x^(4*n)*e
^m + 2568*B*a*b^2*c*d*m^3*n^2*x*x^m*x^(4*n)*e^m + 856*A*b^3*c*d*m^3*n^2*x*x^m*x^(4*n)*e^m + 1284*B*a^2*b*d^2*m
^3*n^2*x*x^m*x^(4*n)*e^m + 1284*A*a*b^2*d^2*m^3*n^2*x*x^m*x^(4*n)*e^m + 921*B*b^3*c^2*m^2*n^3*x*x^m*x^(4*n)*e^
m + 5526*B*a*b^2*c*d*m^2*n^3*x*x^m*x^(4*n)*e^m + 1842*A*b^3*c*d*m^2*n^3*x*x^m*x^(4*n)*e^m + 2763*B*a^2*b*d^2*m
^2*n^3*x*x^m*x^(4*n)*e^m + 2763*A*a*b^2*d^2*m^2*n^3*x*x^m*x^(4*n)*e^m + 792*B*b^3*c^2*m*n^4*x*x^m*x^(4*n)*e^m
+ 4752*B*a*b^2*c*d*m*n^4*x*x^m*x^(4*n)*e^m + 1584*A*b^3*c*d*m*n^4*x*x^m*x^(4*n)*e^m + 2376*B*a^2*b*d^2*m*n^4*x
*x^m*x^(4*n)*e^m + 2376*A*a*b^2*d^2*m*n^4*x*x^m*x^(4*n)*e^m + 180*B*b^3*c^2*n^5*x*x^m*x^(4*n)*e^m + 1080*B*a*b
^2*c*d*n^5*x*x^m*x^(4*n)*e^m + 360*A*b^3*c*d*n^5*x*x^m*x^(4*n)*e^m + 540*B*a^2*b*d^2*n^5*x*x^m*x^(4*n)*e^m + 5
40*A*a*b^2*d^2*n^5*x*x^m*x^(4*n)*e^m + 18*B*a*b^2*c^2*m^5*x*x^m*x^(3*n)*e^m + 6*A*b^3*c^2*m^5*x*x^m*x^(3*n)*e^
m + 36*B*a^2*b*c*d*m^5*x*x^m*x^(3*n)*e^m + 36*A*a*b^2*c*d*m^5*x*x^m*x^(3*n)*e^m + 6*B*a^3*d^2*m^5*x*x^m*x^(3*n
)*e^m + 18*A*a^2*b*d^2*m^5*x*x^m*x^(3*n)*e^m + 270*B*a*b^2*c^2*m^4*n*x*x^m*x^(3*n)*e^m + 90*A*b^3*c^2*m^4*n*x*
x^m*x^(3*n)*e^m + 540*B*a^2*b*c*d*m^4*n*x*x^m*x^(3*n)*e^m + 540*A*a*b^2*c*d*m^4*n*x*x^m*x^(3*n)*e^m + 90*B*a^3
*d^2*m^4*n*x*x^m*x^(3*n)*e^m + 270*A*a^2*b*d^2*m^4*n*x*x^m*x^(3*n)*e^m + 1452*B*a*b^2*c^2*m^3*n^2*x*x^m*x^(3*n
)*e^m + 484*A*b^3*c^2*m^3*n^2*x*x^m*x^(3*n)*e^m + 2904*B*a^2*b*c*d*m^3*n^2*x*x^m*x^(3*n)*e^m + 2904*A*a*b^2*c*
d*m^3*n^2*x*x^m*x^(3*n)*e^m + 484*B*a^3*d^2*m^3*n^2*x*x^m*x^(3*n)*e^m + 1452*A*a^2*b*d^2*m^3*n^2*x*x^m*x^(3*n)
*e^m + 3348*B*a*b^2*c^2*m^2*n^3*x*x^m*x^(3*n)*e^m + 1116*A*b^3*c^2*m^2*n^3*x*x^m*x^(3*n)*e^m + 6696*B*a^2*b*c*
d*m^2*n^3*x*x^m*x^(3*n)*e^m + 6696*A*a*b^2*c*d*m^2*n^3*x*x^m*x^(3*n)*e^m + 1116*B*a^3*d^2*m^2*n^3*x*x^m*x^(3*n
)*e^m + 3348*A*a^2*b*d^2*m^2*n^3*x*x^m*x^(3*n)*e^m + 3048*B*a*b^2*c^2*m*n^4*x*x^m*x^(3*n)*e^m + 1016*A*b^3*c^2
*m*n^4*x*x^m*x^(3*n)*e^m + 6096*B*a^2*b*c*d*m*n^4*x*x^m*x^(3*n)*e^m + 6096*A*a*b^2*c*d*m*n^4*x*x^m*x^(3*n)*e^m
+ 1016*B*a^3*d^2*m*n^4*x*x^m*x^(3*n)*e^m + 3048*A*a^2*b*d^2*m*n^4*x*x^m*x^(3*n)*e^m + 720*B*a*b^2*c^2*n^5*x*x
^m*x^(3*n)*e^m + 240*A*b^3*c^2*n^5*x*x^m*x^(3*n)*e^m + 1440*B*a^2*b*c*d*n^5*x*x^m*x^(3*n)*e^m + 1440*A*a*b^2*c
*d*n^5*x*x^m*x^(3*n)*e^m + 240*B*a^3*d^2*n^5*x*x^m*x^(3*n)*e^m + 720*A*a^2*b*d^2*n^5*x*x^m*x^(3*n)*e^m + 18*B*
