3.11.53 \(\int (a+b x)^6 (A+B x) (d+e x)^6 \, dx\) [1053]

Optimal. Leaf size=290 \[ \frac {(A b-a B) (b d-a e)^6 (a+b x)^7}{7 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^8}{8 b^8}+\frac {e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^9}{3 b^8}+\frac {e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{10}}{2 b^8}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{11}}{11 b^8}+\frac {e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{12}}{4 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8} \]

[Out]

1/7*(A*b-B*a)*(-a*e+b*d)^6*(b*x+a)^7/b^8+1/8*(-a*e+b*d)^5*(6*A*b*e-7*B*a*e+B*b*d)*(b*x+a)^8/b^8+1/3*e*(-a*e+b*
d)^4*(5*A*b*e-7*B*a*e+2*B*b*d)*(b*x+a)^9/b^8+1/2*e^2*(-a*e+b*d)^3*(4*A*b*e-7*B*a*e+3*B*b*d)*(b*x+a)^10/b^8+5/1
1*e^3*(-a*e+b*d)^2*(3*A*b*e-7*B*a*e+4*B*b*d)*(b*x+a)^11/b^8+1/4*e^4*(-a*e+b*d)*(2*A*b*e-7*B*a*e+5*B*b*d)*(b*x+
a)^12/b^8+1/13*e^5*(A*b*e-7*B*a*e+6*B*b*d)*(b*x+a)^13/b^8+1/14*B*e^6*(b*x+a)^14/b^8

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Rubi [A]
time = 0.65, antiderivative size = 290, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} \frac {e^5 (a+b x)^{13} (-7 a B e+A b e+6 b B d)}{13 b^8}+\frac {e^4 (a+b x)^{12} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{4 b^8}+\frac {5 e^3 (a+b x)^{11} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{11 b^8}+\frac {e^2 (a+b x)^{10} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{2 b^8}+\frac {e (a+b x)^9 (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{3 b^8}+\frac {(a+b x)^8 (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{8 b^8}+\frac {(a+b x)^7 (A b-a B) (b d-a e)^6}{7 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^7)/(7*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^8)/(8*b
^8) + (e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^9)/(3*b^8) + (e^2*(b*d - a*e)^3*(3*b*B*d + 4*A*
b*e - 7*a*B*e)*(a + b*x)^10)/(2*b^8) + (5*e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^11)/(11*b^
8) + (e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^12)/(4*b^8) + (e^5*(6*b*B*d + A*b*e - 7*a*B*e)*(
a + b*x)^13)/(13*b^8) + (B*e^6*(a + b*x)^14)/(14*b^8)

Rule 78

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)^6 (A+B x) (d+e x)^6 \, dx &=\int \left (\frac {(A b-a B) (b d-a e)^6 (a+b x)^6}{b^7}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^7}{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)^8}{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)^9}{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)^{10}}{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)^{11}}{b^7}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{12}}{b^7}+\frac {B e^6 (a+b x)^{13}}{b^7}\right ) \, dx\\ &=\frac {(A b-a B) (b d-a e)^6 (a+b x)^7}{7 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^8}{8 b^8}+\frac {e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^9}{3 b^8}+\frac {e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{10}}{2 b^8}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{11}}{11 b^8}+\frac {e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{12}}{4 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {B e^6 (a+b x)^{14}}{14 b^8}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1069\) vs. \(2(290)=580\).
time = 0.27, size = 1069, normalized size = 3.69 \begin {gather*} a^6 A d^6 x+\frac {1}{2} a^5 d^5 (a B d+6 A (b d+a e)) x^2+a^4 d^4 \left (2 a B d (b d+a e)+A \left (5 b^2 d^2+12 a b d e+5 a^2 e^2\right )\right ) x^3+\frac {1}{4} a^3 d^3 \left (3 a B d \left (5 b^2 d^2+12 a b d e+5 a^2 e^2\right )+10 A \left (2 b^3 d^3+9 a b^2 d^2 e+9 a^2 b d e^2+2 a^3 e^3\right )\right ) x^4+a^2 d^2 \left (2 a B d \left (2 b^3 d^3+9 a b^2 d^2 e+9 a^2 b d e^2+2 a^3 e^3\right )+3 A \left (b^4 d^4+8 a b^3 d^3 e+15 a^2 b^2 d^2 e^2+8 a^3 b d e^3+a^4 e^4\right )\right ) x^5+\frac {1}{2} a d \left (5 a B d \left (b^4 d^4+8 a b^3 d^3 e+15 a^2 b^2 d^2 e^2+8 a^3 b d e^3+a^4 e^4\right )+2 A \left (b^5 d^5+15 a b^4 d^4 e+50 a^2 b^3 d^3 e^2+50 a^3 b^2 d^2 e^3+15 a^4 b d e^4+a^5 e^5\right )\right ) x^6+\frac {1}{7} \left (6 a B d \left (b^5 d^5+15 a b^4 d^4 e+50 a^2 b^3 d^3 e^2+50 a^3 b^2 d^2 e^3+15 a^4 b d e^4+a^5 e^5\right )+A \left (b^6 d^6+36 a b^5 d^5 e+225 a^2 b^4 d^4 e^2+400 a^3 b^3 d^3 e^3+225 a^4 b^2 d^2 e^4+36 a^5 b d e^5+a^6 e^6\right )\right ) x^7+\frac {1}{8} \left (a^6 B e^6+6 a^5 b e^5 (6 B d+A e)+45 a^4 b^2 d e^4 (5 B d+2 A e)+100 a^3 b^3 d^2 e^3 (4 B d+3 A e)+75 a^2 b^4 d^3 e^2 (3 B d+4 A e)+18 a b^5 d^4 e (2 B d+5 A e)+b^6 d^5 (B d+6 A e)\right ) x^8+\frac {1}{3} b e \left (2 a^5 B e^5+5 a^4 b e^4 (6 B d+A e)+20 a^3 b^2 d e^3 (5 B d+2 A e)+25 a^2 b^3 d^2 e^2 (4 B d+3 A e)+10 a b^4 d^3 e (3 B d+4 A e)+b^5 d^4 (2 B d+5 A e)\right ) x^9+\frac {1}{2} b^2 e^2 \left (3 a^4 B e^4+4 a^3 b e^3 (6 B d+A e)+9 a^2 b^2 d e^2 (5 B d+2 A e)+6 a b^3 d^2 e (4 B d+3 A e)+b^4 d^3 (3 B d+4 A e)\right ) x^{10}+\frac {1}{11} b^3 e^3 \left (20 a^3 B e^3+15 a^2 b e^2 (6 B d+A e)+18 a b^2 d e (5 B d+2 A e)+5 b^3 d^2 (4 B d+3 A e)\right ) x^{11}+\frac {1}{4} b^4 e^4 \left (5 a^2 B e^2+2 a b e (6 B d+A e)+b^2 d (5 B d+2 A e)\right ) x^{12}+\frac {1}{13} b^5 e^5 (6 b B d+A b e+6 a B e) x^{13}+\frac {1}{14} b^6 B e^6 x^{14} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

