3.1082 \(\int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx\)

Optimal. Leaf size=290 \[ \frac{e^5 (a+b x)^{17} (-7 a B e+A b e+6 b B d)}{17 b^8}+\frac{3 e^4 (a+b x)^{16} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{16 b^8}+\frac{e^3 (a+b x)^{15} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{3 b^8}+\frac{5 e^2 (a+b x)^{14} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{14 b^8}+\frac{3 e (a+b x)^{13} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{13 b^8}+\frac{(a+b x)^{12} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{12 b^8}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^6}{11 b^8}+\frac{B e^6 (a+b x)^{18}}{18 b^8} \]

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^11)/(11*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^12)/(
12*b^8) + (3*e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (5*e^2*(b*d - a*e)^3*(3*b*
B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^14)/(14*b^8) + (e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^1
5)/(3*b^8) + (3*e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^16)/(16*b^8) + (e^5*(6*b*B*d + A*b*e -
7*a*B*e)*(a + b*x)^17)/(17*b^8) + (B*e^6*(a + b*x)^18)/(18*b^8)

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Rubi [A]  time = 1.72227, antiderivative size = 290, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{e^5 (a+b x)^{17} (-7 a B e+A b e+6 b B d)}{17 b^8}+\frac{3 e^4 (a+b x)^{16} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{16 b^8}+\frac{e^3 (a+b x)^{15} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{3 b^8}+\frac{5 e^2 (a+b x)^{14} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{14 b^8}+\frac{3 e (a+b x)^{13} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{13 b^8}+\frac{(a+b x)^{12} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{12 b^8}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^6}{11 b^8}+\frac{B e^6 (a+b x)^{18}}{18 b^8} \]

Antiderivative was successfully verified.

[In]

Int[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^11)/(11*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^12)/(
12*b^8) + (3*e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (5*e^2*(b*d - a*e)^3*(3*b*
B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^14)/(14*b^8) + (e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^1
5)/(3*b^8) + (3*e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^16)/(16*b^8) + (e^5*(6*b*B*d + A*b*e -
7*a*B*e)*(a + b*x)^17)/(17*b^8) + (B*e^6*(a + b*x)^18)/(18*b^8)

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx &=\int \left (\frac{(A b-a B) (b d-a e)^6 (a+b x)^{10}}{b^7}+\frac{(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{11}}{b^7}+\frac{3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{12}}{b^7}+\frac{5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{13}}{b^7}+\frac{5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{14}}{b^7}+\frac{3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{15}}{b^7}+\frac{e^5 (6 b B d+A b e-7 a B e) (a+b x)^{16}}{b^7}+\frac{B e^6 (a+b x)^{17}}{b^7}\right ) \, dx\\ &=\frac{(A b-a B) (b d-a e)^6 (a+b x)^{11}}{11 b^8}+\frac{(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{12}}{12 b^8}+\frac{3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac{5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{14}}{14 b^8}+\frac{e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{15}}{3 b^8}+\frac{3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{16}}{16 b^8}+\frac{e^5 (6 b B d+A b e-7 a B e) (a+b x)^{17}}{17 b^8}+\frac{B e^6 (a+b x)^{18}}{18 b^8}\\ \end{align*}

Mathematica [B]  time = 0.600388, size = 1788, normalized size = 6.17 \[ \text{result too large to display} \]

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]

[Out]

a^10*A*d^6*x + (a^9*d^5*(10*A*b*d + a*B*d + 6*a*A*e)*x^2)/2 + (a^8*d^4*(2*a*B*d*(5*b*d + 3*a*e) + 15*A*(3*b^2*
d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + (5*a^7*d^3*(3*a*B*d*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + A*(24*b^3*d^3 + 5
4*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + a^6*d^2*(2*a*B*d*(12*b^3*d^3 + 27*a*b^2*d^2*e + 15*a^2*b
*d*e^2 + 2*a^3*e^3) + A*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4))*x^5
+ (a^5*d*(5*a*B*d*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4) + 6*A*(42
*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + (
a^4*(6*a*B*d*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*
e^5) + A*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 +
60*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + (a^3*(10*A*b*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^
3*b^3*d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6) + a*B*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a
^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 + a^6*e^6))*x^8)/8 + (5*a^2*b*(9*
A*b*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5
+ a^6*e^6) + 2*a*B*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 180*a^4*b^2*d^
2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6))*x^9)/9 + (a*b^2*(9*a*B*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112
*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5 + a^6*e^6) + 2*A*b*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*
b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 12*a^6*e^6))*x^10)/2 + (b^3*(10*a*
B*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^
5 + 12*a^6*e^6) + A*b*(b^6*d^6 + 60*a*b^5*d^5*e + 675*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 3150*a^4*b^2*d^
2*e^4 + 1512*a^5*b*d*e^5 + 210*a^6*e^6))*x^11)/11 + (b^4*(210*a^6*B*e^6 + 252*a^5*b*e^5*(6*B*d + A*e) + 630*a^
4*b^2*d*e^4*(5*B*d + 2*A*e) + 600*a^3*b^3*d^2*e^3*(4*B*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(3*B*d + 4*A*e) + 30*a
*b^5*d^4*e*(2*B*d + 5*A*e) + b^6*d^5*(B*d + 6*A*e))*x^12)/12 + (b^5*e*(252*a^5*B*e^5 + 210*a^4*b*e^4*(6*B*d +
A*e) + 360*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 225*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 50*a*b^4*d^3*e*(3*B*d + 4*A*e
) + 3*b^5*d^4*(2*B*d + 5*A*e))*x^13)/13 + (5*b^6*e^2*(42*a^4*B*e^4 + 24*a^3*b*e^3*(6*B*d + A*e) + 27*a^2*b^2*d
*e^2*(5*B*d + 2*A*e) + 10*a*b^3*d^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^14)/14 + (b^7*e^3*(24*a^3*B
*e^3 + 9*a^2*b*e^2*(6*B*d + A*e) + 6*a*b^2*d*e*(5*B*d + 2*A*e) + b^3*d^2*(4*B*d + 3*A*e))*x^15)/3 + (b^8*e^4*(
45*a^2*B*e^2 + 10*a*b*e*(6*B*d + A*e) + 3*b^2*d*(5*B*d + 2*A*e))*x^16)/16 + (b^9*e^5*(6*b*B*d + A*b*e + 10*a*B
*e)*x^17)/17 + (b^10*B*e^6*x^18)/18