a^2*b*c^2*m^5*x*x^m*x^(2*n)*e^m + 18*A*a*b^2*c^2*m^5*x*x^m*x^(2*n)*e^m + 12*B*a^3*c*d*m^5*x*x^m*x^(2*n)*e^m +
36*A*a^2*b*c*d*m^5*x*x^m*x^(2*n)*e^m + 6*A*a^3*d^2*m^5*x*x^m*x^(2*n)*e^m + 285*B*a^2*b*c^2*m^4*n*x*x^m*x^(2*n)
*e^m + 285*A*a*b^2*c^2*m^4*n*x*x^m*x^(2*n)*e^m + 190*B*a^3*c*d*m^4*n*x*x^m*x^(2*n)*e^m + 570*A*a^2*b*c*d*m^4*n
*x*x^m*x^(2*n)*e^m + 95*A*a^3*d^2*m^4*n*x*x^m*x^(2*n)*e^m + 1644*B*a^2*b*c^2*m^3*n^2*x*x^m*x^(2*n)*e^m + 1644*
A*a*b^2*c^2*m^3*n^2*x*x^m*x^(2*n)*e^m + 1096*B*a^3*c*d*m^3*n^2*x*x^m*x^(2*n)*e^m + 3288*A*a^2*b*c*d*m^3*n^2*x*
x^m*x^(2*n)*e^m + 548*A*a^3*d^2*m^3*n^2*x*x^m*x^(2*n)*e^m + 4149*B*a^2*b*c^2*m^2*n^3*x*x^m*x^(2*n)*e^m + 4149*
A*a*b^2*c^2*m^2*n^3*x*x^m*x^(2*n)*e^m + 2766*B*a^3*c*d*m^2*n^3*x*x^m*x^(2*n)*e^m + 8298*A*a^2*b*c*d*m^2*n^3*x*
x^m*x^(2*n)*e^m + 1383*A*a^3*d^2*m^2*n^3*x*x^m*x^(2*n)*e^m + 4212*B*a^2*b*c^2*m*n^4*x*x^m*x^(2*n)*e^m + 4212*A
*a*b^2*c^2*m*n^4*x*x^m*x^(2*n)*e^m + 2808*B*a^3*c*d*m*n^4*x*x^m*x^(2*n)*e^m + 8424*A*a^2*b*c*d*m*n^4*x*x^m*x^(
2*n)*e^m + 1404*A*a^3*d^2*m*n^4*x*x^m*x^(2*n)*e^m + 1080*B*a^2*b*c^2*n^5*x*x^m*x^(2*n)*e^m + 1080*A*a*b^2*c^2*
n^5*x*x^m*x^(2*n)*e^m + 720*B*a^3*c*d*n^5*x*x^m*x^(2*n)*e^m + 2160*A*a^2*b*c*d*n^5*x*x^m*x^(2*n)*e^m + 360*A*a
^3*d^2*n^5*x*x^m*x^(2*n)*e^m + 6*B*a^3*c^2*m^5*x*x^m*x^n*e^m + 18*A*a^2*b*c^2*m^5*x*x^m*x^n*e^m + 12*A*a^3*c*d
*m^5*x*x^m*x^n*e^m + 100*B*a^3*c^2*m^4*n*x*x^m*x^n*e^m + 300*A*a^2*b*c^2*m^4*n*x*x^m*x^n*e^m + 200*A*a^3*c*d*m
^4*n*x*x^m*x^n*e^m + 620*B*a^3*c^2*m^3*n^2*x*x^m*x^n*e^m + 1860*A*a^2*b*c^2*m^3*n^2*x*x^m*x^n*e^m + 1240*A*a^3
*c*d*m^3*n^2*x*x^m*x^n*e^m + 1740*B*a^3*c^2*m^2*n^3*x*x^m*x^n*e^m + 5220*A*a^2*b*c^2*m^2*n^3*x*x^m*x^n*e^m + 3
480*A*a^3*c*d*m^2*n^3*x*x^m*x^n*e^m + 2088*B*a^3*c^2*m*n^4*x*x^m*x^n*e^m + 6264*A*a^2*b*c^2*m*n^4*x*x^m*x^n*e^
m + 4176*A*a^3*c*d*m*n^4*x*x^m*x^n*e^m + 720*B*a^3*c^2*n^5*x*x^m*x^n*e^m + 2160*A*a^2*b*c^2*n^5*x*x^m*x^n*e^m
+ 1440*A*a^3*c*d*n^5*x*x^m*x^n*e^m + 6*A*a^3*c^2*m^5*x*x^m*e^m + 105*A*a^3*c^2*m^4*n*x*x^m*e^m + 700*A*a^3*c^2
*m^3*n^2*x*x^m*e^m + 2205*A*a^3*c^2*m^2*n^3*x*x^m*e^m + 3248*A*a^3*c^2*m*n^4*x*x^m*e^m + 1764*A*a^3*c^2*n^5*x*
x^m*e^m + 15*B*b^3*d^2*m^4*x*x^m*x^(6*n)*e^m + 150*B*b^3*d^2*m^3*n*x*x^m*x^(6*n)*e^m + 510*B*b^3*d^2*m^2*n^2*x
*x^m*x^(6*n)*e^m + 675*B*b^3*d^2*m*n^3*x*x^m*x^(6*n)*e^m + 274*B*b^3*d^2*n^4*x*x^m*x^(6*n)*e^m + 30*B*b^3*c*d*