a^6*A*d^6*x + (a^5*d^5*(a*B*d + 6*A*(b*d + a*e))*x^2)/2 + a^4*d^4*(2*a*B*d*(b*d + a*e) + A*(5*b^2*d^2 + 12*a*b
*d*e + 5*a^2*e^2))*x^3 + (a^3*d^3*(3*a*B*d*(5*b^2*d^2 + 12*a*b*d*e + 5*a^2*e^2) + 10*A*(2*b^3*d^3 + 9*a*b^2*d^
2*e + 9*a^2*b*d*e^2 + 2*a^3*e^3))*x^4)/4 + a^2*d^2*(2*a*B*d*(2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + 2*a^3
*e^3) + 3*A*(b^4*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 8*a^3*b*d*e^3 + a^4*e^4))*x^5 + (a*d*(5*a*B*d*(b^4
*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 8*a^3*b*d*e^3 + a^4*e^4) + 2*A*(b^5*d^5 + 15*a*b^4*d^4*e + 50*a^2*
b^3*d^3*e^2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^5*e^5))*x^6)/2 + ((6*a*B*d*(b^5*d^5 + 15*a*b^4*d^4*e + 5
0*a^2*b^3*d^3*e^2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^5*e^5) + A*(b^6*d^6 + 36*a*b^5*d^5*e + 225*a^2*b^4
*d^4*e^2 + 400*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 36*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + ((a^6*B*e^6 + 6*a^5
*b*e^5*(6*B*d + A*e) + 45*a^4*b^2*d*e^4*(5*B*d + 2*A*e) + 100*a^3*b^3*d^2*e^3*(4*B*d + 3*A*e) + 75*a^2*b^4*d^3
*e^2*(3*B*d + 4*A*e) + 18*a*b^5*d^4*e*(2*B*d + 5*A*e) + b^6*d^5*(B*d + 6*A*e))*x^8)/8 + (b*e*(2*a^5*B*e^5 + 5*
a^4*b*e^4*(6*B*d + A*e) + 20*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 25*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 10*a*b^4*d^3
*e*(3*B*d + 4*A*e) + b^5*d^4*(2*B*d + 5*A*e))*x^9)/3 + (b^2*e^2*(3*a^4*B*e^4 + 4*a^3*b*e^3*(6*B*d + A*e) + 9*a
^2*b^2*d*e^2*(5*B*d + 2*A*e) + 6*a*b^3*d^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^10)/2 + (b^3*e^3*(20
*a^3*B*e^3 + 15*a^2*b*e^2*(6*B*d + A*e) + 18*a*b^2*d*e*(5*B*d + 2*A*e) + 5*b^3*d^2*(4*B*d + 3*A*e))*x^11)/11 +
(b^4*e^4*(5*a^2*B*e^2 + 2*a*b*e*(6*B*d + A*e) + b^2*d*(5*B*d + 2*A*e))*x^12)/4 + (b^5*e^5*(6*b*B*d + A*b*e +
6*a*B*e)*x^13)/13 + (b^6*B*e^6*x^14)/14

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1172\) vs. \(2(274)=548\).
time = 0.07, size = 1173, normalized size = 4.04 Too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^6*(B*x+A)*(e*x+d)^6,x,method=_RETURNVERBOSE)

[Out]

1/14*b^6*B*e^6*x^14+1/13*((A*b^6+6*B*a*b^5)*e^6+6*b^6*B*d*e^5)*x^13+1/12*((6*A*a*b^5+15*B*a^2*b^4)*e^6+6*(A*b^
6+6*B*a*b^5)*d*e^5+15*b^6*B*d^2*e^4)*x^12+1/11*((15*A*a^2*b^4+20*B*a^3*b^3)*e^6+6*(6*A*a*b^5+15*B*a^2*b^4)*d*e
^5+15*(A*b^6+6*B*a*b^5)*d^2*e^4+20*b^6*B*d^3*e^3)*x^11+1/10*((20*A*a^3*b^3+15*B*a^4*b^2)*e^6+6*(15*A*a^2*b^4+2
0*B*a^3*b^3)*d*e^5+15*(6*A*a*b^5+15*B*a^2*b^4)*d^2*e^4+20*(A*b^6+6*B*a*b^5)*d^3*e^3+15*b^6*B*d^4*e^2)*x^10+1/9
*((15*A*a^4*b^2+6*B*a^5*b)*e^6+6*(20*A*a^3*b^3+15*B*a^4*b^2)*d*e^5+15*(15*A*a^2*b^4+20*B*a^3*b^3)*d^2*e^4+20*(
6*A*a*b^5+15*B*a^2*b^4)*d^3*e^3+15*(A*b^6+6*B*a*b^5)*d^4*e^2+6*b^6*B*d^5*e)*x^9+1/8*((6*A*a^5*b+B*a^6)*e^6+6*(
15*A*a^4*b^2+6*B*a^5*b)*d*e^5+15*(20*A*a^3*b^3+15*B*a^4*b^2)*d^2*e^4+20*(15*A*a^2*b^4+20*B*a^3*b^3)*d^3*e^3+15
*(6*A*a*b^5+15*B*a^2*b^4)*d^4*e^2+6*(A*b^6+6*B*a*b^5)*d^5*e+b^6*B*d^6)*x^8+1/7*(a^6*A*e^6+6*(6*A*a^5*b+B*a^6)*
d*e^5+15*(15*A*a^4*b^2+6*B*a^5*b)*d^2*e^4+20*(20*A*a^3*b^3+15*B*a^4*b^2)*d^3*e^3+15*(15*A*a^2*b^4+20*B*a^3*b^3
)*d^4*e^2+6*(6*A*a*b^5+15*B*a^2*b^4)*d^5*e+(A*b^6+6*B*a*b^5)*d^6)*x^7+1/6*(6*a^6*A*d*e^5+15*(6*A*a^5*b+B*a^6)*
d^2*e^4+20*(15*A*a^4*b^2+6*B*a^5*b)*d^3*e^3+15*(20*A*a^3*b^3+15*B*a^4*b^2)*d^4*e^2+6*(15*A*a^2*b^4+20*B*a^3*b^
3)*d^5*e+(6*A*a*b^5+15*B*a^2*b^4)*d^6)*x^6+1/5*(15*a^6*A*d^2*e^4+20*(6*A*a^5*b+B*a^6)*d^3*e^3+15*(15*A*a^4*b^2
+6*B*a^5*b)*d^4*e^2+6*(20*A*a^3*b^3+15*B*a^4*b^2)*d^5*e+(15*A*a^2*b^4+20*B*a^3*b^3)*d^6)*x^5+1/4*(20*a^6*A*d^3
*e^3+15*(6*A*a^5*b+B*a^6)*d^4*e^2+6*(15*A*a^4*b^2+6*B*a^5*b)*d^5*e+(20*A*a^3*b^3+15*B*a^4*b^2)*d^6)*x^4+1/3*(1
5*a^6*A*d^4*e^2+6*(6*A*a^5*b+B*a^6)*d^5*e+(15*A*a^4*b^2+6*B*a^5*b)*d^6)*x^3+1/2*(6*a^6*A*d^5*e+(6*A*a^5*b+B*a^
6)*d^6)*x^2+a^6*A*d^6*x