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Maple [B]  time = 0.003, size = 1905, normalized size = 6.6 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)*(e*x+d)^6,x)

[Out]

1/18*b^10*B*e^6*x^18+1/17*((A*b^10+10*B*a*b^9)*e^6+6*b^10*B*d*e^5)*x^17+1/16*((10*A*a*b^9+45*B*a^2*b^8)*e^6+6*
(A*b^10+10*B*a*b^9)*d*e^5+15*b^10*B*d^2*e^4)*x^16+1/15*((45*A*a^2*b^8+120*B*a^3*b^7)*e^6+6*(10*A*a*b^9+45*B*a^
2*b^8)*d*e^5+15*(A*b^10+10*B*a*b^9)*d^2*e^4+20*b^10*B*d^3*e^3)*x^15+1/14*((120*A*a^3*b^7+210*B*a^4*b^6)*e^6+6*
(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^5+15*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^4+20*(A*b^10+10*B*a*b^9)*d^3*e^3+15*b^10
*B*d^4*e^2)*x^14+1/13*((210*A*a^4*b^6+252*B*a^5*b^5)*e^6+6*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^5+15*(45*A*a^2*b^
8+120*B*a^3*b^7)*d^2*e^4+20*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^3+15*(A*b^10+10*B*a*b^9)*d^4*e^2+6*b^10*B*d^5*e)*x
^13+1/12*((252*A*a^5*b^5+210*B*a^6*b^4)*e^6+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^5+15*(120*A*a^3*b^7+210*B*a^4*
b^6)*d^2*e^4+20*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^3+15*(10*A*a*b^9+45*B*a^2*b^8)*d^4*e^2+6*(A*b^10+10*B*a*b^9
)*d^5*e+b^10*B*d^6)*x^12+1/11*((210*A*a^6*b^4+120*B*a^7*b^3)*e^6+6*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^5+15*(210
*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^4+20*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*e^3+15*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4
*e^2+6*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e+(A*b^10+10*B*a*b^9)*d^6)*x^11+1/10*((120*A*a^7*b^3+45*B*a^8*b^2)*e^6+6*
(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^5+15*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^4+20*(210*A*a^4*b^6+252*B*a^5*b^5)*
d^3*e^3+15*(120*A*a^3*b^7+210*B*a^4*b^6)*d^4*e^2+6*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e+(10*A*a*b^9+45*B*a^2*b^8
)*d^6)*x^10+1/9*((45*A*a^8*b^2+10*B*a^9*b)*e^6+6*(120*A*a^7*b^3+45*B*a^8*b^2)*d*e^5+15*(210*A*a^6*b^4+120*B*a^
7*b^3)*d^2*e^4+20*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^3+15*(210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^2+6*(120*A*a^3*
b^7+210*B*a^4*b^6)*d^5*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^6)*x^9+1/8*((10*A*a^9*b+B*a^10)*e^6+6*(45*A*a^8*b^2+10
*B*a^9*b)*d*e^5+15*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^4+20*(210*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^3+15*(252*A*a^5
*b^5+210*B*a^6*b^4)*d^4*e^2+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^6)*x^8+1/7*(
a^10*A*e^6+6*(10*A*a^9*b+B*a^10)*d*e^5+15*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^4+20*(120*A*a^7*b^3+45*B*a^8*b^2)*d^
3*e^3+15*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^2+6*(252*A*a^5*b^5+210*B*a^6*b^4)*d^5*e+(210*A*a^4*b^6+252*B*a^5*
b^5)*d^6)*x^7+1/6*(6*a^10*A*d*e^5+15*(10*A*a^9*b+B*a^10)*d^2*e^4+20*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e^3+15*(120*
A*a^7*b^3+45*B*a^8*b^2)*d^4*e^2+6*(210*A*a^6*b^4+120*B*a^7*b^3)*d^5*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^6)*x^6+1
/5*(15*a^10*A*d^2*e^4+20*(10*A*a^9*b+B*a^10)*d^3*e^3+15*(45*A*a^8*b^2+10*B*a^9*b)*d^4*e^2+6*(120*A*a^7*b^3+45*
B*a^8*b^2)*d^5*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^6)*x^5+1/4*(20*a^10*A*d^3*e^3+15*(10*A*a^9*b+B*a^10)*d^4*e^2+
6*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e+(120*A*a^7*b^3+45*B*a^8*b^2)*d^6)*x^4+1/3*(15*a^10*A*d^4*e^2+6*(10*A*a^9*b+B
*a^10)*d^5*e+(45*A*a^8*b^2+10*B*a^9*b)*d^6)*x^3+1/2*(6*a^10*A*d^5*e+(10*A*a^9*b+B*a^10)*d^6)*x^2+a^10*A*d^6*x

