3.1059 \(\int (a+b x)^{10} (A+B x) (d+e x)^{12} \, dx\)

Optimal. Leaf size=464 \[ -\frac{b^9 (d+e x)^{23} (-10 a B e-A b e+11 b B d)}{23 e^{12}}+\frac{5 b^8 (d+e x)^{22} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{22 e^{12}}-\frac{5 b^7 (d+e x)^{21} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{7 e^{12}}+\frac{3 b^6 (d+e x)^{20} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12}}-\frac{42 b^5 (d+e x)^{19} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{19 e^{12}}+\frac{7 b^4 (d+e x)^{18} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{3 e^{12}}-\frac{30 b^3 (d+e x)^{17} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{17 e^{12}}+\frac{15 b^2 (d+e x)^{16} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{16 e^{12}}-\frac{b (d+e x)^{15} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12}}+\frac{(d+e x)^{14} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{14 e^{12}}-\frac{(d+e x)^{13} (b d-a e)^{10} (B d-A e)}{13 e^{12}}+\frac{b^{10} B (d+e x)^{24}}{24 e^{12}} \]

[Out]

-((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^13)/(13*e^12) + ((b*d - a*e)^9*(11*b*B*d
- 10*A*b*e - a*B*e)*(d + e*x)^14)/(14*e^12) - (b*(b*d - a*e)^8*(11*b*B*d - 9*A*b
*e - 2*a*B*e)*(d + e*x)^15)/(3*e^12) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e
- 3*a*B*e)*(d + e*x)^16)/(16*e^12) - (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e
- 4*a*B*e)*(d + e*x)^17)/(17*e^12) + (7*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e -
5*a*B*e)*(d + e*x)^18)/(3*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*
a*B*e)*(d + e*x)^19)/(19*e^12) + (3*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*
B*e)*(d + e*x)^20)/(2*e^12) - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e
)*(d + e*x)^21)/(7*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d
+ e*x)^22)/(22*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^23)/(23*e^12
) + (b^10*B*(d + e*x)^24)/(24*e^12)

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Rubi [A]  time = 20.667, antiderivative size = 464, 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 \[ -\frac{b^9 (d+e x)^{23} (-10 a B e-A b e+11 b B d)}{23 e^{12}}+\frac{5 b^8 (d+e x)^{22} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{22 e^{12}}-\frac{5 b^7 (d+e x)^{21} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{7 e^{12}}+\frac{3 b^6 (d+e x)^{20} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12}}-\frac{42 b^5 (d+e x)^{19} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{19 e^{12}}+\frac{7 b^4 (d+e x)^{18} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{3 e^{12}}-\frac{30 b^3 (d+e x)^{17} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{17 e^{12}}+\frac{15 b^2 (d+e x)^{16} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{16 e^{12}}-\frac{b (d+e x)^{15} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12}}+\frac{(d+e x)^{14} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{14 e^{12}}-\frac{(d+e x)^{13} (b d-a e)^{10} (B d-A e)}{13 e^{12}}+\frac{b^{10} B (d+e x)^{24}}{24 e^{12}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^10*(A + B*x)*(d + e*x)^12,x]

[Out]

-((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^13)/(13*e^12) + ((b*d - a*e)^9*(11*b*B*d
- 10*A*b*e - a*B*e)*(d + e*x)^14)/(14*e^12) - (b*(b*d - a*e)^8*(11*b*B*d - 9*A*b
*e - 2*a*B*e)*(d + e*x)^15)/(3*e^12) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e
- 3*a*B*e)*(d + e*x)^16)/(16*e^12) - (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e
- 4*a*B*e)*(d + e*x)^17)/(17*e^12) + (7*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e -
5*a*B*e)*(d + e*x)^18)/(3*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*
a*B*e)*(d + e*x)^19)/(19*e^12) + (3*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*
B*e)*(d + e*x)^20)/(2*e^12) - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e
)*(d + e*x)^21)/(7*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d
+ e*x)^22)/(22*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^23)/(23*e^12
) + (b^10*B*(d + e*x)^24)/(24*e^12)

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Rubi in Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**10*(B*x+A)*(e*x+d)**12,x)

[Out]

Timed out

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Mathematica [B]  time = 3.09988, size = 3320, normalized size = 7.16 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^12,x]

[Out]