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1199 vs. \(2 (288) = 576\).
time = 0.32, size = 1199, normalized size = 4.13 \begin {gather*} \frac {1}{14} \, B b^{6} x^{14} e^{6} + A a^{6} d^{6} x + \frac {1}{13} \, {\left (6 \, B b^{6} d e^{5} + 6 \, B a b^{5} e^{6} + A b^{6} e^{6}\right )} x^{13} + \frac {1}{4} \, {\left (5 \, B b^{6} d^{2} e^{4} + 5 \, B a^{2} b^{4} e^{6} + 2 \, A a b^{5} e^{6} + 2 \, {\left (6 \, B a b^{5} e^{5} + A b^{6} e^{5}\right )} d\right )} x^{12} + \frac {1}{11} \, {\left (20 \, B b^{6} d^{3} e^{3} + 20 \, B a^{3} b^{3} e^{6} + 15 \, A a^{2} b^{4} e^{6} + 15 \, {\left (6 \, B a b^{5} e^{4} + A b^{6} e^{4}\right )} d^{2} + 18 \, {\left (5 \, B a^{2} b^{4} e^{5} + 2 \, A a b^{5} e^{5}\right )} d\right )} x^{11} + \frac {1}{2} \, {\left (3 \, B b^{6} d^{4} e^{2} + 3 \, B a^{4} b^{2} e^{6} + 4 \, A a^{3} b^{3} e^{6} + 4 \, {\left (6 \, B a b^{5} e^{3} + A b^{6} e^{3}\right )} d^{3} + 9 \, {\left (5 \, B a^{2} b^{4} e^{4} + 2 \, A a b^{5} e^{4}\right )} d^{2} + 6 \, {\left (4 \, B a^{3} b^{3} e^{5} + 3 \, A a^{2} b^{4} e^{5}\right )} d\right )} x^{10} + \frac {1}{3} \, {\left (2 \, B b^{6} d^{5} e + 2 \, B a^{5} b e^{6} + 5 \, A a^{4} b^{2} e^{6} + 5 \, {\left (6 \, B a b^{5} e^{2} + A b^{6} e^{2}\right )} d^{4} + 20 \, {\left (5 \, B a^{2} b^{4} e^{3} + 2 \, A a b^{5} e^{3}\right )} d^{3} + 25 \, {\left (4 \, B a^{3} b^{3} e^{4} + 3 \, A a^{2} b^{4} e^{4}\right )} d^{2} + 10 \, {\left (3 \, B a^{4} b^{2} e^{5} + 4 \, A a^{3} b^{3} e^{5}\right )} d\right )} x^{9} + \frac {1}{8} \, {\left (B b^{6} d^{6} + B a^{6} e^{6} + 6 \, A a^{5} b e^{6} + 6 \, {\left (6 \, B a b^{5} e + A b^{6} e\right )} d^{5} + 45 \, {\left (5 \, B a^{2} b^{4} e^{2} + 2 \, A a b^{5} e^{2}\right )} d^{4} + 100 \, {\left (4 \, B a^{3} b^{3} e^{3} + 3 \, A a^{2} b^{4} e^{3}\right )} d^{3} + 75 \, {\left (3 \, B a^{4} b^{2} e^{4} + 4 \, A a^{3} b^{3} e^{4}\right )} d^{2} + 18 \, {\left (2 \, B a^{5} b e^{5} + 5 \, A a^{4} b^{2} e^{5}\right )} d\right )} x^{8} + \frac {1}{7} \, {\left (A a^{6} e^{6} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} + 18 \, {\left (5 \, B a^{2} b^{4} e + 2 \, A a b^{5} e\right )} d^{5} + 75 \, {\left (4 \, B a^{3} b^{3} e^{2} + 3 \, A a^{2} b^{4} e^{2}\right )} d^{4} + 100 \, {\left (3 \, B a^{4} b^{2} e^{3} + 4 \, A a^{3} b^{3} e^{3}\right )} d^{3} + 45 \, {\left (2 \, B a^{5} b e^{4} + 5 \, A a^{4} b^{2} e^{4}\right )} d^{2} + 6 \, {\left (B a^{6} e^{5} + 6 \, A a^{5} b e^{5}\right )} d\right )} x^{7} + \frac {1}{2} \, {\left (2 \, A a^{6} d e^{5} + {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{6} + 10 \, {\left (4 \, B a^{3} b^{3} e + 3 \, A a^{2} b^{4} e\right )} d^{5} + 25 \, {\left (3 \, B a^{4} b^{2} e^{2} + 4 \, A a^{3} b^{3} e^{2}\right )} d^{4} + 20 \, {\left (2 \, B a^{5} b e^{3} + 5 \, A a^{4} b^{2} e^{3}\right )} d^{3} + 5 \, {\left (B a^{6} e^{4} + 6 \, A a^{5} b e^{4}\right )} d^{2}\right )} x^{6} + {\left (3 \, A a^{6} d^{2} e^{4} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{6} + 6 \, {\left (3 \, B a^{4} b^{2} e + 4 \, A a^{3} b^{3} e\right )} d^{5} + 9 \, {\left (2 \, B a^{5} b e^{2} + 5 \, A a^{4} b^{2} e^{2}\right )} d^{4} + 4 \, {\left (B a^{6} e^{3} + 6 \, A a^{5} b e^{3}\right )} d^{3}\right )} x^{5} + \frac {1}{4} \, {\left (20 \, A a^{6} d^{3} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{6} + 18 \, {\left (2 \, B a^{5} b e + 5 \, A a^{4} b^{2} e\right )} d^{5} + 15 \, {\left (B a^{6} e^{2} + 6 \, A a^{5} b e^{2}\right )} d^{4}\right )} x^{4} + {\left (5 \, A a^{6} d^{4} e^{2} + {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{6} + 2 \, {\left (B a^{6} e + 6 \, A a^{5} b e\right )} d^{5}\right )} x^{3} + \frac {1}{2} \, {\left (6 \, A a^{6} d^{5} e + {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{6}\right )} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^6,x, algorithm="maxima")

[Out]

1/14*B*b^6*x^14*e^6 + A*a^6*d^6*x + 1/13*(6*B*b^6*d*e^5 + 6*B*a*b^5*e^6 + A*b^6*e^6)*x^13 + 1/4*(5*B*b^6*d^2*e
^4 + 5*B*a^2*b^4*e^6 + 2*A*a*b^5*e^6 + 2*(6*B*a*b^5*e^5 + A*b^6*e^5)*d)*x^12 + 1/11*(20*B*b^6*d^3*e^3 + 20*B*a
^3*b^3*e^6 + 15*A*a^2*b^4*e^6 + 15*(6*B*a*b^5*e^4 + A*b^6*e^4)*d^2 + 18*(5*B*a^2*b^4*e^5 + 2*A*a*b^5*e^5)*d)*x
^11 + 1/2*(3*B*b^6*d^4*e^2 + 3*B*a^4*b^2*e^6 + 4*A*a^3*b^3*e^6 + 4*(6*B*a*b^5*e^3 + A*b^6*e^3)*d^3 + 9*(5*B*a^
2*b^4*e^4 + 2*A*a*b^5*e^4)*d^2 + 6*(4*B*a^3*b^3*e^5 + 3*A*a^2*b^4*e^5)*d)*x^10 + 1/3*(2*B*b^6*d^5*e + 2*B*a^5*
b*e^6 + 5*A*a^4*b^2*e^6 + 5*(6*B*a*b^5*e^2 + A*b^6*e^2)*d^4 + 20*(5*B*a^2*b^4*e^3 + 2*A*a*b^5*e^3)*d^3 + 25*(4
*B*a^3*b^3*e^4 + 3*A*a^2*b^4*e^4)*d^2 + 10*(3*B*a^4*b^2*e^5 + 4*A*a^3*b^3*e^5)*d)*x^9 + 1/8*(B*b^6*d^6 + B*a^6
*e^6 + 6*A*a^5*b*e^6 + 6*(6*B*a*b^5*e + A*b^6*e)*d^5 + 45*(5*B*a^2*b^4*e^2 + 2*A*a*b^5*e^2)*d^4 + 100*(4*B*a^3
*b^3*e^3 + 3*A*a^2*b^4*e^3)*d^3 + 75*(3*B*a^4*b^2*e^4 + 4*A*a^3*b^3*e^4)*d^2 + 18*(2*B*a^5*b*e^5 + 5*A*a^4*b^2
*e^5)*d)*x^8 + 1/7*(A*a^6*e^6 + (6*B*a*b^5 + A*b^6)*d^6 + 18*(5*B*a^2*b^4*e + 2*A*a*b^5*e)*d^5 + 75*(4*B*a^3*b
^3*e^2 + 3*A*a^2*b^4*e^2)*d^4 + 100*(3*B*a^4*b^2*e^3 + 4*A*a^3*b^3*e^3)*d^3 + 45*(2*B*a^5*b*e^4 + 5*A*a^4*b^2*
e^4)*d^2 + 6*(B*a^6*e^5 + 6*A*a^5*b*e^5)*d)*x^7 + 1/2*(2*A*a^6*d*e^5 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^6 + 10*(4*B
*a^3*b^3*e + 3*A*a^2*b^4*e)*d^5 + 25*(3*B*a^4*b^2*e^2 + 4*A*a^3*b^3*e^2)*d^4 + 20*(2*B*a^5*b*e^3 + 5*A*a^4*b^2
*e^3)*d^3 + 5*(B*a^6*e^4 + 6*A*a^5*b*e^4)*d^2)*x^6 + (3*A*a^6*d^2*e^4 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^6 + 6*(3
*B*a^4*b^2*e + 4*A*a^3*b^3*e)*d^5 + 9*(2*B*a^5*b*e^2 + 5*A*a^4*b^2*e^2)*d^4 + 4*(B*a^6*e^3 + 6*A*a^5*b*e^3)*d^
3)*x^5 + 1/4*(20*A*a^6*d^3*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^6 + 18*(2*B*a^5*b*e + 5*A*a^4*b^2*e)*d^5 + 15
*(B*a^6*e^2 + 6*A*a^5*b*e^2)*d^4)*x^4 + (5*A*a^6*d^4*e^2 + (2*B*a^5*b + 5*A*a^4*b^2)*d^6 + 2*(B*a^6*e + 6*A*a^
5*b*e)*d^5)*x^3 + 1/2*(6*A*a^6*d^5*e + (B*a^6 + 6*A*a^5*b)*d^6)*x^2