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Maxima [B]  time = 1.15929, size = 2588, normalized size = 8.92 \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)^10*(B*x+A)*(e*x+d)^6,x, algorithm="maxima")

[Out]

1/18*B*b^10*e^6*x^18 + A*a^10*d^6*x + 1/17*(6*B*b^10*d*e^5 + (10*B*a*b^9 + A*b^10)*e^6)*x^17 + 1/16*(15*B*b^10
*d^2*e^4 + 6*(10*B*a*b^9 + A*b^10)*d*e^5 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^6)*x^16 + 1/3*(4*B*b^10*d^3*e^3 + 3*(
10*B*a*b^9 + A*b^10)*d^2*e^4 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^5 + 3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^6)*x^15 + 5
/14*(3*B*b^10*d^4*e^2 + 4*(10*B*a*b^9 + A*b^10)*d^3*e^3 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^4 + 18*(8*B*a^3*b
^7 + 3*A*a^2*b^8)*d*e^5 + 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^6)*x^14 + 1/13*(6*B*b^10*d^5*e + 15*(10*B*a*b^9 + A*
b^10)*d^4*e^2 + 100*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^3 + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^4 + 180*(7*B*a^4
*b^6 + 4*A*a^3*b^7)*d*e^5 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^6)*x^13 + 1/12*(B*b^10*d^6 + 6*(10*B*a*b^9 + A*b^
10)*d^5*e + 75*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^2 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^3 + 450*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^2*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^6)*x^12 + 1/
11*((10*B*a*b^9 + A*b^10)*d^6 + 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^2 +
600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^3 + 630*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^4 + 252*(5*B*a^6*b^4 + 6*A*a^
5*b^5)*d*e^5 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^6)*x^11 + 1/2*((9*B*a^2*b^8 + 2*A*a*b^9)*d^6 + 18*(8*B*a^3*b^7
+ 3*A*a^2*b^8)*d^5*e + 90*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^2 + 168*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^3 + 126
*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^4 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^5 + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^
6)*x^10 + 5/9*(3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6 + 36*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e + 126*(6*B*a^5*b^5 + 5
*A*a^4*b^6)*d^4*e^2 + 168*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^3 + 90*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^4 + 18*(3
*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^5 + (2*B*a^9*b + 9*A*a^8*b^2)*e^6)*x^9 + 1/8*(30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6
+ 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e + 630*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^2 + 600*(4*B*a^7*b^3 + 7*A*a^
6*b^4)*d^3*e^3 + 225*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^4 + 30*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^5 + (B*a^10 + 10*A
*a^9*b)*e^6)*x^8 + 1/7*(A*a^10*e^6 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6 + 252*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*
e + 450*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^2 + 300*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^3 + 75*(2*B*a^9*b + 9*A*a^
8*b^2)*d^2*e^4 + 6*(B*a^10 + 10*A*a^9*b)*d*e^5)*x^7 + 1/6*(6*A*a^10*d*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6
+ 180*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^5*e + 225*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*e^2 + 100*(2*B*a^9*b + 9*A*a^8*
b^2)*d^3*e^3 + 15*(B*a^10 + 10*A*a^9*b)*d^2*e^4)*x^6 + (3*A*a^10*d^2*e^4 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6 +
18*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*e + 15*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*e^2 + 4*(B*a^10 + 10*A*a^9*b)*d^3*e^3
)*x^5 + 5/4*(4*A*a^10*d^3*e^3 + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6 + 6*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*e + 3*(B*a
^10 + 10*A*a^9*b)*d^4*e^2)*x^4 + 1/3*(15*A*a^10*d^4*e^2 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^6 + 6*(B*a^10 + 10*A*a
^9*b)*d^5*e)*x^3 + 1/2*(6*A*a^10*d^5*e + (B*a^10 + 10*A*a^9*b)*d^6)*x^2

________________________________________________________________________________________

Fricas [B]  time = 1.65495, size = 5485, normalized size = 18.91 \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)^10*(B*x+A)*(e*x+d)^6,x, algorithm="fricas")

[Out]