m^4*x*x^m*x^(5*n)*e^m + 45*B*a*b^2*d^2*m^4*x*x^m*x^(5*n)*e^m + 15*A*b^3*d^2*m^4*x*x^m*x^(5*n)*e^m + 320*B*b^3*
c*d*m^3*n*x*x^m*x^(5*n)*e^m + 480*B*a*b^2*d^2*m^3*n*x*x^m*x^(5*n)*e^m + 160*A*b^3*d^2*m^3*n*x*x^m*x^(5*n)*e^m
+ 1140*B*b^3*c*d*m^2*n^2*x*x^m*x^(5*n)*e^m + 1710*B*a*b^2*d^2*m^2*n^2*x*x^m*x^(5*n)*e^m + 570*A*b^3*d^2*m^2*n^
2*x*x^m*x^(5*n)*e^m + 1560*B*b^3*c*d*m*n^3*x*x^m*x^(5*n)*e^m + 2340*B*a*b^2*d^2*m*n^3*x*x^m*x^(5*n)*e^m + 780*
A*b^3*d^2*m*n^3*x*x^m*x^(5*n)*e^m + 648*B*b^3*c*d*n^4*x*x^m*x^(5*n)*e^m + 972*B*a*b^2*d^2*n^4*x*x^m*x^(5*n)*e^
m + 324*A*b^3*d^2*n^4*x*x^m*x^(5*n)*e^m + 15*B*b^3*c^2*m^4*x*x^m*x^(4*n)*e^m + 90*B*a*b^2*c*d*m^4*x*x^m*x^(4*n
)*e^m + 30*A*b^3*c*d*m^4*x*x^m*x^(4*n)*e^m + 45*B*a^2*b*d^2*m^4*x*x^m*x^(4*n)*e^m + 45*A*a*b^2*d^2*m^4*x*x^m*x
^(4*n)*e^m + 170*B*b^3*c^2*m^3*n*x*x^m*x^(4*n)*e^m + 1020*B*a*b^2*c*d*m^3*n*x*x^m*x^(4*n)*e^m + 340*A*b^3*c*d*
m^3*n*x*x^m*x^(4*n)*e^m + 510*B*a^2*b*d^2*m^3*n*x*x^m*x^(4*n)*e^m + 510*A*a*b^2*d^2*m^3*n*x*x^m*x^(4*n)*e^m +
642*B*b^3*c^2*m^2*n^2*x*x^m*x^(4*n)*e^m + 3852*B*a*b^2*c*d*m^2*n^2*x*x^m*x^(4*n)*e^m + 1284*A*b^3*c*d*m^2*n^2*
x*x^m*x^(4*n)*e^m + 1926*B*a^2*b*d^2*m^2*n^2*x*x^m*x^(4*n)*e^m + 1926*A*a*b^2*d^2*m^2*n^2*x*x^m*x^(4*n)*e^m +
921*B*b^3*c^2*m*n^3*x*x^m*x^(4*n)*e^m + 5526*B*a*b^2*c*d*m*n^3*x*x^m*x^(4*n)*e^m + 1842*A*b^3*c*d*m*n^3*x*x^m*
x^(4*n)*e^m + 2763*B*a^2*b*d^2*m*n^3*x*x^m*x^(4*n)*e^m + 2763*A*a*b^2*d^2*m*n^3*x*x^m*x^(4*n)*e^m + 396*B*b^3*
c^2*n^4*x*x^m*x^(4*n)*e^m + 2376*B*a*b^2*c*d*n^4*x*x^m*x^(4*n)*e^m + 792*A*b^3*c*d*n^4*x*x^m*x^(4*n)*e^m + 118
8*B*a^2*b*d^2*n^4*x*x^m*x^(4*n)*e^m + 1188*A*a*b^2*d^2*n^4*x*x^m*x^(4*n)*e^m + 45*B*a*b^2*c^2*m^4*x*x^m*x^(3*n
)*e^m + 15*A*b^3*c^2*m^4*x*x^m*x^(3*n)*e^m + 90*B*a^2*b*c*d*m^4*x*x^m*x^(3*n)*e^m + 90*A*a*b^2*c*d*m^4*x*x^m*x
^(3*n)*e^m + 15*B*a^3*d^2*m^4*x*x^m*x^(3*n)*e^m + 45*A*a^2*b*d^2*m^4*x*x^m*x^(3*n)*e^m + 540*B*a*b^2*c^2*m^3*n
*x*x^m*x^(3*n)*e^m + 180*A*b^3*c^2*m^3*n*x*x^m*x^(3*n)*e^m + 1080*B*a^2*b*c*d*m^3*n*x*x^m*x^(3*n)*e^m + 1080*A
*a*b^2*c*d*m^3*n*x*x^m*x^(3*n)*e^m + 180*B*a^3*d^2*m^3*n*x*x^m*x^(3*n)*e^m + 540*A*a^2*b*d^2*m^3*n*x*x^m*x^(3*
n)*e^m + 2178*B*a*b^2*c^2*m^2*n^2*x*x^m*x^(3*n)*e^m + 726*A*b^3*c^2*m^2*n^2*x*x^m*x^(3*n)*e^m + 4356*B*a^2*b*c
*d*m^2*n^2*x*x^m*x^(3*n)*e^m + 4356*A*a*b^2*c*d*m^2*n^2*x*x^m*x^(3*n)*e^m + 726*B*a^3*d^2*m^2*n^2*x*x^m*x^(3*n