a^10*A*d^12*x + (a^9*d^11*(a*B*d + 2*A*(5*b*d + 6*a*e))*x^2)/2 + (a^8*d^10*(2*a*
B*d*(5*b*d + 6*a*e) + 3*A*(15*b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2))*x^3)/3 + (a^7*
d^9*(3*a*B*d*(15*b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2) + 20*A*(6*b^3*d^3 + 27*a*b^2
*d^2*e + 33*a^2*b*d*e^2 + 11*a^3*e^3))*x^4)/4 + a^6*d^8*(4*a*B*d*(6*b^3*d^3 + 27
*a*b^2*d^2*e + 33*a^2*b*d*e^2 + 11*a^3*e^3) + A*(42*b^4*d^4 + 288*a*b^3*d^3*e +
594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 + 99*a^4*e^4))*x^5 + (a^5*d^7*(5*a*B*d*(42
*b^4*d^4 + 288*a*b^3*d^3*e + 594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 + 99*a^4*e^4)
+ 18*A*(14*b^5*d^5 + 140*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*d^2*e^
3 + 275*a^4*b*d*e^4 + 44*a^5*e^5))*x^6)/6 + (3*a^4*d^6*(6*a*B*d*(14*b^5*d^5 + 14
0*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*d^2*e^3 + 275*a^4*b*d*e^4 + 44
*a^5*e^5) + A*(70*b^6*d^6 + 1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3*b
^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308*a^6*e^6))*x^7)/7 + (3
*a^3*d^5*(a*B*d*(70*b^6*d^6 + 1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3
*b^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308*a^6*e^6) + 8*A*(5*b
^7*d^7 + 105*a*b^6*d^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^4*d^4*e^3 + 2475*a^4
*b^3*d^3*e^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*e^6 + 33*a^7*e^7))*x^8)/8 + (a
^2*d^4*(8*a*B*d*(5*b^7*d^7 + 105*a*b^6*d^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^
4*d^4*e^3 + 2475*a^4*b^3*d^3*e^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*e^6 + 33*a
^7*e^7) + 15*A*(b^8*d^8 + 32*a*b^7*d^7*e + 308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^
5*e^3 + 2310*a^4*b^4*d^4*e^4 + 2112*a^5*b^3*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*
a^7*b*d*e^7 + 11*a^8*e^8))*x^9)/3 + (a*d^3*(9*a*B*d*(b^8*d^8 + 32*a*b^7*d^7*e +
308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^5*e^3 + 2310*a^4*b^4*d^4*e^4 + 2112*a^5*b^3
*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*a^7*b*d*e^7 + 11*a^8*e^8) + 2*A*(b^9*d^9 +
54*a*b^8*d^8*e + 792*a^2*b^7*d^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*
e^4 + 16632*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 3564*a^7*b^2*d^2*e^7 + 495
*a^8*b*d*e^8 + 22*a^9*e^9))*x^10)/2 + (d^2*(10*a*B*d*(b^9*d^9 + 54*a*b^8*d^8*e +
792*a^2*b^7*d^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*e^4 + 16632*a^5*
b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 3564*a^7*b^2*d^2*e^7 + 495*a^8*b*d*e^8 + 2
2*a^9*e^9) + A*(b^10*d^10 + 120*a*b^9*d^9*e + 2970*a^2*b^8*d^8*e^2 + 26400*a^3*b
^7*d^7*e^3 + 103950*a^4*b^6*d^6*e^4 + 199584*a^5*b^5*d^5*e^5 + 194040*a^6*b^4*d^
4*e^6 + 95040*a^7*b^3*d^3*e^7 + 22275*a^8*b^2*d^2*e^8 + 2200*a^9*b*d*e^9 + 66*a^
10*e^10))*x^11)/11 + (d*(6*a^10*e^10*(11*B*d + 2*A*e) + 220*a^9*b*d*e^9*(10*B*d
+ 3*A*e) + 2475*a^8*b^2*d^2*e^8*(9*B*d + 4*A*e) + 11880*a^7*b^3*d^3*e^7*(8*B*d +