1/18*x^18*e^6*b^10*B + 6/17*x^17*e^5*d*b^10*B + 10/17*x^17*e^6*b^9*a*B + 1/17*x^17*e^6*b^10*A + 15/16*x^16*e^4
*d^2*b^10*B + 15/4*x^16*e^5*d*b^9*a*B + 45/16*x^16*e^6*b^8*a^2*B + 3/8*x^16*e^5*d*b^10*A + 5/8*x^16*e^6*b^9*a*
A + 4/3*x^15*e^3*d^3*b^10*B + 10*x^15*e^4*d^2*b^9*a*B + 18*x^15*e^5*d*b^8*a^2*B + 8*x^15*e^6*b^7*a^3*B + x^15*
e^4*d^2*b^10*A + 4*x^15*e^5*d*b^9*a*A + 3*x^15*e^6*b^8*a^2*A + 15/14*x^14*e^2*d^4*b^10*B + 100/7*x^14*e^3*d^3*
b^9*a*B + 675/14*x^14*e^4*d^2*b^8*a^2*B + 360/7*x^14*e^5*d*b^7*a^3*B + 15*x^14*e^6*b^6*a^4*B + 10/7*x^14*e^3*d
^3*b^10*A + 75/7*x^14*e^4*d^2*b^9*a*A + 135/7*x^14*e^5*d*b^8*a^2*A + 60/7*x^14*e^6*b^7*a^3*A + 6/13*x^13*e*d^5
*b^10*B + 150/13*x^13*e^2*d^4*b^9*a*B + 900/13*x^13*e^3*d^3*b^8*a^2*B + 1800/13*x^13*e^4*d^2*b^7*a^3*B + 1260/
13*x^13*e^5*d*b^6*a^4*B + 252/13*x^13*e^6*b^5*a^5*B + 15/13*x^13*e^2*d^4*b^10*A + 200/13*x^13*e^3*d^3*b^9*a*A
+ 675/13*x^13*e^4*d^2*b^8*a^2*A + 720/13*x^13*e^5*d*b^7*a^3*A + 210/13*x^13*e^6*b^6*a^4*A + 1/12*x^12*d^6*b^10
*B + 5*x^12*e*d^5*b^9*a*B + 225/4*x^12*e^2*d^4*b^8*a^2*B + 200*x^12*e^3*d^3*b^7*a^3*B + 525/2*x^12*e^4*d^2*b^6
*a^4*B + 126*x^12*e^5*d*b^5*a^5*B + 35/2*x^12*e^6*b^4*a^6*B + 1/2*x^12*e*d^5*b^10*A + 25/2*x^12*e^2*d^4*b^9*a*
A + 75*x^12*e^3*d^3*b^8*a^2*A + 150*x^12*e^4*d^2*b^7*a^3*A + 105*x^12*e^5*d*b^6*a^4*A + 21*x^12*e^6*b^5*a^5*A
+ 10/11*x^11*d^6*b^9*a*B + 270/11*x^11*e*d^5*b^8*a^2*B + 1800/11*x^11*e^2*d^4*b^7*a^3*B + 4200/11*x^11*e^3*d^3
*b^6*a^4*B + 3780/11*x^11*e^4*d^2*b^5*a^5*B + 1260/11*x^11*e^5*d*b^4*a^6*B + 120/11*x^11*e^6*b^3*a^7*B + 1/11*
x^11*d^6*b^10*A + 60/11*x^11*e*d^5*b^9*a*A + 675/11*x^11*e^2*d^4*b^8*a^2*A + 2400/11*x^11*e^3*d^3*b^7*a^3*A +
3150/11*x^11*e^4*d^2*b^6*a^4*A + 1512/11*x^11*e^5*d*b^5*a^5*A + 210/11*x^11*e^6*b^4*a^6*A + 9/2*x^10*d^6*b^8*a
^2*B + 72*x^10*e*d^5*b^7*a^3*B + 315*x^10*e^2*d^4*b^6*a^4*B + 504*x^10*e^3*d^3*b^5*a^5*B + 315*x^10*e^4*d^2*b^
4*a^6*B + 72*x^10*e^5*d*b^3*a^7*B + 9/2*x^10*e^6*b^2*a^8*B + x^10*d^6*b^9*a*A + 27*x^10*e*d^5*b^8*a^2*A + 180*