)*e^m + 2178*A*a^2*b*d^2*m^2*n^2*x*x^m*x^(3*n)*e^m + 3348*B*a*b^2*c^2*m*n^3*x*x^m*x^(3*n)*e^m + 1116*A*b^3*c^2
*m*n^3*x*x^m*x^(3*n)*e^m + 6696*B*a^2*b*c*d*m*n^3*x*x^m*x^(3*n)*e^m + 6696*A*a*b^2*c*d*m*n^3*x*x^m*x^(3*n)*e^m
+ 1116*B*a^3*d^2*m*n^3*x*x^m*x^(3*n)*e^m + 3348*A*a^2*b*d^2*m*n^3*x*x^m*x^(3*n)*e^m + 1524*B*a*b^2*c^2*n^4*x*
x^m*x^(3*n)*e^m + 508*A*b^3*c^2*n^4*x*x^m*x^(3*n)*e^m + 3048*B*a^2*b*c*d*n^4*x*x^m*x^(3*n)*e^m + 3048*A*a*b^2*
c*d*n^4*x*x^m*x^(3*n)*e^m + 508*B*a^3*d^2*n^4*x*x^m*x^(3*n)*e^m + 1524*A*a^2*b*d^2*n^4*x*x^m*x^(3*n)*e^m + 45*
B*a^2*b*c^2*m^4*x*x^m*x^(2*n)*e^m + 45*A*a*b^2*c^2*m^4*x*x^m*x^(2*n)*e^m + 30*B*a^3*c*d*m^4*x*x^m*x^(2*n)*e^m
+ 90*A*a^2*b*c*d*m^4*x*x^m*x^(2*n)*e^m + 15*A*a^3*d^2*m^4*x*x^m*x^(2*n)*e^m + 570*B*a^2*b*c^2*m^3*n*x*x^m*x^(2
*n)*e^m + 570*A*a*b^2*c^2*m^3*n*x*x^m*x^(2*n)*e^m + 380*B*a^3*c*d*m^3*n*x*x^m*x^(2*n)*e^m + 1140*A*a^2*b*c*d*m
^3*n*x*x^m*x^(2*n)*e^m + 190*A*a^3*d^2*m^3*n*x*x^m*x^(2*n)*e^m + 2466*B*a^2*b*c^2*m^2*n^2*x*x^m*x^(2*n)*e^m +
2466*A*a*b^2*c^2*m^2*n^2*x*x^m*x^(2*n)*e^m + 1644*B*a^3*c*d*m^2*n^2*x*x^m*x^(2*n)*e^m + 4932*A*a^2*b*c*d*m^2*n
^2*x*x^m*x^(2*n)*e^m + 822*A*a^3*d^2*m^2*n^2*x*x^m*x^(2*n)*e^m + 4149*B*a^2*b*c^2*m*n^3*x*x^m*x^(2*n)*e^m + 41
49*A*a*b^2*c^2*m*n^3*x*x^m*x^(2*n)*e^m + 2766*B*a^3*c*d*m*n^3*x*x^m*x^(2*n)*e^m + 8298*A*a^2*b*c*d*m*n^3*x*x^m
*x^(2*n)*e^m + 1383*A*a^3*d^2*m*n^3*x*x^m*x^(2*n)*e^m + 2106*B*a^2*b*c^2*n^4*x*x^m*x^(2*n)*e^m + 2106*A*a*b^2*
c^2*n^4*x*x^m*x^(2*n)*e^m + 1404*B*a^3*c*d*n^4*x*x^m*x^(2*n)*e^m + 4212*A*a^2*b*c*d*n^4*x*x^m*x^(2*n)*e^m + 70
2*A*a^3*d^2*n^4*x*x^m*x^(2*n)*e^m + 15*B*a^3*c^2*m^4*x*x^m*x^n*e^m + 45*A*a^2*b*c^2*m^4*x*x^m*x^n*e^m + 30*A*a
^3*c*d*m^4*x*x^m*x^n*e^m + 200*B*a^3*c^2*m^3*n*x*x^m*x^n*e^m + 600*A*a^2*b*c^2*m^3*n*x*x^m*x^n*e^m + 400*A*a^3
*c*d*m^3*n*x*x^m*x^n*e^m + 930*B*a^3*c^2*m^2*n^2*x*x^m*x^n*e^m + 2790*A*a^2*b*c^2*m^2*n^2*x*x^m*x^n*e^m + 1860
*A*a^3*c*d*m^2*n^2*x*x^m*x^n*e^m + 1740*B*a^3*c^2*m*n^3*x*x^m*x^n*e^m + 5220*A*a^2*b*c^2*m*n^3*x*x^m*x^n*e^m +
3480*A*a^3*c*d*m*n^3*x*x^m*x^n*e^m + 1044*B*a^3*c^2*n^4*x*x^m*x^n*e^m + 3132*A*a^2*b*c^2*n^4*x*x^m*x^n*e^m +
2088*A*a^3*c*d*n^4*x*x^m*x^n*e^m + 15*A*a^3*c^2*m^4*x*x^m*e^m + 210*A*a^3*c^2*m^3*n*x*x^m*e^m + 1050*A*a^3*c^2
*m^2*n^2*x*x^m*e^m + 2205*A*a^3*c^2*m*n^3*x*x^m*e^m + 1624*A*a^3*c^2*n^4*x*x^m*e^m + 20*B*b^3*d^2*m^3*x*x^m*x^