5*A*e) + 27720*a^6*b^4*d^4*e^6*(7*B*d + 6*A*e) + 33264*a^5*b^5*d^5*e^5*(6*B*d +
7*A*e) + 20790*a^4*b^6*d^6*e^4*(5*B*d + 8*A*e) + 6600*a^3*b^7*d^7*e^3*(4*B*d +
9*A*e) + 990*a^2*b^8*d^8*e^2*(3*B*d + 10*A*e) + 60*a*b^9*d^9*e*(2*B*d + 11*A*e)
+ b^10*d^10*(B*d + 12*A*e))*x^12)/12 + (e*(a^10*e^10*(12*B*d + A*e) + 60*a^9*b*d
*e^9*(11*B*d + 2*A*e) + 990*a^8*b^2*d^2*e^8*(10*B*d + 3*A*e) + 6600*a^7*b^3*d^3*
e^7*(9*B*d + 4*A*e) + 20790*a^6*b^4*d^4*e^6*(8*B*d + 5*A*e) + 33264*a^5*b^5*d^5*
e^5*(7*B*d + 6*A*e) + 27720*a^4*b^6*d^6*e^4*(6*B*d + 7*A*e) + 11880*a^3*b^7*d^7*
e^3*(5*B*d + 8*A*e) + 2475*a^2*b^8*d^8*e^2*(4*B*d + 9*A*e) + 220*a*b^9*d^9*e*(3*
B*d + 10*A*e) + 6*b^10*d^10*(2*B*d + 11*A*e))*x^13)/13 + (e^2*(a^10*B*e^10 + 10*
a^9*b*e^9*(12*B*d + A*e) + 270*a^8*b^2*d*e^8*(11*B*d + 2*A*e) + 2640*a^7*b^3*d^2
*e^7*(10*B*d + 3*A*e) + 11550*a^6*b^4*d^3*e^6*(9*B*d + 4*A*e) + 24948*a^5*b^5*d^
4*e^5*(8*B*d + 5*A*e) + 27720*a^4*b^6*d^5*e^4*(7*B*d + 6*A*e) + 15840*a^3*b^7*d^
6*e^3*(6*B*d + 7*A*e) + 4455*a^2*b^8*d^7*e^2*(5*B*d + 8*A*e) + 550*a*b^9*d^8*e*(
4*B*d + 9*A*e) + 22*b^10*d^9*(3*B*d + 10*A*e))*x^14)/14 + (b*e^3*(2*a^9*B*e^9 +
9*a^8*b*e^8*(12*B*d + A*e) + 144*a^7*b^2*d*e^7*(11*B*d + 2*A*e) + 924*a^6*b^3*d^
2*e^6*(10*B*d + 3*A*e) + 2772*a^5*b^4*d^3*e^5*(9*B*d + 4*A*e) + 4158*a^4*b^5*d^4
*e^4*(8*B*d + 5*A*e) + 3168*a^3*b^6*d^5*e^3*(7*B*d + 6*A*e) + 1188*a^2*b^7*d^6*e
^2*(6*B*d + 7*A*e) + 198*a*b^8*d^7*e*(5*B*d + 8*A*e) + 11*b^9*d^8*(4*B*d + 9*A*e
))*x^15)/3 + (3*b^2*e^4*(15*a^8*B*e^8 + 40*a^7*b*e^7*(12*B*d + A*e) + 420*a^6*b^
2*d*e^6*(11*B*d + 2*A*e) + 1848*a^5*b^3*d^2*e^5*(10*B*d + 3*A*e) + 3850*a^4*b^4*
d^3*e^4*(9*B*d + 4*A*e) + 3960*a^3*b^5*d^4*e^3*(8*B*d + 5*A*e) + 1980*a^2*b^6*d^
5*e^2*(7*B*d + 6*A*e) + 440*a*b^7*d^6*e*(6*B*d + 7*A*e) + 33*b^8*d^7*(5*B*d + 8*
A*e))*x^16)/16 + (3*b^3*e^5*(40*a^7*B*e^7 + 70*a^6*b*e^6*(12*B*d + A*e) + 504*a^
5*b^2*d*e^5*(11*B*d + 2*A*e) + 1540*a^4*b^3*d^2*e^4*(10*B*d + 3*A*e) + 2200*a^3*
b^4*d^3*e^3*(9*B*d + 4*A*e) + 1485*a^2*b^5*d^4*e^2*(8*B*d + 5*A*e) + 440*a*b^6*d
^5*e*(7*B*d + 6*A*e) + 44*b^7*d^6*(6*B*d + 7*A*e))*x^17)/17 + (b^4*e^6*(70*a^6*B
*e^6 + 84*a^5*b*e^5*(12*B*d + A*e) + 420*a^4*b^2*d*e^4*(11*B*d + 2*A*e) + 880*a^
3*b^3*d^2*e^3*(10*B*d + 3*A*e) + 825*a^2*b^4*d^3*e^2*(9*B*d + 4*A*e) + 330*a*b^5
*d^4*e*(8*B*d + 5*A*e) + 44*b^6*d^5*(7*B*d + 6*A*e))*x^18)/6 + (b^5*e^7*(252*a^5
*B*e^5 + 210*a^4*b*e^4*(12*B*d + A*e) + 720*a^3*b^2*d*e^3*(11*B*d + 2*A*e) + 990
*a^2*b^3*d^2*e^2*(10*B*d + 3*A*e) + 550*a*b^4*d^3*e*(9*B*d + 4*A*e) + 99*b^5*d^4
*(8*B*d + 5*A*e))*x^19)/19 + (b^6*e^8*(42*a^4*B*e^4 + 24*a^3*b*e^3*(12*B*d + A*e
) + 54*a^2*b^2*d*e^2*(11*B*d + 2*A*e) + 44*a*b^3*d^2*e*(10*B*d + 3*A*e) + 11*b^4
*d^3*(9*B*d + 4*A*e))*x^20)/4 + (b^7*e^9*(120*a^3*B*e^3 + 45*a^2*b*e^2*(12*B*d +
A*e) + 60*a*b^2*d*e*(11*B*d + 2*A*e) + 22*b^3*d^2*(10*B*d + 3*A*e))*x^21)/21 +
(b^8*e^10*(45*a^2*B*e^2 + 10*a*b*e*(12*B*d + A*e) + 6*b^2*d*(11*B*d + 2*A*e))*x^
22)/22 + (b^9*e^11*(12*b*B*d + A*b*e + 10*a*B*e)*x^23)/23 + (b^10*B*e^12*x^24)/2
4