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1176 vs. \(2 (288) = 576\).
time = 1.12, size = 1176, normalized size = 4.06 \begin {gather*} \frac {1}{8} \, B b^{6} d^{6} x^{8} + A a^{6} d^{6} x + \frac {1}{7} \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} x^{7} + \frac {1}{2} \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{6} x^{6} + {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{6} x^{5} + \frac {5}{4} \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{6} x^{4} + {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{6} x^{3} + \frac {1}{2} \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{6} x^{2} + \frac {1}{24024} \, {\left (1716 \, B b^{6} x^{14} + 3432 \, A a^{6} x^{7} + 1848 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{13} + 6006 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{12} + 10920 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{11} + 12012 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{10} + 8008 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{9} + 3003 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x^{8}\right )} e^{6} + \frac {1}{12012} \, {\left (5544 \, B b^{6} d x^{13} + 12012 \, A a^{6} d x^{6} + 6006 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d x^{12} + 19656 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d x^{11} + 36036 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d x^{10} + 40040 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d x^{9} + 27027 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d x^{8} + 10296 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d x^{7}\right )} e^{5} + \frac {1}{1848} \, {\left (2310 \, B b^{6} d^{2} x^{12} + 5544 \, A a^{6} d^{2} x^{5} + 2520 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} x^{11} + 8316 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} x^{10} + 15400 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} x^{9} + 17325 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} x^{8} + 11880 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} x^{7} + 4620 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{2} x^{6}\right )} e^{4} + \frac {1}{462} \, {\left (840 \, B b^{6} d^{3} x^{11} + 2310 \, A a^{6} d^{3} x^{4} + 924 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} x^{10} + 3080 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} x^{9} + 5775 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} x^{8} + 6600 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} x^{7} + 4620 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{3} x^{6} + 1848 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{3} x^{5}\right )} e^{3} + \frac {1}{168} \, {\left (252 \, B b^{6} d^{4} x^{10} + 840 \, A a^{6} d^{4} x^{3} + 280 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} x^{9} + 945 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} x^{8} + 1800 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} x^{7} + 2100 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{4} x^{6} + 1512 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{4} x^{5} + 630 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{4} x^{4}\right )} e^{2} + \frac {1}{84} \, {\left (56 \, B b^{6} d^{5} x^{9} + 252 \, A a^{6} d^{5} x^{2} + 63 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} x^{8} + 216 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} x^{7} + 420 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{5} x^{6} + 504 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{5} x^{5} + 378 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{5} x^{4} + 168 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{5} x^{3}\right )} e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^6,x, algorithm="fricas")

[Out]

1/8*B*b^6*d^6*x^8 + A*a^6*d^6*x + 1/7*(6*B*a*b^5 + A*b^6)*d^6*x^7 + 1/2*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*x^6 + (4
*B*a^3*b^3 + 3*A*a^2*b^4)*d^6*x^5 + 5/4*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^6*x^4 + (2*B*a^5*b + 5*A*a^4*b^2)*d^6*x^
3 + 1/2*(B*a^6 + 6*A*a^5*b)*d^6*x^2 + 1/24024*(1716*B*b^6*x^14 + 3432*A*a^6*x^7 + 1848*(6*B*a*b^5 + A*b^6)*x^1
3 + 6006*(5*B*a^2*b^4 + 2*A*a*b^5)*x^12 + 10920*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^11 + 12012*(3*B*a^4*b^2 + 4*A*a^
3*b^3)*x^10 + 8008*(2*B*a^5*b + 5*A*a^4*b^2)*x^9 + 3003*(B*a^6 + 6*A*a^5*b)*x^8)*e^6 + 1/12012*(5544*B*b^6*d*x
^13 + 12012*A*a^6*d*x^6 + 6006*(6*B*a*b^5 + A*b^6)*d*x^12 + 19656*(5*B*a^2*b^4 + 2*A*a*b^5)*d*x^11 + 36036*(4*
B*a^3*b^3 + 3*A*a^2*b^4)*d*x^10 + 40040*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*x^9 + 27027*(2*B*a^5*b + 5*A*a^4*b^2)*d*
x^8 + 10296*(B*a^6 + 6*A*a^5*b)*d*x^7)*e^5 + 1/1848*(2310*B*b^6*d^2*x^12 + 5544*A*a^6*d^2*x^5 + 2520*(6*B*a*b^
5 + A*b^6)*d^2*x^11 + 8316*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*x^10 + 15400*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*x^9 + 17
325*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*x^8 + 11880*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*x^7 + 4620*(B*a^6 + 6*A*a^5*b)*d
^2*x^6)*e^4 + 1/462*(840*B*b^6*d^3*x^11 + 2310*A*a^6*d^3*x^4 + 924*(6*B*a*b^5 + A*b^6)*d^3*x^10 + 3080*(5*B*a^
2*b^4 + 2*A*a*b^5)*d^3*x^9 + 5775*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*x^8 + 6600*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*x
^7 + 4620*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*x^6 + 1848*(B*a^6 + 6*A*a^5*b)*d^3*x^5)*e^3 + 1/168*(252*B*b^6*d^4*x^1
0 + 840*A*a^6*d^4*x^3 + 280*(6*B*a*b^5 + A*b^6)*d^4*x^9 + 945*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*x^8 + 1800*(4*B*a^
3*b^3 + 3*A*a^2*b^4)*d^4*x^7 + 2100*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*x^6 + 1512*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*x
^5 + 630*(B*a^6 + 6*A*a^5*b)*d^4*x^4)*e^2 + 1/84*(56*B*b^6*d^5*x^9 + 252*A*a^6*d^5*x^2 + 63*(6*B*a*b^5 + A*b^6
)*d^5*x^8 + 216*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*x^7 + 420*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*x^6 + 504*(3*B*a^4*b^2
+ 4*A*a^3*b^3)*d^5*x^5 + 378*(2*B*a^5*b + 5*A*a^4*b^2)*d^5*x^4 + 168*(B*a^6 + 6*A*a^5*b)*d^5*x^3)*e