x^10*e^2*d^4*b^7*a^3*A + 420*x^10*e^3*d^3*b^6*a^4*A + 378*x^10*e^4*d^2*b^5*a^5*A + 126*x^10*e^5*d*b^4*a^6*A +
12*x^10*e^6*b^3*a^7*A + 40/3*x^9*d^6*b^7*a^3*B + 140*x^9*e*d^5*b^6*a^4*B + 420*x^9*e^2*d^4*b^5*a^5*B + 1400/3*
x^9*e^3*d^3*b^4*a^6*B + 200*x^9*e^4*d^2*b^3*a^7*B + 30*x^9*e^5*d*b^2*a^8*B + 10/9*x^9*e^6*b*a^9*B + 5*x^9*d^6*
b^8*a^2*A + 80*x^9*e*d^5*b^7*a^3*A + 350*x^9*e^2*d^4*b^6*a^4*A + 560*x^9*e^3*d^3*b^5*a^5*A + 350*x^9*e^4*d^2*b
^4*a^6*A + 80*x^9*e^5*d*b^3*a^7*A + 5*x^9*e^6*b^2*a^8*A + 105/4*x^8*d^6*b^6*a^4*B + 189*x^8*e*d^5*b^5*a^5*B +
1575/4*x^8*e^2*d^4*b^4*a^6*B + 300*x^8*e^3*d^3*b^3*a^7*B + 675/8*x^8*e^4*d^2*b^2*a^8*B + 15/2*x^8*e^5*d*b*a^9*
B + 1/8*x^8*e^6*a^10*B + 15*x^8*d^6*b^7*a^3*A + 315/2*x^8*e*d^5*b^6*a^4*A + 945/2*x^8*e^2*d^4*b^5*a^5*A + 525*
x^8*e^3*d^3*b^4*a^6*A + 225*x^8*e^4*d^2*b^3*a^7*A + 135/4*x^8*e^5*d*b^2*a^8*A + 5/4*x^8*e^6*b*a^9*A + 36*x^7*d
^6*b^5*a^5*B + 180*x^7*e*d^5*b^4*a^6*B + 1800/7*x^7*e^2*d^4*b^3*a^7*B + 900/7*x^7*e^3*d^3*b^2*a^8*B + 150/7*x^
7*e^4*d^2*b*a^9*B + 6/7*x^7*e^5*d*a^10*B + 30*x^7*d^6*b^6*a^4*A + 216*x^7*e*d^5*b^5*a^5*A + 450*x^7*e^2*d^4*b^
4*a^6*A + 2400/7*x^7*e^3*d^3*b^3*a^7*A + 675/7*x^7*e^4*d^2*b^2*a^8*A + 60/7*x^7*e^5*d*b*a^9*A + 1/7*x^7*e^6*a^
10*A + 35*x^6*d^6*b^4*a^6*B + 120*x^6*e*d^5*b^3*a^7*B + 225/2*x^6*e^2*d^4*b^2*a^8*B + 100/3*x^6*e^3*d^3*b*a^9*
B + 5/2*x^6*e^4*d^2*a^10*B + 42*x^6*d^6*b^5*a^5*A + 210*x^6*e*d^5*b^4*a^6*A + 300*x^6*e^2*d^4*b^3*a^7*A + 150*
x^6*e^3*d^3*b^2*a^8*A + 25*x^6*e^4*d^2*b*a^9*A + x^6*e^5*d*a^10*A + 24*x^5*d^6*b^3*a^7*B + 54*x^5*e*d^5*b^2*a^
8*B + 30*x^5*e^2*d^4*b*a^9*B + 4*x^5*e^3*d^3*a^10*B + 42*x^5*d^6*b^4*a^6*A + 144*x^5*e*d^5*b^3*a^7*A + 135*x^5
*e^2*d^4*b^2*a^8*A + 40*x^5*e^3*d^3*b*a^9*A + 3*x^5*e^4*d^2*a^10*A + 45/4*x^4*d^6*b^2*a^8*B + 15*x^4*e*d^5*b*a
^9*B + 15/4*x^4*e^2*d^4*a^10*B + 30*x^4*d^6*b^3*a^7*A + 135/2*x^4*e*d^5*b^2*a^8*A + 75/2*x^4*e^2*d^4*b*a^9*A +
5*x^4*e^3*d^3*a^10*A + 10/3*x^3*d^6*b*a^9*B + 2*x^3*e*d^5*a^10*B + 15*x^3*d^6*b^2*a^8*A + 20*x^3*e*d^5*b*a^9*
A + 5*x^3*e^2*d^4*a^10*A + 1/2*x^2*d^6*a^10*B + 5*x^2*d^6*b*a^9*A + 3*x^2*e*d^5*a^10*A + x*d^6*a^10*A