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Maple [B]  time = 0.006, size = 3609, normalized size = 7.8 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^10*(B*x+A)*(e*x+d)^12,x)

[Out]

1/24*b^10*B*e^12*x^24+1/23*((A*b^10+10*B*a*b^9)*e^12+12*b^10*B*d*e^11)*x^23+1/22
*((10*A*a*b^9+45*B*a^2*b^8)*e^12+12*(A*b^10+10*B*a*b^9)*d*e^11+66*b^10*B*d^2*e^1
0)*x^22+1/21*((45*A*a^2*b^8+120*B*a^3*b^7)*e^12+12*(10*A*a*b^9+45*B*a^2*b^8)*d*e
^11+66*(A*b^10+10*B*a*b^9)*d^2*e^10+220*b^10*B*d^3*e^9)*x^21+1/20*((120*A*a^3*b^
7+210*B*a^4*b^6)*e^12+12*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^11+66*(10*A*a*b^9+45*B
*a^2*b^8)*d^2*e^10+220*(A*b^10+10*B*a*b^9)*d^3*e^9+495*b^10*B*d^4*e^8)*x^20+1/19
*((210*A*a^4*b^6+252*B*a^5*b^5)*e^12+12*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^11+66*
(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^10+220*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^9+495*
(A*b^10+10*B*a*b^9)*d^4*e^8+792*b^10*B*d^5*e^7)*x^19+1/18*((252*A*a^5*b^5+210*B*
a^6*b^4)*e^12+12*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^11+66*(120*A*a^3*b^7+210*B*a^
4*b^6)*d^2*e^10+220*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^9+495*(10*A*a*b^9+45*B*a^
2*b^8)*d^4*e^8+792*(A*b^10+10*B*a*b^9)*d^5*e^7+924*b^10*B*d^6*e^6)*x^18+1/17*((2
10*A*a^6*b^4+120*B*a^7*b^3)*e^12+12*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^11+66*(210
*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^10+220*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*e^9+495
*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*e^8+792*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e^7+924*
(A*b^10+10*B*a*b^9)*d^6*e^6+792*b^10*B*d^7*e^5)*x^17+1/16*((120*A*a^7*b^3+45*B*a
^8*b^2)*e^12+12*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^11+66*(252*A*a^5*b^5+210*B*a^6
*b^4)*d^2*e^10+220*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^9+495*(120*A*a^3*b^7+210*
B*a^4*b^6)*d^4*e^8+792*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e^7+924*(10*A*a*b^9+45*B
*a^2*b^8)*d^6*e^6+792*(A*b^10+10*B*a*b^9)*d^7*e^5+495*b^10*B*d^8*e^4)*x^16+1/15*
((45*A*a^8*b^2+10*B*a^9*b)*e^12+12*(120*A*a^7*b^3+45*B*a^8*b^2)*d*e^11+66*(210*A
*a^6*b^4+120*B*a^7*b^3)*d^2*e^10+220*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^9+495*(
210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^8+792*(120*A*a^3*b^7+210*B*a^4*b^6)*d^5*e^7+9
24*(45*A*a^2*b^8+120*B*a^3*b^7)*d^6*e^6+792*(10*A*a*b^9+45*B*a^2*b^8)*d^7*e^5+49
5*(A*b^10+10*B*a*b^9)*d^8*e^4+220*b^10*B*d^9*e^3)*x^15+1/14*((10*A*a^9*b+B*a^10)
*e^12+12*(45*A*a^8*b^2+10*B*a^9*b)*d*e^11+66*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^
10+220*(210*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^9+495*(252*A*a^5*b^5+210*B*a^6*b^4)*d
^4*e^8+792*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e^7+924*(120*A*a^3*b^7+210*B*a^4*b^
6)*d^6*e^6+792*(45*A*a^2*b^8+120*B*a^3*b^7)*d^7*e^5+495*(10*A*a*b^9+45*B*a^2*b^8
)*d^8*e^4+220*(A*b^10+10*B*a*b^9)*d^9*e^3+66*b^10*B*d^10*e^2)*x^14+1/13*(a^10*A*
e^12+12*(10*A*a^9*b+B*a^10)*d*e^11+66*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^10+220*(12
0*A*a^7*b^3+45*B*a^8*b^2)*d^3*e^9+495*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^8+792*