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1504 vs. \(2 (292) = 584\).
time = 0.12, size = 1504, normalized size = 5.19 \begin {gather*} A a^{6} d^{6} x + \frac {B b^{6} e^{6} x^{14}}{14} + x^{13} \left (\frac {A b^{6} e^{6}}{13} + \frac {6 B a b^{5} e^{6}}{13} + \frac {6 B b^{6} d e^{5}}{13}\right ) + x^{12} \left (\frac {A a b^{5} e^{6}}{2} + \frac {A b^{6} d e^{5}}{2} + \frac {5 B a^{2} b^{4} e^{6}}{4} + 3 B a b^{5} d e^{5} + \frac {5 B b^{6} d^{2} e^{4}}{4}\right ) + x^{11} \cdot \left (\frac {15 A a^{2} b^{4} e^{6}}{11} + \frac {36 A a b^{5} d e^{5}}{11} + \frac {15 A b^{6} d^{2} e^{4}}{11} + \frac {20 B a^{3} b^{3} e^{6}}{11} + \frac {90 B a^{2} b^{4} d e^{5}}{11} + \frac {90 B a b^{5} d^{2} e^{4}}{11} + \frac {20 B b^{6} d^{3} e^{3}}{11}\right ) + x^{10} \cdot \left (2 A a^{3} b^{3} e^{6} + 9 A a^{2} b^{4} d e^{5} + 9 A a b^{5} d^{2} e^{4} + 2 A b^{6} d^{3} e^{3} + \frac {3 B a^{4} b^{2} e^{6}}{2} + 12 B a^{3} b^{3} d e^{5} + \frac {45 B a^{2} b^{4} d^{2} e^{4}}{2} + 12 B a b^{5} d^{3} e^{3} + \frac {3 B b^{6} d^{4} e^{2}}{2}\right ) + x^{9} \cdot \left (\frac {5 A a^{4} b^{2} e^{6}}{3} + \frac {40 A a^{3} b^{3} d e^{5}}{3} + 25 A a^{2} b^{4} d^{2} e^{4} + \frac {40 A a b^{5} d^{3} e^{3}}{3} + \frac {5 A b^{6} d^{4} e^{2}}{3} + \frac {2 B a^{5} b e^{6}}{3} + 10 B a^{4} b^{2} d e^{5} + \frac {100 B a^{3} b^{3} d^{2} e^{4}}{3} + \frac {100 B a^{2} b^{4} d^{3} e^{3}}{3} + 10 B a b^{5} d^{4} e^{2} + \frac {2 B b^{6} d^{5} e}{3}\right ) + x^{8} \cdot \left (\frac {3 A a^{5} b e^{6}}{4} + \frac {45 A a^{4} b^{2} d e^{5}}{4} + \frac {75 A a^{3} b^{3} d^{2} e^{4}}{2} + \frac {75 A a^{2} b^{4} d^{3} e^{3}}{2} + \frac {45 A a b^{5} d^{4} e^{2}}{4} + \frac {3 A b^{6} d^{5} e}{4} + \frac {B a^{6} e^{6}}{8} + \frac {9 B a^{5} b d e^{5}}{2} + \frac {225 B a^{4} b^{2} d^{2} e^{4}}{8} + 50 B a^{3} b^{3} d^{3} e^{3} + \frac {225 B a^{2} b^{4} d^{4} e^{2}}{8} + \frac {9 B a b^{5} d^{5} e}{2} + \frac {B b^{6} d^{6}}{8}\right ) + x^{7} \left (\frac {A a^{6} e^{6}}{7} + \frac {36 A a^{5} b d e^{5}}{7} + \frac {225 A a^{4} b^{2} d^{2} e^{4}}{7} + \frac {400 A a^{3} b^{3} d^{3} e^{3}}{7} + \frac {225 A a^{2} b^{4} d^{4} e^{2}}{7} + \frac {36 A a b^{5} d^{5} e}{7} + \frac {A b^{6} d^{6}}{7} + \frac {6 B a^{6} d e^{5}}{7} + \frac {90 B a^{5} b d^{2} e^{4}}{7} + \frac {300 B a^{4} b^{2} d^{3} e^{3}}{7} + \frac {300 B a^{3} b^{3} d^{4} e^{2}}{7} + \frac {90 B a^{2} b^{4} d^{5} e}{7} + \frac {6 B a b^{5} d^{6}}{7}\right ) + x^{6} \left (A a^{6} d e^{5} + 15 A a^{5} b d^{2} e^{4} + 50 A a^{4} b^{2} d^{3} e^{3} + 50 A a^{3} b^{3} d^{4} e^{2} + 15 A a^{2} b^{4} d^{5} e + A a b^{5} d^{6} + \frac {5 B a^{6} d^{2} e^{4}}{2} + 20 B a^{5} b d^{3} e^{3} + \frac {75 B a^{4} b^{2} d^{4} e^{2}}{2} + 20 B a^{3} b^{3} d^{5} e + \frac {5 B a^{2} b^{4} d^{6}}{2}\right ) + x^{5} \cdot \left (3 A a^{6} d^{2} e^{4} + 24 A a^{5} b d^{3} e^{3} + 45 A a^{4} b^{2} d^{4} e^{2} + 24 A a^{3} b^{3} d^{5} e + 3 A a^{2} b^{4} d^{6} + 4 B a^{6} d^{3} e^{3} + 18 B a^{5} b d^{4} e^{2} + 18 B a^{4} b^{2} d^{5} e + 4 B a^{3} b^{3} d^{6}\right ) + x^{4} \cdot \left (5 A a^{6} d^{3} e^{3} + \frac {45 A a^{5} b d^{4} e^{2}}{2} + \frac {45 A a^{4} b^{2} d^{5} e}{2} + 5 A a^{3} b^{3} d^{6} + \frac {15 B a^{6} d^{4} e^{2}}{4} + 9 B a^{5} b d^{5} e + \frac {15 B a^{4} b^{2} d^{6}}{4}\right ) + x^{3} \cdot \left (5 A a^{6} d^{4} e^{2} + 12 A a^{5} b d^{5} e + 5 A a^{4} b^{2} d^{6} + 2 B a^{6} d^{5} e + 2 B a^{5} b d^{6}\right ) + x^{2} \cdot \left (3 A a^{6} d^{5} e + 3 A a^{5} b d^{6} + \frac {B a^{6} d^{6}}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**6*(B*x+A)*(e*x+d)**6,x)

[Out]