________________________________________________________________________________________

Sympy [B]  time = 0.31106, size = 2424, normalized size = 8.36 \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)**10*(B*x+A)*(e*x+d)**6,x)

[Out]

A*a**10*d**6*x + B*b**10*e**6*x**18/18 + x**17*(A*b**10*e**6/17 + 10*B*a*b**9*e**6/17 + 6*B*b**10*d*e**5/17) +
x**16*(5*A*a*b**9*e**6/8 + 3*A*b**10*d*e**5/8 + 45*B*a**2*b**8*e**6/16 + 15*B*a*b**9*d*e**5/4 + 15*B*b**10*d*
*2*e**4/16) + x**15*(3*A*a**2*b**8*e**6 + 4*A*a*b**9*d*e**5 + A*b**10*d**2*e**4 + 8*B*a**3*b**7*e**6 + 18*B*a*
*2*b**8*d*e**5 + 10*B*a*b**9*d**2*e**4 + 4*B*b**10*d**3*e**3/3) + x**14*(60*A*a**3*b**7*e**6/7 + 135*A*a**2*b*
*8*d*e**5/7 + 75*A*a*b**9*d**2*e**4/7 + 10*A*b**10*d**3*e**3/7 + 15*B*a**4*b**6*e**6 + 360*B*a**3*b**7*d*e**5/
7 + 675*B*a**2*b**8*d**2*e**4/14 + 100*B*a*b**9*d**3*e**3/7 + 15*B*b**10*d**4*e**2/14) + x**13*(210*A*a**4*b**
6*e**6/13 + 720*A*a**3*b**7*d*e**5/13 + 675*A*a**2*b**8*d**2*e**4/13 + 200*A*a*b**9*d**3*e**3/13 + 15*A*b**10*
d**4*e**2/13 + 252*B*a**5*b**5*e**6/13 + 1260*B*a**4*b**6*d*e**5/13 + 1800*B*a**3*b**7*d**2*e**4/13 + 900*B*a*
*2*b**8*d**3*e**3/13 + 150*B*a*b**9*d**4*e**2/13 + 6*B*b**10*d**5*e/13) + x**12*(21*A*a**5*b**5*e**6 + 105*A*a
**4*b**6*d*e**5 + 150*A*a**3*b**7*d**2*e**4 + 75*A*a**2*b**8*d**3*e**3 + 25*A*a*b**9*d**4*e**2/2 + A*b**10*d**
5*e/2 + 35*B*a**6*b**4*e**6/2 + 126*B*a**5*b**5*d*e**5 + 525*B*a**4*b**6*d**2*e**4/2 + 200*B*a**3*b**7*d**3*e*
*3 + 225*B*a**2*b**8*d**4*e**2/4 + 5*B*a*b**9*d**5*e + B*b**10*d**6/12) + x**11*(210*A*a**6*b**4*e**6/11 + 151
2*A*a**5*b**5*d*e**5/11 + 3150*A*a**4*b**6*d**2*e**4/11 + 2400*A*a**3*b**7*d**3*e**3/11 + 675*A*a**2*b**8*d**4
*e**2/11 + 60*A*a*b**9*d**5*e/11 + A*b**10*d**6/11 + 120*B*a**7*b**3*e**6/11 + 1260*B*a**6*b**4*d*e**5/11 + 37
80*B*a**5*b**5*d**2*e**4/11 + 4200*B*a**4*b**6*d**3*e**3/11 + 1800*B*a**3*b**7*d**4*e**2/11 + 270*B*a**2*b**8*
d**5*e/11 + 10*B*a*b**9*d**6/11) + x**10*(12*A*a**7*b**3*e**6 + 126*A*a**6*b**4*d*e**5 + 378*A*a**5*b**5*d**2*
e**4 + 420*A*a**4*b**6*d**3*e**3 + 180*A*a**3*b**7*d**4*e**2 + 27*A*a**2*b**8*d**5*e + A*a*b**9*d**6 + 9*B*a**
8*b**2*e**6/2 + 72*B*a**7*b**3*d*e**5 + 315*B*a**6*b**4*d**2*e**4 + 504*B*a**5*b**5*d**3*e**3 + 315*B*a**4*b**
6*d**4*e**2 + 72*B*a**3*b**7*d**5*e + 9*B*a**2*b**8*d**6/2) + x**9*(5*A*a**8*b**2*e**6 + 80*A*a**7*b**3*d*e**5
+ 350*A*a**6*b**4*d**2*e**4 + 560*A*a**5*b**5*d**3*e**3 + 350*A*a**4*b**6*d**4*e**2 + 80*A*a**3*b**7*d**5*e +
5*A*a**2*b**8*d**6 + 10*B*a**9*b*e**6/9 + 30*B*a**8*b**2*d*e**5 + 200*B*a**7*b**3*d**2*e**4 + 1400*B*a**6*b**
4*d**3*e**3/3 + 420*B*a**5*b**5*d**4*e**2 + 140*B*a**4*b**6*d**5*e + 40*B*a**3*b**7*d**6/3) + x**8*(5*A*a**9*b
*e**6/4 + 135*A*a**8*b**2*d*e**5/4 + 225*A*a**7*b**3*d**2*e**4 + 525*A*a**6*b**4*d**3*e**3 + 945*A*a**5*b**5*d
**4*e**2/2 + 315*A*a**4*b**6*d**5*e/2 + 15*A*a**3*b**7*d**6 + B*a**10*e**6/8 + 15*B*a**9*b*d*e**5/2 + 675*B*a*
*8*b**2*d**2*e**4/8 + 300*B*a**7*b**3*d**3*e**3 + 1575*B*a**6*b**4*d**4*e**2/4 + 189*B*a**5*b**5*d**5*e + 105*
B*a**4*b**6*d**6/4) + x**7*(A*a**10*e**6/7 + 60*A*a**9*b*d*e**5/7 + 675*A*a**8*b**2*d**2*e**4/7 + 2400*A*a**7*
b**3*d**3*e**3/7 + 450*A*a**6*b**4*d**4*e**2 + 216*A*a**5*b**5*d**5*e + 30*A*a**4*b**6*d**6 + 6*B*a**10*d*e**5
/7 + 150*B*a**9*b*d**2*e**4/7 + 900*B*a**8*b**2*d**3*e**3/7 + 1800*B*a**7*b**3*d**4*e**2/7 + 180*B*a**6*b**4*d
**5*e + 36*B*a**5*b**5*d**6) + x**6*(A*a**10*d*e**5 + 25*A*a**9*b*d**2*e**4 + 150*A*a**8*b**2*d**3*e**3 + 300*
A*a**7*b**3*d**4*e**2 + 210*A*a**6*b**4*d**5*e + 42*A*a**5*b**5*d**6 + 5*B*a**10*d**2*e**4/2 + 100*B*a**9*b*d*
*3*e**3/3 + 225*B*a**8*b**2*d**4*e**2/2 + 120*B*a**7*b**3*d**5*e + 35*B*a**6*b**4*d**6) + x**5*(3*A*a**10*d**2
*e**4 + 40*A*a**9*b*d**3*e**3 + 135*A*a**8*b**2*d**4*e**2 + 144*A*a**7*b**3*d**5*e + 42*A*a**6*b**4*d**6 + 4*B
*a**10*d**3*e**3 + 30*B*a**9*b*d**4*e**2 + 54*B*a**8*b**2*d**5*e + 24*B*a**7*b**3*d**6) + x**4*(5*A*a**10*d**3
*e**3 + 75*A*a**9*b*d**4*e**2/2 + 135*A*a**8*b**2*d**5*e/2 + 30*A*a**7*b**3*d**6 + 15*B*a**10*d**4*e**2/4 + 15
*B*a**9*b*d**5*e + 45*B*a**8*b**2*d**6/4) + x**3*(5*A*a**10*d**4*e**2 + 20*A*a**9*b*d**5*e + 15*A*a**8*b**2*d*
*6 + 2*B*a**10*d**5*e + 10*B*a**9*b*d**6/3) + x**2*(3*A*a**10*d**5*e + 5*A*a**9*b*d**6 + B*a**10*d**6/2)