(6*n)*e^m + 150*B*b^3*d^2*m^2*n*x*x^m*x^(6*n)*e^m + 340*B*b^3*d^2*m*n^2*x*x^m*x^(6*n)*e^m + 225*B*b^3*d^2*n^3*
x*x^m*x^(6*n)*e^m + 40*B*b^3*c*d*m^3*x*x^m*x^(5*n)*e^m + 60*B*a*b^2*d^2*m^3*x*x^m*x^(5*n)*e^m + 20*A*b^3*d^2*m
^3*x*x^m*x^(5*n)*e^m + 320*B*b^3*c*d*m^2*n*x*x^m*x^(5*n)*e^m + 480*B*a*b^2*d^2*m^2*n*x*x^m*x^(5*n)*e^m + 160*A
*b^3*d^2*m^2*n*x*x^m*x^(5*n)*e^m + 760*B*b^3*c*d*m*n^2*x*x^m*x^(5*n)*e^m + 1140*B*a*b^2*d^2*m*n^2*x*x^m*x^(5*n
)*e^m + 380*A*b^3*d^2*m*n^2*x*x^m*x^(5*n)*e^m + 520*B*b^3*c*d*n^3*x*x^m*x^(5*n)*e^m + 780*B*a*b^2*d^2*n^3*x*x^
m*x^(5*n)*e^m + 260*A*b^3*d^2*n^3*x*x^m*x^(5*n)*e^m + 20*B*b^3*c^2*m^3*x*x^m*x^(4*n)*e^m + 120*B*a*b^2*c*d*m^3
*x*x^m*x^(4*n)*e^m + 40*A*b^3*c*d*m^3*x*x^m*x^(4*n)*e^m + 60*B*a^2*b*d^2*m^3*x*x^m*x^(4*n)*e^m + 60*A*a*b^2*d^
2*m^3*x*x^m*x^(4*n)*e^m + 170*B*b^3*c^2*m^2*n*x*x^m*x^(4*n)*e^m + 1020*B*a*b^2*c*d*m^2*n*x*x^m*x^(4*n)*e^m + 3
40*A*b^3*c*d*m^2*n*x*x^m*x^(4*n)*e^m + 510*B*a^2*b*d^2*m^2*n*x*x^m*x^(4*n)*e^m + 510*A*a*b^2*d^2*m^2*n*x*x^m*x
^(4*n)*e^m + 428*B*b^3*c^2*m*n^2*x*x^m*x^(4*n)*e^m + 2568*B*a*b^2*c*d*m*n^2*x*x^m*x^(4*n)*e^m + 856*A*b^3*c*d*
m*n^2*x*x^m*x^(4*n)*e^m + 1284*B*a^2*b*d^2*m*n^2*x*x^m*x^(4*n)*e^m + 1284*A*a*b^2*d^2*m*n^2*x*x^m*x^(4*n)*e^m
+ 307*B*b^3*c^2*n^3*x*x^m*x^(4*n)*e^m + 1842*B*a*b^2*c*d*n^3*x*x^m*x^(4*n)*e^m + 614*A*b^3*c*d*n^3*x*x^m*x^(4*
n)*e^m + 921*B*a^2*b*d^2*n^3*x*x^m*x^(4*n)*e^m + 921*A*a*b^2*d^2*n^3*x*x^m*x^(4*n)*e^m + 60*B*a*b^2*c^2*m^3*x*
x^m*x^(3*n)*e^m + 20*A*b^3*c^2*m^3*x*x^m*x^(3*n)*e^m + 120*B*a^2*b*c*d*m^3*x*x^m*x^(3*n)*e^m + 120*A*a*b^2*c*d
*m^3*x*x^m*x^(3*n)*e^m + 20*B*a^3*d^2*m^3*x*x^m*x^(3*n)*e^m + 60*A*a^2*b*d^2*m^3*x*x^m*x^(3*n)*e^m + 540*B*a*b
^2*c^2*m^2*n*x*x^m*x^(3*n)*e^m + 180*A*b^3*c^2*m^2*n*x*x^m*x^(3*n)*e^m + 1080*B*a^2*b*c*d*m^2*n*x*x^m*x^(3*n)*
e^m + 1080*A*a*b^2*c*d*m^2*n*x*x^m*x^(3*n)*e^m + 180*B*a^3*d^2*m^2*n*x*x^m*x^(3*n)*e^m + 540*A*a^2*b*d^2*m^2*n
*x*x^m*x^(3*n)*e^m + 1452*B*a*b^2*c^2*m*n^2*x*x^m*x^(3*n)*e^m + 484*A*b^3*c^2*m*n^2*x*x^m*x^(3*n)*e^m + 2904*B
*a^2*b*c*d*m*n^2*x*x^m*x^(3*n)*e^m + 2904*A*a*b^2*c*d*m*n^2*x*x^m*x^(3*n)*e^m + 484*B*a^3*d^2*m*n^2*x*x^m*x^(3
*n)*e^m + 1452*A*a^2*b*d^2*m*n^2*x*x^m*x^(3*n)*e^m + 1116*B*a*b^2*c^2*n^3*x*x^m*x^(3*n)*e^m + 372*A*b^3*c^2*n^
3*x*x^m*x^(3*n)*e^m + 2232*B*a^2*b*c*d*n^3*x*x^m*x^(3*n)*e^m + 2232*A*a*b^2*c*d*n^3*x*x^m*x^(3*n)*e^m + 372*B*