A*a**6*d**6*x + B*b**6*e**6*x**14/14 + x**13*(A*b**6*e**6/13 + 6*B*a*b**5*e**6/13 + 6*B*b**6*d*e**5/13) + x**1
2*(A*a*b**5*e**6/2 + A*b**6*d*e**5/2 + 5*B*a**2*b**4*e**6/4 + 3*B*a*b**5*d*e**5 + 5*B*b**6*d**2*e**4/4) + x**1
1*(15*A*a**2*b**4*e**6/11 + 36*A*a*b**5*d*e**5/11 + 15*A*b**6*d**2*e**4/11 + 20*B*a**3*b**3*e**6/11 + 90*B*a**
2*b**4*d*e**5/11 + 90*B*a*b**5*d**2*e**4/11 + 20*B*b**6*d**3*e**3/11) + x**10*(2*A*a**3*b**3*e**6 + 9*A*a**2*b
**4*d*e**5 + 9*A*a*b**5*d**2*e**4 + 2*A*b**6*d**3*e**3 + 3*B*a**4*b**2*e**6/2 + 12*B*a**3*b**3*d*e**5 + 45*B*a
**2*b**4*d**2*e**4/2 + 12*B*a*b**5*d**3*e**3 + 3*B*b**6*d**4*e**2/2) + x**9*(5*A*a**4*b**2*e**6/3 + 40*A*a**3*
b**3*d*e**5/3 + 25*A*a**2*b**4*d**2*e**4 + 40*A*a*b**5*d**3*e**3/3 + 5*A*b**6*d**4*e**2/3 + 2*B*a**5*b*e**6/3
+ 10*B*a**4*b**2*d*e**5 + 100*B*a**3*b**3*d**2*e**4/3 + 100*B*a**2*b**4*d**3*e**3/3 + 10*B*a*b**5*d**4*e**2 +
2*B*b**6*d**5*e/3) + x**8*(3*A*a**5*b*e**6/4 + 45*A*a**4*b**2*d*e**5/4 + 75*A*a**3*b**3*d**2*e**4/2 + 75*A*a**
2*b**4*d**3*e**3/2 + 45*A*a*b**5*d**4*e**2/4 + 3*A*b**6*d**5*e/4 + B*a**6*e**6/8 + 9*B*a**5*b*d*e**5/2 + 225*B
*a**4*b**2*d**2*e**4/8 + 50*B*a**3*b**3*d**3*e**3 + 225*B*a**2*b**4*d**4*e**2/8 + 9*B*a*b**5*d**5*e/2 + B*b**6
*d**6/8) + x**7*(A*a**6*e**6/7 + 36*A*a**5*b*d*e**5/7 + 225*A*a**4*b**2*d**2*e**4/7 + 400*A*a**3*b**3*d**3*e**
3/7 + 225*A*a**2*b**4*d**4*e**2/7 + 36*A*a*b**5*d**5*e/7 + A*b**6*d**6/7 + 6*B*a**6*d*e**5/7 + 90*B*a**5*b*d**
2*e**4/7 + 300*B*a**4*b**2*d**3*e**3/7 + 300*B*a**3*b**3*d**4*e**2/7 + 90*B*a**2*b**4*d**5*e/7 + 6*B*a*b**5*d*
*6/7) + x**6*(A*a**6*d*e**5 + 15*A*a**5*b*d**2*e**4 + 50*A*a**4*b**2*d**3*e**3 + 50*A*a**3*b**3*d**4*e**2 + 15
*A*a**2*b**4*d**5*e + A*a*b**5*d**6 + 5*B*a**6*d**2*e**4/2 + 20*B*a**5*b*d**3*e**3 + 75*B*a**4*b**2*d**4*e**2/
2 + 20*B*a**3*b**3*d**5*e + 5*B*a**2*b**4*d**6/2) + x**5*(3*A*a**6*d**2*e**4 + 24*A*a**5*b*d**3*e**3 + 45*A*a*
*4*b**2*d**4*e**2 + 24*A*a**3*b**3*d**5*e + 3*A*a**2*b**4*d**6 + 4*B*a**6*d**3*e**3 + 18*B*a**5*b*d**4*e**2 +
18*B*a**4*b**2*d**5*e + 4*B*a**3*b**3*d**6) + x**4*(5*A*a**6*d**3*e**3 + 45*A*a**5*b*d**4*e**2/2 + 45*A*a**4*b
**2*d**5*e/2 + 5*A*a**3*b**3*d**6 + 15*B*a**6*d**4*e**2/4 + 9*B*a**5*b*d**5*e + 15*B*a**4*b**2*d**6/4) + x**3*
(5*A*a**6*d**4*e**2 + 12*A*a**5*b*d**5*e + 5*A*a**4*b**2*d**6 + 2*B*a**6*d**5*e + 2*B*a**5*b*d**6) + x**2*(3*A
*a**6*d**5*e + 3*A*a**5*b*d**6 + B*a**6*d**6/2)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1424 vs. \(2 (288) = 576\).
time = 2.49, size = 1424, normalized size = 4.91 \begin {gather*} \frac {1}{14} \, B b^{6} x^{14} e^{6} + \frac {6}{13} \, B b^{6} d x^{13} e^{5} + \frac {5}{4} \, B b^{6} d^{2} x^{12} e^{4} + \frac {20}{11} \, B b^{6} d^{3} x^{11} e^{3} + \frac {3}{2} \, B b^{6} d^{4} x^{10} e^{2} + \frac {2}{3} \, B b^{6} d^{5} x^{9} e + \frac {1}{8} \, B b^{6} d^{6} x^{8} + \frac {6}{13} \, B a b^{5} x^{13} e^{6} + \frac {1}{13} \, A b^{6} x^{13} e^{6} + 3 \, B a b^{5} d x^{12} e^{5} + \frac {1}{2} \, A b^{6} d x^{12} e^{5} + \frac {90}{11} \, B a b^{5} d^{2} x^{11} e^{4} + \frac {15}{11} \, A b^{6} d^{2} x^{11} e^{4} + 12 \, B a b^{5} d^{3} x^{10} e^{3} + 2 \, A b^{6} d^{3} x^{10} e^{3} + 10 \, B a b^{5} d^{4} x^{9} e^{2} + \frac {5}{3} \, A b^{6} d^{4} x^{9} e^{2} + \frac {9}{2} \, B a b^{5} d^{5} x^{8} e + \frac {3}{4} \, A b^{6} d^{5} x^{8} e + \frac {6}{7} \, B a b^{5} d^{6} x^{7} + \frac {1}{7} \, A b^{6} d^{6} x^{7} + \frac {5}{4} \, B a^{2} b^{4} x^{12} e^{6} + \frac {1}{2} \, A a b^{5} x^{12} e^{6} + \frac {90}{11} \, B a^{2} b^{4} d x^{11} e^{5} + \frac {36}{11} \, A a b^{5} d x^{11} e^{5} + \frac {45}{2} \, B a^{2} b^{4} d^{2} x^{10} e^{4} + 9 \, A a b^{5} d^{2} x^{10} e^{4} + \frac {100}{3} \, B a^{2} b^{4} d^{3} x^{9} e^{3} + \frac {40}{3} \, A a b^{5} d^{3} x^{9} e^{3} + \frac {225}{8} \, B a^{2} b^{4} d^{4} x^{8} e^{2} + \frac {45}{4} \, A a b^{5} d^{4} x^{8} e^{2} + \frac {90}{7} \, B a^{2} b^{4} d^{5} x^{7} e + \frac {36}{7} \, A a b^{5} d^{5} x^{7} e + \frac {5}{2} \, B a^{2} b^{4} d^{6} x^{6} + A a b^{5} d^{6} x^{6} + \frac {20}{11} \, B a^{3} b^{3} x^{11} e^{6} + \frac {15}{11} \, A a^{2} b^{4} x^{11} e^{6} + 12 \, B a^{3} b^{3} d x^{10} e^{5} + 9 \, A a^{2} b^{4} d x^{10} e^{5} + \frac {100}{3} \, B a^{3} b^{3} d^{2} x^{9} e^{4} + 25 \, A a^{2} b^{4} d^{2} x^{9} e^{4} + 50 \, B a^{3} b^{3} d^{3} x^{8} e^{3} + \frac {75}{2} \, A a^{2} b^{4} d^{3} x^{8} e^{3} + \frac {300}{7} \, B a^{3} b^{3} d^{4} x^{7} e^{2} + \frac {225}{7} \, A a^{2} b^{4} d^{4} x^{7} e^{2} + 20 \, B a^{3} b^{3} d^{5} x^{6} e + 15 \, A a^{2} b^{4} d^{5} x^{6} e + 4 \, B a^{3} b^{3} d^{6} x^{5} + 3 \, A a^{2} b^{4} d^{6} x^{5} + \frac {3}{2} \, B a^{4} b^{2} x^{10} e^{6} + 2 \, A a^{3} b^{3} x^{10} e^{6} + 10 \, B a^{4} b^{2} d x^{9} e^{5} + \frac {40}{3} \, A a^{3} b^{3} d x^{9} e^{5} + \frac {225}{8} \, B a^{4} b^{2} d^{2} x^{8} e^{4} + \frac {75}{2} \, A a^{3} b^{3} d^{2} x^{8} e^{4} + \frac {300}{7} \, B a^{4} b^{2} d^{3} x^{7} e^{3} + \frac {400}{7} \, A a^{3} b^{3} d^{3} x^{7} e^{3} + \frac {75}{2} \, B a^{4} b^{2} d^{4} x^{6} e^{2} + 50 \, A a^{3} b^{3} d^{4} x^{6} e^{2} + 18 \, B a^{4} b^{2} d^{5} x^{5} e + 24 \, A a^{3} b^{3} d^{5} x^{5} e + \frac {15}{4} \, B a^{4} b^{2} d^{6} x^{4} + 5 \, A a^{3} b^{3} d^{6} x^{4} + \frac {2}{3} \, B a^{5} b x^{9} e^{6} + \frac {5}{3} \, A a^{4} b^{2} x^{9} e^{6} + \frac {9}{2} \, B a^{5} b d x^{8} e^{5} + \frac {45}{4} \, A a^{4} b^{2} d x^{8} e^{5} + \frac {90}{7} \, B a^{5} b d^{2} x^{7} e^{4} + \frac {225}{7} \, A a^{4} b^{2} d^{2} x^{7} e^{4} + 20 \, B a^{5} b d^{3} x^{6} e^{3} + 50 \, A a^{4} b^{2} d^{3} x^{6} e^{3} + 18 \, B a^{5} b d^{4} x^{5} e^{2} + 45 \, A a^{4} b^{2} d^{4} x^{5} e^{2} + 9 \, B a^{5} b d^{5} x^{4} e + \frac {45}{2} \, A a^{4} b^{2} d^{5} x^{4} e + 2 \, B a^{5} b d^{6} x^{3} + 5 \, A a^{4} b^{2} d^{6} x^{3} + \frac {1}{8} \, B a^{6} x^{8} e^{6} + \frac {3}{4} \, A a^{5} b x^{8} e^{6} + \frac {6}{7} \, B a^{6} d x^{7} e^{5} + \frac {36}{7} \, A a^{5} b d x^{7} e^{5} + \frac {5}{2} \, B a^{6} d^{2} x^{6} e^{4} + 15 \, A a^{5} b d^{2} x^{6} e^{4} + 4 \, B a^{6} d^{3} x^{5} e^{3} + 24 \, A a^{5} b d^{3} x^{5} e^{3} + \frac {15}{4} \, B a^{6} d^{4} x^{4} e^{2} + \frac {45}{2} \, A a^{5} b d^{4} x^{4} e^{2} + 2 \, B a^{6} d^{5} x^{3} e + 12 \, A a^{5} b d^{5} x^{3} e + \frac {1}{2} \, B a^{6} d^{6} x^{2} + 3 \, A a^{5} b d^{6} x^{2} + \frac {1}{7} \, A a^{6} x^{7} e^{6} + A a^{6} d x^{6} e^{5} + 3 \, A a^{6} d^{2} x^{5} e^{4} + 5 \, A a^{6} d^{3} x^{4} e^{3} + 5 \, A a^{6} d^{4} x^{3} e^{2} + 3 \, A a^{6} d^{5} x^{2} e + A a^{6} d^{6} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^6,x, algorithm="giac")

[Out]