________________________________________________________________________________________

Giac [B]  time = 2.45694, size = 3131, normalized size = 10.8 \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)^10*(B*x+A)*(e*x+d)^6,x, algorithm="giac")

[Out]

1/18*B*b^10*x^18*e^6 + 6/17*B*b^10*d*x^17*e^5 + 15/16*B*b^10*d^2*x^16*e^4 + 4/3*B*b^10*d^3*x^15*e^3 + 15/14*B*
b^10*d^4*x^14*e^2 + 6/13*B*b^10*d^5*x^13*e + 1/12*B*b^10*d^6*x^12 + 10/17*B*a*b^9*x^17*e^6 + 1/17*A*b^10*x^17*
e^6 + 15/4*B*a*b^9*d*x^16*e^5 + 3/8*A*b^10*d*x^16*e^5 + 10*B*a*b^9*d^2*x^15*e^4 + A*b^10*d^2*x^15*e^4 + 100/7*
B*a*b^9*d^3*x^14*e^3 + 10/7*A*b^10*d^3*x^14*e^3 + 150/13*B*a*b^9*d^4*x^13*e^2 + 15/13*A*b^10*d^4*x^13*e^2 + 5*
B*a*b^9*d^5*x^12*e + 1/2*A*b^10*d^5*x^12*e + 10/11*B*a*b^9*d^6*x^11 + 1/11*A*b^10*d^6*x^11 + 45/16*B*a^2*b^8*x
^16*e^6 + 5/8*A*a*b^9*x^16*e^6 + 18*B*a^2*b^8*d*x^15*e^5 + 4*A*a*b^9*d*x^15*e^5 + 675/14*B*a^2*b^8*d^2*x^14*e^
4 + 75/7*A*a*b^9*d^2*x^14*e^4 + 900/13*B*a^2*b^8*d^3*x^13*e^3 + 200/13*A*a*b^9*d^3*x^13*e^3 + 225/4*B*a^2*b^8*
d^4*x^12*e^2 + 25/2*A*a*b^9*d^4*x^12*e^2 + 270/11*B*a^2*b^8*d^5*x^11*e + 60/11*A*a*b^9*d^5*x^11*e + 9/2*B*a^2*
b^8*d^6*x^10 + A*a*b^9*d^6*x^10 + 8*B*a^3*b^7*x^15*e^6 + 3*A*a^2*b^8*x^15*e^6 + 360/7*B*a^3*b^7*d*x^14*e^5 + 1
35/7*A*a^2*b^8*d*x^14*e^5 + 1800/13*B*a^3*b^7*d^2*x^13*e^4 + 675/13*A*a^2*b^8*d^2*x^13*e^4 + 200*B*a^3*b^7*d^3
*x^12*e^3 + 75*A*a^2*b^8*d^3*x^12*e^3 + 1800/11*B*a^3*b^7*d^4*x^11*e^2 + 675/11*A*a^2*b^8*d^4*x^11*e^2 + 72*B*
a^3*b^7*d^5*x^10*e + 27*A*a^2*b^8*d^5*x^10*e + 40/3*B*a^3*b^7*d^6*x^9 + 5*A*a^2*b^8*d^6*x^9 + 15*B*a^4*b^6*x^1
4*e^6 + 60/7*A*a^3*b^7*x^14*e^6 + 1260/13*B*a^4*b^6*d*x^13*e^5 + 720/13*A*a^3*b^7*d*x^13*e^5 + 525/2*B*a^4*b^6
*d^2*x^12*e^4 + 150*A*a^3*b^7*d^2*x^12*e^4 + 4200/11*B*a^4*b^6*d^3*x^11*e^3 + 2400/11*A*a^3*b^7*d^3*x^11*e^3 +
315*B*a^4*b^6*d^4*x^10*e^2 + 180*A*a^3*b^7*d^4*x^10*e^2 + 140*B*a^4*b^6*d^5*x^9*e + 80*A*a^3*b^7*d^5*x^9*e +
105/4*B*a^4*b^6*d^6*x^8 + 15*A*a^3*b^7*d^6*x^8 + 252/13*B*a^5*b^5*x^13*e^6 + 210/13*A*a^4*b^6*x^13*e^6 + 126*B
*a^5*b^5*d*x^12*e^5 + 105*A*a^4*b^6*d*x^12*e^5 + 3780/11*B*a^5*b^5*d^2*x^11*e^4 + 3150/11*A*a^4*b^6*d^2*x^11*e