(252*A*a^5*b^5+210*B*a^6*b^4)*d^5*e^7+924*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^6+
792*(120*A*a^3*b^7+210*B*a^4*b^6)*d^7*e^5+495*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e
^4+220*(10*A*a*b^9+45*B*a^2*b^8)*d^9*e^3+66*(A*b^10+10*B*a*b^9)*d^10*e^2+12*b^10
*B*d^11*e)*x^13+1/12*(12*a^10*A*d*e^11+66*(10*A*a^9*b+B*a^10)*d^2*e^10+220*(45*A
*a^8*b^2+10*B*a^9*b)*d^3*e^9+495*(120*A*a^7*b^3+45*B*a^8*b^2)*d^4*e^8+792*(210*A
*a^6*b^4+120*B*a^7*b^3)*d^5*e^7+924*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^6+792*(2
10*A*a^4*b^6+252*B*a^5*b^5)*d^7*e^5+495*(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e^4+22
0*(45*A*a^2*b^8+120*B*a^3*b^7)*d^9*e^3+66*(10*A*a*b^9+45*B*a^2*b^8)*d^10*e^2+12*
(A*b^10+10*B*a*b^9)*d^11*e+b^10*B*d^12)*x^12+1/11*(66*a^10*A*d^2*e^10+220*(10*A*
a^9*b+B*a^10)*d^3*e^9+495*(45*A*a^8*b^2+10*B*a^9*b)*d^4*e^8+792*(120*A*a^7*b^3+4
5*B*a^8*b^2)*d^5*e^7+924*(210*A*a^6*b^4+120*B*a^7*b^3)*d^6*e^6+792*(252*A*a^5*b^
5+210*B*a^6*b^4)*d^7*e^5+495*(210*A*a^4*b^6+252*B*a^5*b^5)*d^8*e^4+220*(120*A*a^
3*b^7+210*B*a^4*b^6)*d^9*e^3+66*(45*A*a^2*b^8+120*B*a^3*b^7)*d^10*e^2+12*(10*A*a
*b^9+45*B*a^2*b^8)*d^11*e+(A*b^10+10*B*a*b^9)*d^12)*x^11+1/10*(220*a^10*A*d^3*e^
9+495*(10*A*a^9*b+B*a^10)*d^4*e^8+792*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e^7+924*(120
*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^6+792*(210*A*a^6*b^4+120*B*a^7*b^3)*d^7*e^5+495*(
252*A*a^5*b^5+210*B*a^6*b^4)*d^8*e^4+220*(210*A*a^4*b^6+252*B*a^5*b^5)*d^9*e^3+6
6*(120*A*a^3*b^7+210*B*a^4*b^6)*d^10*e^2+12*(45*A*a^2*b^8+120*B*a^3*b^7)*d^11*e+
(10*A*a*b^9+45*B*a^2*b^8)*d^12)*x^10+1/9*(495*a^10*A*d^4*e^8+792*(10*A*a^9*b+B*a
^10)*d^5*e^7+924*(45*A*a^8*b^2+10*B*a^9*b)*d^6*e^6+792*(120*A*a^7*b^3+45*B*a^8*b
^2)*d^7*e^5+495*(210*A*a^6*b^4+120*B*a^7*b^3)*d^8*e^4+220*(252*A*a^5*b^5+210*B*a
^6*b^4)*d^9*e^3+66*(210*A*a^4*b^6+252*B*a^5*b^5)*d^10*e^2+12*(120*A*a^3*b^7+210*
B*a^4*b^6)*d^11*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^12)*x^9+1/8*(792*a^10*A*d^5*e^7
+924*(10*A*a^9*b+B*a^10)*d^6*e^6+792*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^5+495*(120*
A*a^7*b^3+45*B*a^8*b^2)*d^8*e^4+220*(210*A*a^6*b^4+120*B*a^7*b^3)*d^9*e^3+66*(25
2*A*a^5*b^5+210*B*a^6*b^4)*d^10*e^2+12*(210*A*a^4*b^6+252*B*a^5*b^5)*d^11*e+(120
*A*a^3*b^7+210*B*a^4*b^6)*d^12)*x^8+1/7*(924*a^10*A*d^6*e^6+792*(10*A*a^9*b+B*a^
10)*d^7*e^5+495*(45*A*a^8*b^2+10*B*a^9*b)*d^8*e^4+220*(120*A*a^7*b^3+45*B*a^8*b^
2)*d^9*e^3+66*(210*A*a^6*b^4+120*B*a^7*b^3)*d^10*e^2+12*(252*A*a^5*b^5+210*B*a^6
*b^4)*d^11*e+(210*A*a^4*b^6+252*B*a^5*b^5)*d^12)*x^7+1/6*(792*a^10*A*d^7*e^5+495
*(10*A*a^9*b+B*a^10)*d^8*e^4+220*(45*A*a^8*b^2+10*B*a^9*b)*d^9*e^3+66*(120*A*a^7
*b^3+45*B*a^8*b^2)*d^10*e^2+12*(210*A*a^6*b^4+120*B*a^7*b^3)*d^11*e+(252*A*a^5*b
^5+210*B*a^6*b^4)*d^12)*x^6+1/5*(495*a^10*A*d^8*e^4+220*(10*A*a^9*b+B*a^10)*d^9*
e^3+66*(45*A*a^8*b^2+10*B*a^9*b)*d^10*e^2+12*(120*A*a^7*b^3+45*B*a^8*b^2)*d^11*e
+(210*A*a^6*b^4+120*B*a^7*b^3)*d^12)*x^5+1/4*(220*a^10*A*d^9*e^3+66*(10*A*a^9*b+
B*a^10)*d^10*e^2+12*(45*A*a^8*b^2+10*B*a^9*b)*d^11*e+(120*A*a^7*b^3+45*B*a^8*b^2
)*d^12)*x^4+1/3*(66*a^10*A*d^10*e^2+12*(10*A*a^9*b+B*a^10)*d^11*e+(45*A*a^8*b^2+
10*B*a^9*b)*d^12)*x^3+1/2*(12*a^10*A*d^11*e+(10*A*a^9*b+B*a^10)*d^12)*x^2+a^10*A
*d^12*x