1/14*B*b^6*x^14*e^6 + 6/13*B*b^6*d*x^13*e^5 + 5/4*B*b^6*d^2*x^12*e^4 + 20/11*B*b^6*d^3*x^11*e^3 + 3/2*B*b^6*d^
4*x^10*e^2 + 2/3*B*b^6*d^5*x^9*e + 1/8*B*b^6*d^6*x^8 + 6/13*B*a*b^5*x^13*e^6 + 1/13*A*b^6*x^13*e^6 + 3*B*a*b^5
*d*x^12*e^5 + 1/2*A*b^6*d*x^12*e^5 + 90/11*B*a*b^5*d^2*x^11*e^4 + 15/11*A*b^6*d^2*x^11*e^4 + 12*B*a*b^5*d^3*x^
10*e^3 + 2*A*b^6*d^3*x^10*e^3 + 10*B*a*b^5*d^4*x^9*e^2 + 5/3*A*b^6*d^4*x^9*e^2 + 9/2*B*a*b^5*d^5*x^8*e + 3/4*A
*b^6*d^5*x^8*e + 6/7*B*a*b^5*d^6*x^7 + 1/7*A*b^6*d^6*x^7 + 5/4*B*a^2*b^4*x^12*e^6 + 1/2*A*a*b^5*x^12*e^6 + 90/
11*B*a^2*b^4*d*x^11*e^5 + 36/11*A*a*b^5*d*x^11*e^5 + 45/2*B*a^2*b^4*d^2*x^10*e^4 + 9*A*a*b^5*d^2*x^10*e^4 + 10
0/3*B*a^2*b^4*d^3*x^9*e^3 + 40/3*A*a*b^5*d^3*x^9*e^3 + 225/8*B*a^2*b^4*d^4*x^8*e^2 + 45/4*A*a*b^5*d^4*x^8*e^2
+ 90/7*B*a^2*b^4*d^5*x^7*e + 36/7*A*a*b^5*d^5*x^7*e + 5/2*B*a^2*b^4*d^6*x^6 + A*a*b^5*d^6*x^6 + 20/11*B*a^3*b^
3*x^11*e^6 + 15/11*A*a^2*b^4*x^11*e^6 + 12*B*a^3*b^3*d*x^10*e^5 + 9*A*a^2*b^4*d*x^10*e^5 + 100/3*B*a^3*b^3*d^2
*x^9*e^4 + 25*A*a^2*b^4*d^2*x^9*e^4 + 50*B*a^3*b^3*d^3*x^8*e^3 + 75/2*A*a^2*b^4*d^3*x^8*e^3 + 300/7*B*a^3*b^3*
d^4*x^7*e^2 + 225/7*A*a^2*b^4*d^4*x^7*e^2 + 20*B*a^3*b^3*d^5*x^6*e + 15*A*a^2*b^4*d^5*x^6*e + 4*B*a^3*b^3*d^6*
x^5 + 3*A*a^2*b^4*d^6*x^5 + 3/2*B*a^4*b^2*x^10*e^6 + 2*A*a^3*b^3*x^10*e^6 + 10*B*a^4*b^2*d*x^9*e^5 + 40/3*A*a^
3*b^3*d*x^9*e^5 + 225/8*B*a^4*b^2*d^2*x^8*e^4 + 75/2*A*a^3*b^3*d^2*x^8*e^4 + 300/7*B*a^4*b^2*d^3*x^7*e^3 + 400
/7*A*a^3*b^3*d^3*x^7*e^3 + 75/2*B*a^4*b^2*d^4*x^6*e^2 + 50*A*a^3*b^3*d^4*x^6*e^2 + 18*B*a^4*b^2*d^5*x^5*e + 24
*A*a^3*b^3*d^5*x^5*e + 15/4*B*a^4*b^2*d^6*x^4 + 5*A*a^3*b^3*d^6*x^4 + 2/3*B*a^5*b*x^9*e^6 + 5/3*A*a^4*b^2*x^9*
e^6 + 9/2*B*a^5*b*d*x^8*e^5 + 45/4*A*a^4*b^2*d*x^8*e^5 + 90/7*B*a^5*b*d^2*x^7*e^4 + 225/7*A*a^4*b^2*d^2*x^7*e^
4 + 20*B*a^5*b*d^3*x^6*e^3 + 50*A*a^4*b^2*d^3*x^6*e^3 + 18*B*a^5*b*d^4*x^5*e^2 + 45*A*a^4*b^2*d^4*x^5*e^2 + 9*
B*a^5*b*d^5*x^4*e + 45/2*A*a^4*b^2*d^5*x^4*e + 2*B*a^5*b*d^6*x^3 + 5*A*a^4*b^2*d^6*x^3 + 1/8*B*a^6*x^8*e^6 + 3
/4*A*a^5*b*x^8*e^6 + 6/7*B*a^6*d*x^7*e^5 + 36/7*A*a^5*b*d*x^7*e^5 + 5/2*B*a^6*d^2*x^6*e^4 + 15*A*a^5*b*d^2*x^6
*e^4 + 4*B*a^6*d^3*x^5*e^3 + 24*A*a^5*b*d^3*x^5*e^3 + 15/4*B*a^6*d^4*x^4*e^2 + 45/2*A*a^5*b*d^4*x^4*e^2 + 2*B*
a^6*d^5*x^3*e + 12*A*a^5*b*d^5*x^3*e + 1/2*B*a^6*d^6*x^2 + 3*A*a^5*b*d^6*x^2 + 1/7*A*a^6*x^7*e^6 + A*a^6*d*x^6
*e^5 + 3*A*a^6*d^2*x^5*e^4 + 5*A*a^6*d^3*x^4*e^3 + 5*A*a^6*d^4*x^3*e^2 + 3*A*a^6*d^5*x^2*e + A*a^6*d^6*x