^4 + 504*B*a^5*b^5*d^3*x^10*e^3 + 420*A*a^4*b^6*d^3*x^10*e^3 + 420*B*a^5*b^5*d^4*x^9*e^2 + 350*A*a^4*b^6*d^4*x
^9*e^2 + 189*B*a^5*b^5*d^5*x^8*e + 315/2*A*a^4*b^6*d^5*x^8*e + 36*B*a^5*b^5*d^6*x^7 + 30*A*a^4*b^6*d^6*x^7 + 3
5/2*B*a^6*b^4*x^12*e^6 + 21*A*a^5*b^5*x^12*e^6 + 1260/11*B*a^6*b^4*d*x^11*e^5 + 1512/11*A*a^5*b^5*d*x^11*e^5 +
315*B*a^6*b^4*d^2*x^10*e^4 + 378*A*a^5*b^5*d^2*x^10*e^4 + 1400/3*B*a^6*b^4*d^3*x^9*e^3 + 560*A*a^5*b^5*d^3*x^
9*e^3 + 1575/4*B*a^6*b^4*d^4*x^8*e^2 + 945/2*A*a^5*b^5*d^4*x^8*e^2 + 180*B*a^6*b^4*d^5*x^7*e + 216*A*a^5*b^5*d
^5*x^7*e + 35*B*a^6*b^4*d^6*x^6 + 42*A*a^5*b^5*d^6*x^6 + 120/11*B*a^7*b^3*x^11*e^6 + 210/11*A*a^6*b^4*x^11*e^6
+ 72*B*a^7*b^3*d*x^10*e^5 + 126*A*a^6*b^4*d*x^10*e^5 + 200*B*a^7*b^3*d^2*x^9*e^4 + 350*A*a^6*b^4*d^2*x^9*e^4
+ 300*B*a^7*b^3*d^3*x^8*e^3 + 525*A*a^6*b^4*d^3*x^8*e^3 + 1800/7*B*a^7*b^3*d^4*x^7*e^2 + 450*A*a^6*b^4*d^4*x^7
*e^2 + 120*B*a^7*b^3*d^5*x^6*e + 210*A*a^6*b^4*d^5*x^6*e + 24*B*a^7*b^3*d^6*x^5 + 42*A*a^6*b^4*d^6*x^5 + 9/2*B
*a^8*b^2*x^10*e^6 + 12*A*a^7*b^3*x^10*e^6 + 30*B*a^8*b^2*d*x^9*e^5 + 80*A*a^7*b^3*d*x^9*e^5 + 675/8*B*a^8*b^2*
d^2*x^8*e^4 + 225*A*a^7*b^3*d^2*x^8*e^4 + 900/7*B*a^8*b^2*d^3*x^7*e^3 + 2400/7*A*a^7*b^3*d^3*x^7*e^3 + 225/2*B
*a^8*b^2*d^4*x^6*e^2 + 300*A*a^7*b^3*d^4*x^6*e^2 + 54*B*a^8*b^2*d^5*x^5*e + 144*A*a^7*b^3*d^5*x^5*e + 45/4*B*a
^8*b^2*d^6*x^4 + 30*A*a^7*b^3*d^6*x^4 + 10/9*B*a^9*b*x^9*e^6 + 5*A*a^8*b^2*x^9*e^6 + 15/2*B*a^9*b*d*x^8*e^5 +
135/4*A*a^8*b^2*d*x^8*e^5 + 150/7*B*a^9*b*d^2*x^7*e^4 + 675/7*A*a^8*b^2*d^2*x^7*e^4 + 100/3*B*a^9*b*d^3*x^6*e^
3 + 150*A*a^8*b^2*d^3*x^6*e^3 + 30*B*a^9*b*d^4*x^5*e^2 + 135*A*a^8*b^2*d^4*x^5*e^2 + 15*B*a^9*b*d^5*x^4*e + 13
5/2*A*a^8*b^2*d^5*x^4*e + 10/3*B*a^9*b*d^6*x^3 + 15*A*a^8*b^2*d^6*x^3 + 1/8*B*a^10*x^8*e^6 + 5/4*A*a^9*b*x^8*e
^6 + 6/7*B*a^10*d*x^7*e^5 + 60/7*A*a^9*b*d*x^7*e^5 + 5/2*B*a^10*d^2*x^6*e^4 + 25*A*a^9*b*d^2*x^6*e^4 + 4*B*a^1
0*d^3*x^5*e^3 + 40*A*a^9*b*d^3*x^5*e^3 + 15/4*B*a^10*d^4*x^4*e^2 + 75/2*A*a^9*b*d^4*x^4*e^2 + 2*B*a^10*d^5*x^3
*e + 20*A*a^9*b*d^5*x^3*e + 1/2*B*a^10*d^6*x^2 + 5*A*a^9*b*d^6*x^2 + 1/7*A*a^10*x^7*e^6 + A*a^10*d*x^6*e^5 + 3
*A*a^10*d^2*x^5*e^4 + 5*A*a^10*d^3*x^4*e^3 + 5*A*a^10*d^4*x^3*e^2 + 3*A*a^10*d^5*x^2*e + A*a^10*d^6*x