a^3*d^2*n^3*x*x^m*x^(3*n)*e^m + 1116*A*a^2*b*d^2*n^3*x*x^m*x^(3*n)*e^m + 60*B*a^2*b*c^2*m^3*x*x^m*x^(2*n)*e^m
+ 60*A*a*b^2*c^2*m^3*x*x^m*x^(2*n)*e^m + 40*B*a^3*c*d*m^3*x*x^m*x^(2*n)*e^m + 120*A*a^2*b*c*d*m^3*x*x^m*x^(2*n
)*e^m + 20*A*a^3*d^2*m^3*x*x^m*x^(2*n)*e^m + 570*B*a^2*b*c^2*m^2*n*x*x^m*x^(2*n)*e^m + 570*A*a*b^2*c^2*m^2*n*x
*x^m*x^(2*n)*e^m + 380*B*a^3*c*d*m^2*n*x*x^m*x^(2*n)*e^m + 1140*A*a^2*b*c*d*m^2*n*x*x^m*x^(2*n)*e^m + 190*A*a^
3*d^2*m^2*n*x*x^m*x^(2*n)*e^m + 1644*B*a^2*b*c^2*m*n^2*x*x^m*x^(2*n)*e^m + 1644*A*a*b^2*c^2*m*n^2*x*x^m*x^(2*n
)*e^m + 1096*B*a^3*c*d*m*n^2*x*x^m*x^(2*n)*e^m + 3288*A*a^2*b*c*d*m*n^2*x*x^m*x^(2*n)*e^m + 548*A*a^3*d^2*m*n^
2*x*x^m*x^(2*n)*e^m + 1383*B*a^2*b*c^2*n^3*x*x^m*x^(2*n)*e^m + 1383*A*a*b^2*c^2*n^3*x*x^m*x^(2*n)*e^m + 922*B*
a^3*c*d*n^3*x*x^m*x^(2*n)*e^m + 2766*A*a^2*b*c*d*n^3*x*x^m*x^(2*n)*e^m + 461*A*a^3*d^2*n^3*x*x^m*x^(2*n)*e^m +
20*B*a^3*c^2*m^3*x*x^m*x^n*e^m + 60*A*a^2*b*c^2*m^3*x*x^m*x^n*e^m + 40*A*a^3*c*d*m^3*x*x^m*x^n*e^m + 200*B*a^
3*c^2*m^2*n*x*x^m*x^n*e^m + 600*A*a^2*b*c^2*m^2*n*x*x^m*x^n*e^m + 400*A*a^3*c*d*m^2*n*x*x^m*x^n*e^m + 620*B*a^
3*c^2*m*n^2*x*x^m*x^n*e^m + 1860*A*a^2*b*c^2*m*n^2*x*x^m*x^n*e^m + 1240*A*a^3*c*d*m*n^2*x*x^m*x^n*e^m + 580*B*
a^3*c^2*n^3*x*x^m*x^n*e^m + 1740*A*a^2*b*c^2*n^3*x*x^m*x^n*e^m + 1160*A*a^3*c*d*n^3*x*x^m*x^n*e^m + 20*A*a^3*c
^2*m^3*x*x^m*e^m + 210*A*a^3*c^2*m^2*n*x*x^m*e^m + 700*A*a^3*c^2*m*n^2*x*x^m*e^m + 735*A*a^3*c^2*n^3*x*x^m*e^m
+ 15*B*b^3*d^2*m^2*x*x^m*x^(6*n)*e^m + 75*B*b^3*d^2*m*n*x*x^m*x^(6*n)*e^m + 85*B*b^3*d^2*n^2*x*x^m*x^(6*n)*e^
m + 30*B*b^3*c*d*m^2*x*x^m*x^(5*n)*e^m + 45*B*a*b^2*d^2*m^2*x*x^m*x^(5*n)*e^m + 15*A*b^3*d^2*m^2*x*x^m*x^(5*n)
*e^m + 160*B*b^3*c*d*m*n*x*x^m*x^(5*n)*e^m + 240*B*a*b^2*d^2*m*n*x*x^m*x^(5*n)*e^m + 80*A*b^3*d^2*m*n*x*x^m*x^
(5*n)*e^m + 190*B*b^3*c*d*n^2*x*x^m*x^(5*n)*e^m + 285*B*a*b^2*d^2*n^2*x*x^m*x^(5*n)*e^m + 95*A*b^3*d^2*n^2*x*x
^m*x^(5*n)*e^m + 15*B*b^3*c^2*m^2*x*x^m*x^(4*n)*e^m + 90*B*a*b^2*c*d*m^2*x*x^m*x^(4*n)*e^m + 30*A*b^3*c*d*m^2*
x*x^m*x^(4*n)*e^m + 45*B*a^2*b*d^2*m^2*x*x^m*x^(4*n)*e^m + 45*A*a*b^2*d^2*m^2*x*x^m*x^(4*n)*e^m + 85*B*b^3*c^2
*m*n*x*x^m*x^(4*n)*e^m + 510*B*a*b^2*c*d*m*n*x*x^m*x^(4*n)*e^m + 170*A*b^3*c*d*m*n*x*x^m*x^(4*n)*e^m + 255*B*a
^2*b*d^2*m*n*x*x^m*x^(4*n)*e^m + 255*A*a*b^2*d^2*m*n*x*x^m*x^(4*n)*e^m + 107*B*b^3*c^2*n^2*x*x^m*x^(4*n)*e^m +