_______________________________________________________________________________________

Maxima [A]  time = 1.42141, size = 4888, normalized size = 10.53 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^12,x, algorithm="maxima")

[Out]

1/24*B*b^10*e^12*x^24 + A*a^10*d^12*x + 1/23*(12*B*b^10*d*e^11 + (10*B*a*b^9 + A
*b^10)*e^12)*x^23 + 1/22*(66*B*b^10*d^2*e^10 + 12*(10*B*a*b^9 + A*b^10)*d*e^11 +
5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^12)*x^22 + 1/21*(220*B*b^10*d^3*e^9 + 66*(10*B*a*
b^9 + A*b^10)*d^2*e^10 + 60*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^11 + 15*(8*B*a^3*b^7 +
3*A*a^2*b^8)*e^12)*x^21 + 1/4*(99*B*b^10*d^4*e^8 + 44*(10*B*a*b^9 + A*b^10)*d^3
*e^9 + 66*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^10 + 36*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*
e^11 + 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^12)*x^20 + 1/19*(792*B*b^10*d^5*e^7 + 495
*(10*B*a*b^9 + A*b^10)*d^4*e^8 + 1100*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^9 + 990*(8
*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^10 + 360*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^11 + 42
*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^12)*x^19 + 1/6*(308*B*b^10*d^6*e^6 + 264*(10*B*a*
b^9 + A*b^10)*d^5*e^7 + 825*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^8 + 1100*(8*B*a^3*b^
7 + 3*A*a^2*b^8)*d^3*e^9 + 660*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^10 + 168*(6*B*a
^5*b^5 + 5*A*a^4*b^6)*d*e^11 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^12)*x^18 + 3/17*
(264*B*b^10*d^7*e^5 + 308*(10*B*a*b^9 + A*b^10)*d^6*e^6 + 1320*(9*B*a^2*b^8 + 2*
A*a*b^9)*d^5*e^7 + 2475*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^8 + 2200*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^3*e^9 + 924*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^10 + 168*(5*B*a^6
*b^4 + 6*A*a^5*b^5)*d*e^11 + 10*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^12)*x^17 + 3/16*(1
65*B*b^10*d^8*e^4 + 264*(10*B*a*b^9 + A*b^10)*d^7*e^5 + 1540*(9*B*a^2*b^8 + 2*A*
a*b^9)*d^6*e^6 + 3960*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^7 + 4950*(7*B*a^4*b^6 +
4*A*a^3*b^7)*d^4*e^8 + 3080*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^9 + 924*(5*B*a^6*b
^4 + 6*A*a^5*b^5)*d^2*e^10 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^11 + 5*(3*B*a^8
*b^2 + 8*A*a^7*b^3)*e^12)*x^16 + 1/3*(44*B*b^10*d^9*e^3 + 99*(10*B*a*b^9 + A*b^1
0)*d^8*e^4 + 792*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^5 + 2772*(8*B*a^3*b^7 + 3*A*a^2
*b^8)*d^6*e^6 + 4752*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^7 + 4158*(6*B*a^5*b^5 + 5
*A*a^4*b^6)*d^4*e^8 + 1848*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^9 + 396*(4*B*a^7*b^
3 + 7*A*a^6*b^4)*d^2*e^10 + 36*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^11 + (2*B*a^9*b +
9*A*a^8*b^2)*e^12)*x^15 + 1/14*(66*B*b^10*d^10*e^2 + 220*(10*B*a*b^9 + A*b^10)*
d^9*e^3 + 2475*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^4 + 11880*(8*B*a^3*b^7 + 3*A*a^2*
b^8)*d^7*e^5 + 27720*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^6 + 33264*(6*B*a^5*b^5 +
5*A*a^4*b^6)*d^5*e^7 + 20790*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^8 + 6600*(4*B*a^7
*b^3 + 7*A*a^6*b^4)*d^3*e^9 + 990*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^10 + 60*(2*B
*a^9*b + 9*A*a^8*b^2)*d*e^11 + (B*a^10 + 10*A*a^9*b)*e^12)*x^14 + 1/13*(12*B*b^1
0*d^11*e + A*a^10*e^12 + 66*(10*B*a*b^9 + A*b^10)*d^10*e^2 + 1100*(9*B*a^2*b^8 +
2*A*a*b^9)*d^9*e^3 + 7425*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^4 + 23760*(7*B*a^4*
b^6 + 4*A*a^3*b^7)*d^7*e^5 + 38808*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^6 + 33264*(
5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^7 + 14850*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^8 +