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Mupad [B]
time = 1.39, size = 1221, normalized size = 4.21 \begin {gather*} x^5\,\left (4\,B\,a^6\,d^3\,e^3+3\,A\,a^6\,d^2\,e^4+18\,B\,a^5\,b\,d^4\,e^2+24\,A\,a^5\,b\,d^3\,e^3+18\,B\,a^4\,b^2\,d^5\,e+45\,A\,a^4\,b^2\,d^4\,e^2+4\,B\,a^3\,b^3\,d^6+24\,A\,a^3\,b^3\,d^5\,e+3\,A\,a^2\,b^4\,d^6\right )+x^{10}\,\left (\frac {3\,B\,a^4\,b^2\,e^6}{2}+12\,B\,a^3\,b^3\,d\,e^5+2\,A\,a^3\,b^3\,e^6+\frac {45\,B\,a^2\,b^4\,d^2\,e^4}{2}+9\,A\,a^2\,b^4\,d\,e^5+12\,B\,a\,b^5\,d^3\,e^3+9\,A\,a\,b^5\,d^2\,e^4+\frac {3\,B\,b^6\,d^4\,e^2}{2}+2\,A\,b^6\,d^3\,e^3\right )+x^6\,\left (\frac {5\,B\,a^6\,d^2\,e^4}{2}+A\,a^6\,d\,e^5+20\,B\,a^5\,b\,d^3\,e^3+15\,A\,a^5\,b\,d^2\,e^4+\frac {75\,B\,a^4\,b^2\,d^4\,e^2}{2}+50\,A\,a^4\,b^2\,d^3\,e^3+20\,B\,a^3\,b^3\,d^5\,e+50\,A\,a^3\,b^3\,d^4\,e^2+\frac {5\,B\,a^2\,b^4\,d^6}{2}+15\,A\,a^2\,b^4\,d^5\,e+A\,a\,b^5\,d^6\right )+x^9\,\left (\frac {2\,B\,a^5\,b\,e^6}{3}+10\,B\,a^4\,b^2\,d\,e^5+\frac {5\,A\,a^4\,b^2\,e^6}{3}+\frac {100\,B\,a^3\,b^3\,d^2\,e^4}{3}+\frac {40\,A\,a^3\,b^3\,d\,e^5}{3}+\frac {100\,B\,a^2\,b^4\,d^3\,e^3}{3}+25\,A\,a^2\,b^4\,d^2\,e^4+10\,B\,a\,b^5\,d^4\,e^2+\frac {40\,A\,a\,b^5\,d^3\,e^3}{3}+\frac {2\,B\,b^6\,d^5\,e}{3}+\frac {5\,A\,b^6\,d^4\,e^2}{3}\right )+x^7\,\left (\frac {6\,B\,a^6\,d\,e^5}{7}+\frac {A\,a^6\,e^6}{7}+\frac {90\,B\,a^5\,b\,d^2\,e^4}{7}+\frac {36\,A\,a^5\,b\,d\,e^5}{7}+\frac {300\,B\,a^4\,b^2\,d^3\,e^3}{7}+\frac {225\,A\,a^4\,b^2\,d^2\,e^4}{7}+\frac {300\,B\,a^3\,b^3\,d^4\,e^2}{7}+\frac {400\,A\,a^3\,b^3\,d^3\,e^3}{7}+\frac {90\,B\,a^2\,b^4\,d^5\,e}{7}+\frac {225\,A\,a^2\,b^4\,d^4\,e^2}{7}+\frac {6\,B\,a\,b^5\,d^6}{7}+\frac {36\,A\,a\,b^5\,d^5\,e}{7}+\frac {A\,b^6\,d^6}{7}\right )+x^4\,\left (\frac {15\,B\,a^6\,d^4\,e^2}{4}+5\,A\,a^6\,d^3\,e^3+9\,B\,a^5\,b\,d^5\,e+\frac {45\,A\,a^5\,b\,d^4\,e^2}{2}+\frac {15\,B\,a^4\,b^2\,d^6}{4}+\frac {45\,A\,a^4\,b^2\,d^5\,e}{2}+5\,A\,a^3\,b^3\,d^6\right )+x^8\,\left (\frac {B\,a^6\,e^6}{8}+\frac {9\,B\,a^5\,b\,d\,e^5}{2}+\frac {3\,A\,a^5\,b\,e^6}{4}+\frac {225\,B\,a^4\,b^2\,d^2\,e^4}{8}+\frac {45\,A\,a^4\,b^2\,d\,e^5}{4}+50\,B\,a^3\,b^3\,d^3\,e^3+\frac {75\,A\,a^3\,b^3\,d^2\,e^4}{2}+\frac {225\,B\,a^2\,b^4\,d^4\,e^2}{8}+\frac {75\,A\,a^2\,b^4\,d^3\,e^3}{2}+\frac {9\,B\,a\,b^5\,d^5\,e}{2}+\frac {45\,A\,a\,b^5\,d^4\,e^2}{4}+\frac {B\,b^6\,d^6}{8}+\frac {3\,A\,b^6\,d^5\,e}{4}\right )+x^{11}\,\left (\frac {20\,B\,a^3\,b^3\,e^6}{11}+\frac {90\,B\,a^2\,b^4\,d\,e^5}{11}+\frac {15\,A\,a^2\,b^4\,e^6}{11}+\frac {90\,B\,a\,b^5\,d^2\,e^4}{11}+\frac {36\,A\,a\,b^5\,d\,e^5}{11}+\frac {20\,B\,b^6\,d^3\,e^3}{11}+\frac {15\,A\,b^6\,d^2\,e^4}{11}\right )+\frac {a^5\,d^5\,x^2\,\left (6\,A\,a\,e+6\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^5\,e^5\,x^{13}\,\left (A\,b\,e+6\,B\,a\,e+6\,B\,b\,d\right )}{13}+A\,a^6\,d^6\,x+a^4\,d^4\,x^3\,\left (2\,B\,a^2\,d\,e+5\,A\,a^2\,e^2+2\,B\,a\,b\,d^2+12\,A\,a\,b\,d\,e+5\,A\,b^2\,d^2\right )+\frac {b^4\,e^4\,x^{12}\,\left (5\,B\,a^2\,e^2+12\,B\,a\,b\,d\,e+2\,A\,a\,b\,e^2+5\,B\,b^2\,d^2+2\,A\,b^2\,d\,e\right )}{4}+\frac {B\,b^6\,e^6\,x^{14}}{14} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^5*(3*A*a^2*b^4*d^6 + 4*B*a^3*b^3*d^6 + 3*A*a^6*d^2*e^4 + 4*B*a^6*d^3*e^3 + 24*A*a^3*b^3*d^5*e + 24*A*a^5*b*d
^3*e^3 + 18*B*a^4*b^2*d^5*e + 18*B*a^5*b*d^4*e^2 + 45*A*a^4*b^2*d^4*e^2) + x^10*(2*A*a^3*b^3*e^6 + (3*B*a^4*b^
2*e^6)/2 + 2*A*b^6*d^3*e^3 + (3*B*b^6*d^4*e^2)/2 + 9*A*a*b^5*d^2*e^4 + 9*A*a^2*b^4*d*e^5 + 12*B*a*b^5*d^3*e^3
+ 12*B*a^3*b^3*d*e^5 + (45*B*a^2*b^4*d^2*e^4)/2) + x^6*(A*a*b^5*d^6 + A*a^6*d*e^5 + (5*B*a^2*b^4*d^6)/2 + (5*B
*a^6*d^2*e^4)/2 + 15*A*a^2*b^4*d^5*e + 15*A*a^5*b*d^2*e^4 + 20*B*a^3*b^3*d^5*e + 20*B*a^5*b*d^3*e^3 + 50*A*a^3
*b^3*d^4*e^2 + 50*A*a^4*b^2*d^3*e^3 + (75*B*a^4*b^2*d^4*e^2)/2) + x^9*((2*B*a^5*b*e^6)/3 + (2*B*b^6*d^5*e)/3 +
(5*A*a^4*b^2*e^6)/3 + (5*A*b^6*d^4*e^2)/3 + (40*A*a*b^5*d^3*e^3)/3 + (40*A*a^3*b^3*d*e^5)/3 + 10*B*a*b^5*d^4*
e^2 + 10*B*a^4*b^2*d*e^5 + 25*A*a^2*b^4*d^2*e^4 + (100*B*a^2*b^4*d^3*e^3)/3 + (100*B*a^3*b^3*d^2*e^4)/3) + x^7
*((A*a^6*e^6)/7 + (A*b^6*d^6)/7 + (6*B*a*b^5*d^6)/7 + (6*B*a^6*d*e^5)/7 + (90*B*a^2*b^4*d^5*e)/7 + (90*B*a^5*b
*d^2*e^4)/7 + (225*A*a^2*b^4*d^4*e^2)/7 + (400*A*a^3*b^3*d^3*e^3)/7 + (225*A*a^4*b^2*d^2*e^4)/7 + (300*B*a^3*b
^3*d^4*e^2)/7 + (300*B*a^4*b^2*d^3*e^3)/7 + (36*A*a*b^5*d^5*e)/7 + (36*A*a^5*b*d*e^5)/7) + x^4*(5*A*a^3*b^3*d^
6 + (15*B*a^4*b^2*d^6)/4 + 5*A*a^6*d^3*e^3 + (15*B*a^6*d^4*e^2)/4 + (45*A*a^4*b^2*d^5*e)/2 + (45*A*a^5*b*d^4*e
^2)/2 + 9*B*a^5*b*d^5*e) + x^8*((B*a^6*e^6)/8 + (B*b^6*d^6)/8 + (3*A*a^5*b*e^6)/4 + (3*A*b^6*d^5*e)/4 + (45*A*
a*b^5*d^4*e^2)/4 + (45*A*a^4*b^2*d*e^5)/4 + (75*A*a^2*b^4*d^3*e^3)/2 + (75*A*a^3*b^3*d^2*e^4)/2 + (225*B*a^2*b
^4*d^4*e^2)/8 + 50*B*a^3*b^3*d^3*e^3 + (225*B*a^4*b^2*d^2*e^4)/8 + (9*B*a*b^5*d^5*e)/2 + (9*B*a^5*b*d*e^5)/2)
+ x^11*((15*A*a^2*b^4*e^6)/11 + (20*B*a^3*b^3*e^6)/11 + (15*A*b^6*d^2*e^4)/11 + (20*B*b^6*d^3*e^3)/11 + (90*B*
a*b^5*d^2*e^4)/11 + (90*B*a^2*b^4*d*e^5)/11 + (36*A*a*b^5*d*e^5)/11) + (a^5*d^5*x^2*(6*A*a*e + 6*A*b*d + B*a*d
))/2 + (b^5*e^5*x^13*(A*b*e + 6*B*a*e + 6*B*b*d))/13 + A*a^6*d^6*x + a^4*d^4*x^3*(5*A*a^2*e^2 + 5*A*b^2*d^2 +
2*B*a*b*d^2 + 2*B*a^2*d*e + 12*A*a*b*d*e) + (b^4*e^4*x^12*(5*B*a^2*e^2 + 5*B*b^2*d^2 + 2*A*a*b*e^2 + 2*A*b^2*d
*e + 12*B*a*b*d*e))/4 + (B*b^6*e^6*x^14)/14

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