642*B*a*b^2*c*d*n^2*x*x^m*x^(4*n)*e^m + 214*A*b^3*c*d*n^2*x*x^m*x^(4*n)*e^m + 321*B*a^2*b*d^2*n^2*x*x^m*x^(4*
n)*e^m + 321*A*a*b^2*d^2*n^2*x*x^m*x^(4*n)*e^m + 45*B*a*b^2*c^2*m^2*x*x^m*x^(3*n)*e^m + 15*A*b^3*c^2*m^2*x*x^m
*x^(3*n)*e^m + 90*B*a^2*b*c*d*m^2*x*x^m*x^(3*n)*e^m + 90*A*a*b^2*c*d*m^2*x*x^m*x^(3*n)*e^m + 15*B*a^3*d^2*m^2*
x*x^m*x^(3*n)*e^m + 45*A*a^2*b*d^2*m^2*x*x^m*x^(3*n)*e^m + 270*B*a*b^2*c^2*m*n*x*x^m*x^(3*n)*e^m + 90*A*b^3*c^
2*m*n*x*x^m*x^(3*n)*e^m + 540*B*a^2*b*c*d*m*n*x*x^m*x^(3*n)*e^m + 540*A*a*b^2*c*d*m*n*x*x^m*x^(3*n)*e^m + 90*B
*a^3*d^2*m*n*x*x^m*x^(3*n)*e^m + 270*A*a^2*b*d^2*m*n*x*x^m*x^(3*n)*e^m + 363*B*a*b^2*c^2*n^2*x*x^m*x^(3*n)*e^m
+ 121*A*b^3*c^2*n^2*x*x^m*x^(3*n)*e^m + 726*B*a^2*b*c*d*n^2*x*x^m*x^(3*n)*e^m + 726*A*a*b^2*c*d*n^2*x*x^m*x^(
3*n)*e^m + 121*B*a^3*d^2*n^2*x*x^m*x^(3*n)*e^m + 363*A*a^2*b*d^2*n^2*x*x^m*x^(3*n)*e^m + 45*B*a^2*b*c^2*m^2*x*
x^m*x^(2*n)*e^m + 45*A*a*b^2*c^2*m^2*x*x^m*x^(2*n)*e^m + 30*B*a^3*c*d*m^2*x*x^m*x^(2*n)*e^m + 90*A*a^2*b*c*d*m
^2*x*x^m*x^(2*n)*e^m + 15*A*a^3*d^2*m^2*x*x^m*x^(2*n)*e^m + 285*B*a^2*b*c^2*m*n*x*x^m*x^(2*n)*e^m + 285*A*a*b^
2*c^2*m*n*x*x^m*x^(2*n)*e^m + 190*B*a^3*c*d*m*n*x*x^m*x^(2*n)*e^m + 570*A*a^2*b*c*d*m*n*x*x^m*x^(2*n)*e^m + 95
*A*a^3*d^2*m*n*x*x^m*x^(2*n)*e^m + 411*B*a^2*b*c^2*n^2*x*x^m*x^(2*n)*e^m + 411*A*a*b^2*c^2*n^2*x*x^m*x^(2*n)*e
^m + 274*B*a^3*c*d*n^2*x*x^m*x^(2*n)*e^m + 822*A*a^2*b*c*d*n^2*x*x^m*x^(2*n)*e^m + 137*A*a^3*d^2*n^2*x*x^m*x^(
2*n)*e^m + 15*B*a^3*c^2*m^2*x*x^m*x^n*e^m + 45*A*a^2*b*c^2*m^2*x*x^m*x^n*e^m + 30*A*a^3*c*d*m^2*x*x^m*x^n*e^m
+ 100*B*a^3*c^2*m*n*x*x^m*x^n*e^m + 300*A*a^2*b*c^2*m*n*x*x^m*x^n*e^m + 200*A*a^3*c*d*m*n*x*x^m*x^n*e^m + 155*
B*a^3*c^2*n^2*x*x^m*x^n*e^m + 465*A*a^2*b*c^2*n^2*x*x^m*x^n*e^m + 310*A*a^3*c*d*n^2*x*x^m*x^n*e^m + 15*A*a^3*c
^2*m^2*x*x^m*e^m + 105*A*a^3*c^2*m*n*x*x^m*e^m + 175*A*a^3*c^2*n^2*x*x^m*e^m + 6*B*b^3*d^2*m*x*x^m*x^(6*n)*e^m
+ 15*B*b^3*d^2*n*x*x^m*x^(6*n)*e^m + 12*B*b^3*c*d*m*x*x^m*x^(5*n)*e^m + 18*B*a*b^2*d^2*m*x*x^m*x^(5*n)*e^m +
6*A*b^3*d^2*m*x*x^m*x^(5*n)*e^m + 32*B*b^3*c*d*n*x*x^m*x^(5*n)*e^m + 48*B*a*b^2*d^2*n*x*x^m*x^(5*n)*e^m + 16*A
*b^3*d^2*n*x*x^m*x^(5*n)*e^m + 6*B*b^3*c^2*m*x*x^m*x^(4*n)*e^m + 36*B*a*b^2*c*d*m*x*x^m*x^(4*n)*e^m + 12*A*b^3
*c*d*m*x*x^m*x^(4*n)*e^m + 18*B*a^2*b*d^2*m*x*x^m*x^(4*n)*e^m + 18*A*a*b^2*d^2*m*x*x^m*x^(4*n)*e^m + 17*B*b^3*