3300*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^9 + 330*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^
10 + 12*(B*a^10 + 10*A*a^9*b)*d*e^11)*x^13 + 1/12*(B*b^10*d^12 + 12*A*a^10*d*e^1
1 + 12*(10*B*a*b^9 + A*b^10)*d^11*e + 330*(9*B*a^2*b^8 + 2*A*a*b^9)*d^10*e^2 + 3
300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^9*e^3 + 14850*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*
e^4 + 33264*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*e^5 + 38808*(5*B*a^6*b^4 + 6*A*a^5*b
^5)*d^6*e^6 + 23760*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^5*e^7 + 7425*(3*B*a^8*b^2 + 8*
A*a^7*b^3)*d^4*e^8 + 1100*(2*B*a^9*b + 9*A*a^8*b^2)*d^3*e^9 + 66*(B*a^10 + 10*A*
a^9*b)*d^2*e^10)*x^12 + 1/11*(66*A*a^10*d^2*e^10 + (10*B*a*b^9 + A*b^10)*d^12 +
60*(9*B*a^2*b^8 + 2*A*a*b^9)*d^11*e + 990*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10*e^2 +
6600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^9*e^3 + 20790*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^
8*e^4 + 33264*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^7*e^5 + 27720*(4*B*a^7*b^3 + 7*A*a^6
*b^4)*d^6*e^6 + 11880*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*e^7 + 2475*(2*B*a^9*b + 9*
A*a^8*b^2)*d^4*e^8 + 220*(B*a^10 + 10*A*a^9*b)*d^3*e^9)*x^11 + 1/2*(44*A*a^10*d^
3*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^12 + 36*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^11*e +
396*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^10*e^2 + 1848*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^9
*e^3 + 4158*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*e^4 + 4752*(4*B*a^7*b^3 + 7*A*a^6*b^
4)*d^7*e^5 + 2772*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*e^6 + 792*(2*B*a^9*b + 9*A*a^8
*b^2)*d^5*e^7 + 99*(B*a^10 + 10*A*a^9*b)*d^4*e^8)*x^10 + 1/3*(165*A*a^10*d^4*e^8
+ 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^12 + 120*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^11*e +
924*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^10*e^2 + 3080*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^9
*e^3 + 4950*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*e^4 + 3960*(3*B*a^8*b^2 + 8*A*a^7*b^
3)*d^7*e^5 + 1540*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*e^6 + 264*(B*a^10 + 10*A*a^9*b)*
d^5*e^7)*x^9 + 3/8*(264*A*a^10*d^5*e^7 + 10*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^12 + 1
68*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^11*e + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^10*e^2
+ 2200*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^9*e^3 + 2475*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d
^8*e^4 + 1320*(2*B*a^9*b + 9*A*a^8*b^2)*d^7*e^5 + 308*(B*a^10 + 10*A*a^9*b)*d^6*
e^6)*x^8 + 3/7*(308*A*a^10*d^6*e^6 + 14*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^12 + 168*(
5*B*a^6*b^4 + 6*A*a^5*b^5)*d^11*e + 660*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^10*e^2 + 1
100*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^9*e^3 + 825*(2*B*a^9*b + 9*A*a^8*b^2)*d^8*e^4
+ 264*(B*a^10 + 10*A*a^9*b)*d^7*e^5)*x^7 + 1/6*(792*A*a^10*d^7*e^5 + 42*(5*B*a^6
*b^4 + 6*A*a^5*b^5)*d^12 + 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^11*e + 990*(3*B*a^8
*b^2 + 8*A*a^7*b^3)*d^10*e^2 + 1100*(2*B*a^9*b + 9*A*a^8*b^2)*d^9*e^3 + 495*(B*a
^10 + 10*A*a^9*b)*d^8*e^4)*x^6 + (99*A*a^10*d^8*e^4 + 6*(4*B*a^7*b^3 + 7*A*a^6*b
^4)*d^12 + 36*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^11*e + 66*(2*B*a^9*b + 9*A*a^8*b^2)*
d^10*e^2 + 44*(B*a^10 + 10*A*a^9*b)*d^9*e^3)*x^5 + 1/4*(220*A*a^10*d^9*e^3 + 15*
(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^12 + 60*(2*B*a^9*b + 9*A*a^8*b^2)*d^11*e + 66*(B*a
^10 + 10*A*a^9*b)*d^10*e^2)*x^4 + 1/3*(66*A*a^10*d^10*e^2 + 5*(2*B*a^9*b + 9*A*a
^8*b^2)*d^12 + 12*(B*a^10 + 10*A*a^9*b)*d^11*e)*x^3 + 1/2*(12*A*a^10*d^11*e + (B
*a^10 + 10*A*a^9*b)*d^12)*x^2