c^2*n*x*x^m*x^(4*n)*e^m + 102*B*a*b^2*c*d*n*x*x^m*x^(4*n)*e^m + 34*A*b^3*c*d*n*x*x^m*x^(4*n)*e^m + 51*B*a^2*b*
d^2*n*x*x^m*x^(4*n)*e^m + 51*A*a*b^2*d^2*n*x*x^m*x^(4*n)*e^m + 18*B*a*b^2*c^2*m*x*x^m*x^(3*n)*e^m + 6*A*b^3*c^
2*m*x*x^m*x^(3*n)*e^m + 36*B*a^2*b*c*d*m*x*x^m*x^(3*n)*e^m + 36*A*a*b^2*c*d*m*x*x^m*x^(3*n)*e^m + 6*B*a^3*d^2*
m*x*x^m*x^(3*n)*e^m + 18*A*a^2*b*d^2*m*x*x^m*x^(3*n)*e^m + 54*B*a*b^2*c^2*n*x*x^m*x^(3*n)*e^m + 18*A*b^3*c^2*n
*x*x^m*x^(3*n)*e^m + 108*B*a^2*b*c*d*n*x*x^m*x^(3*n)*e^m + 108*A*a*b^2*c*d*n*x*x^m*x^(3*n)*e^m + 18*B*a^3*d^2*
n*x*x^m*x^(3*n)*e^m + 54*A*a^2*b*d^2*n*x*x^m*x^(3*n)*e^m + 18*B*a^2*b*c^2*m*x*x^m*x^(2*n)*e^m + 18*A*a*b^2*c^2
*m*x*x^m*x^(2*n)*e^m + 12*B*a^3*c*d*m*x*x^m*x^(2*n)*e^m + 36*A*a^2*b*c*d*m*x*x^m*x^(2*n)*e^m + 6*A*a^3*d^2*m*x
*x^m*x^(2*n)*e^m + 57*B*a^2*b*c^2*n*x*x^m*x^(2*n)*e^m + 57*A*a*b^2*c^2*n*x*x^m*x^(2*n)*e^m + 38*B*a^3*c*d*n*x*
x^m*x^(2*n)*e^m + 114*A*a^2*b*c*d*n*x*x^m*x^(2*n)*e^m + 19*A*a^3*d^2*n*x*x^m*x^(2*n)*e^m + 6*B*a^3*c^2*m*x*x^m
*x^n*e^m + 18*A*a^2*b*c^2*m*x*x^m*x^n*e^m + 12*A*a^3*c*d*m*x*x^m*x^n*e^m + 20*B*a^3*c^2*n*x*x^m*x^n*e^m + 60*A
*a^2*b*c^2*n*x*x^m*x^n*e^m + 40*A*a^3*c*d*n*x*x^m*x^n*e^m + 6*A*a^3*c^2*m*x*x^m*e^m + 21*A*a^3*c^2*n*x*x^m*e^m
+ B*b^3*d^2*x*x^m*x^(6*n)*e^m + 2*B*b^3*c*d*x*x^m*x^(5*n)*e^m + 3*B*a*b^2*d^2*x*x^m*x^(5*n)*e^m + A*b^3*d^2*x
*x^m*x^(5*n)*e^m + B*b^3*c^2*x*x^m*x^(4*n)*e^m + 6*B*a*b^2*c*d*x*x^m*x^(4*n)*e^m + 2*A*b^3*c*d*x*x^m*x^(4*n)*e
^m + 3*B*a^2*b*d^2*x*x^m*x^(4*n)*e^m + 3*A*a*b^2*d^2*x*x^m*x^(4*n)*e^m + 3*B*a*b^2*c^2*x*x^m*x^(3*n)*e^m + A*b
^3*c^2*x*x^m*x^(3*n)*e^m + 6*B*a^2*b*c*d*x*x^m*x^(3*n)*e^m + 6*A*a*b^2*c*d*x*x^m*x^(3*n)*e^m + B*a^3*d^2*x*x^m
*x^(3*n)*e^m + 3*A*a^2*b*d^2*x*x^m*x^(3*n)*e^m + 3*B*a^2*b*c^2*x*x^m*x^(2*n)*e^m + 3*A*a*b^2*c^2*x*x^m*x^(2*n)
*e^m + 2*B*a^3*c*d*x*x^m*x^(2*n)*e^m + 6*A*a^2*b*c*d*x*x^m*x^(2*n)*e^m + A*a^3*d^2*x*x^m*x^(2*n)*e^m + B*a^3*c
^2*x*x^m*x^n*e^m + 3*A*a^2*b*c^2*x*x^m*x^n*e^m + 2*A*a^3*c*d*x*x^m*x^n*e^m + A*a^3*c^2*x*x^m*e^m)/(m^7 + 21*m^
6*n + 175*m^5*n^2 + 735*m^4*n^3 + 1624*m^3*n^4 + 1764*m^2*n^5 + 720*m*n^6 + 7*m^6 + 126*m^5*n + 875*m^4*n^2 +
2940*m^3*n^3 + 4872*m^2*n^4 + 3528*m*n^5 + 720*n^6 + 21*m^5 + 315*m^4*n + 1750*m^3*n^2 + 4410*m^2*n^3 + 4872*m
*n^4 + 1764*n^5 + 35*m^4 + 420*m^3*n + 1750*m^2*n^2 + 2940*m*n^3 + 1624*n^4 + 35*m^3 + 315*m^2*n + 875*m*n^2 +
735*n^3 + 21*m^2 + 126*m*n + 175*n^2 + 7*m + 21*n + 1)