_______________________________________________________________________________________

Fricas [A]  time = 0.191254, size = 1, normalized size = 0. \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^12,x, algorithm="fricas")

[Out]

1/24*x^24*e^12*b^10*B + 12/23*x^23*e^11*d*b^10*B + 10/23*x^23*e^12*b^9*a*B + 1/2
3*x^23*e^12*b^10*A + 3*x^22*e^10*d^2*b^10*B + 60/11*x^22*e^11*d*b^9*a*B + 45/22*
x^22*e^12*b^8*a^2*B + 6/11*x^22*e^11*d*b^10*A + 5/11*x^22*e^12*b^9*a*A + 220/21*
x^21*e^9*d^3*b^10*B + 220/7*x^21*e^10*d^2*b^9*a*B + 180/7*x^21*e^11*d*b^8*a^2*B
+ 40/7*x^21*e^12*b^7*a^3*B + 22/7*x^21*e^10*d^2*b^10*A + 40/7*x^21*e^11*d*b^9*a*
A + 15/7*x^21*e^12*b^8*a^2*A + 99/4*x^20*e^8*d^4*b^10*B + 110*x^20*e^9*d^3*b^9*a
*B + 297/2*x^20*e^10*d^2*b^8*a^2*B + 72*x^20*e^11*d*b^7*a^3*B + 21/2*x^20*e^12*b
^6*a^4*B + 11*x^20*e^9*d^3*b^10*A + 33*x^20*e^10*d^2*b^9*a*A + 27*x^20*e^11*d*b^
8*a^2*A + 6*x^20*e^12*b^7*a^3*A + 792/19*x^19*e^7*d^5*b^10*B + 4950/19*x^19*e^8*
d^4*b^9*a*B + 9900/19*x^19*e^9*d^3*b^8*a^2*B + 7920/19*x^19*e^10*d^2*b^7*a^3*B +
2520/19*x^19*e^11*d*b^6*a^4*B + 252/19*x^19*e^12*b^5*a^5*B + 495/19*x^19*e^8*d^
4*b^10*A + 2200/19*x^19*e^9*d^3*b^9*a*A + 2970/19*x^19*e^10*d^2*b^8*a^2*A + 1440
/19*x^19*e^11*d*b^7*a^3*A + 210/19*x^19*e^12*b^6*a^4*A + 154/3*x^18*e^6*d^6*b^10
*B + 440*x^18*e^7*d^5*b^9*a*B + 2475/2*x^18*e^8*d^4*b^8*a^2*B + 4400/3*x^18*e^9*
d^3*b^7*a^3*B + 770*x^18*e^10*d^2*b^6*a^4*B + 168*x^18*e^11*d*b^5*a^5*B + 35/3*x
^18*e^12*b^4*a^6*B + 44*x^18*e^7*d^5*b^10*A + 275*x^18*e^8*d^4*b^9*a*A + 550*x^1
8*e^9*d^3*b^8*a^2*A + 440*x^18*e^10*d^2*b^7*a^3*A + 140*x^18*e^11*d*b^6*a^4*A +
14*x^18*e^12*b^5*a^5*A + 792/17*x^17*e^5*d^7*b^10*B + 9240/17*x^17*e^6*d^6*b^9*a
*B + 35640/17*x^17*e^7*d^5*b^8*a^2*B + 59400/17*x^17*e^8*d^4*b^7*a^3*B + 46200/1
7*x^17*e^9*d^3*b^6*a^4*B + 16632/17*x^17*e^10*d^2*b^5*a^5*B + 2520/17*x^17*e^11*
d*b^4*a^6*B + 120/17*x^17*e^12*b^3*a^7*B + 924/17*x^17*e^6*d^6*b^10*A + 7920/17*
x^17*e^7*d^5*b^9*a*A + 22275/17*x^17*e^8*d^4*b^8*a^2*A + 26400/17*x^17*e^9*d^3*b
^7*a^3*A + 13860/17*x^17*e^10*d^2*b^6*a^4*A + 3024/17*x^17*e^11*d*b^5*a^5*A + 21
0/17*x^17*e^12*b^4*a^6*A + 495/16*x^16*e^4*d^8*b^10*B + 495*x^16*e^5*d^7*b^9*a*B
+ 10395/4*x^16*e^6*d^6*b^8*a^2*B + 5940*x^16*e^7*d^5*b^7*a^3*B + 51975/8*x^16*e
^8*d^4*b^6*a^4*B + 3465*x^16*e^9*d^3*b^5*a^5*B + 3465/4*x^16*e^10*d^2*b^4*a^6*B
+ 90*x^16*e^11*d*b^3*a^7*B + 45/16*x^16*e^12*b^2*a^8*B + 99/2*x^16*e^5*d^7*b^10*
A + 1155/2*x^16*e^6*d^6*b^9*a*A + 4455/2*x^16*e^7*d^5*b^8*a^2*A + 7425/2*x^16*e^
8*d^4*b^7*a^3*A + 5775/2*x^16*e^9*d^3*b^6*a^4*A + 2079/2*x^16*e^10*d^2*b^5*a^5*A
+ 315/2*x^16*e^11*d*b^4*a^6*A + 15/2*x^16*e^12*b^3*a^7*A + 44/3*x^15*e^3*d^9*b^
10*B + 330*x^15*e^4*d^8*b^9*a*B + 2376*x^15*e^5*d^7*b^8*a^2*B + 7392*x^15*e^6*d^
6*b^7*a^3*B + 11088*x^15*e^7*d^5*b^6*a^4*B + 8316*x^15*e^8*d^4*b^5*a^5*B + 3080*
x^15*e^9*d^3*b^4*a^6*B + 528*x^15*e^10*d^2*b^3*a^7*B + 36*x^15*e^11*d*b^2*a^8*B
+ 2/3*x^15*e^12*b*a^9*B + 33*x^15*e^4*d^8*b^10*A + 528*x^15*e^5*d^7*b^9*a*A + 27
72*x^15*e^6*d^6*b^8*a^2*A + 6336*x^15*e^7*d^5*b^7*a^3*A + 6930*x^15*e^8*d^4*b^6*
a^4*A + 3696*x^15*e^9*d^3*b^5*a^5*A + 924*x^15*e^10*d^2*b^4*a^6*A + 96*x^15*e^11
*d*b^3*a^7*A + 3*x^15*e^12*b^2*a^8*A + 33/7*x^14*e^2*d^10*b^10*B + 1100/7*x^14*e
^3*d^9*b^9*a*B + 22275/14*x^14*e^4*d^8*b^8*a^2*B + 47520/7*x^14*e^5*d^7*b^7*a^3*
B + 13860*x^14*e^6*d^6*b^6*a^4*B + 14256*x^14*e^7*d^5*b^5*a^5*B + 7425*x^14*e^8*
d^4*b^4*a^6*B + 13200/7*x^14*e^9*d^3*b^3*a^7*B + 1485/7*x^14*e^10*d^2*b^2*a^8*B
+ 60/7*x^14*e^11*d*b*a^9*B + 1/14*x^14*e^12*a^10*B + 110/7*x^14*e^3*d^9*b^10*A +
2475/7*x^14*e^4*d^8*b^9*a*A + 17820/7*x^14*e^5*d^7*b^8*a^2*A + 7920*x^14*e^6*d^
6*b^7*a^3*A + 11880*x^14*e^7*d^5*b^6*a^4*A + 8910*x^14*e^8*d^4*b^5*a^5*A + 3300*
x^14*e^9*d^3*b^4*a^6*A + 3960/7*x^14*e^10*d^2*b^3*a^7*A + 270/7*x^14*e^11*d*b^2*
a^8*A + 5/7*x^14*e^12*b*a^9*A + 12/13*x^13*e*d^11*b^10*B + 660/13*x^13*e^2*d^10*
b^9*a*B + 9900/13*x^13*e^3*d^9*b^8*a^2*B + 59400/13*x^13*e^4*d^8*b^7*a^3*B + 166
320/13*x^13*e^5*d^7*b^6*a^4*B + 232848/13*x^13*e^6*d^6*b^5*a^5*B + 166320/13*x^1
3*e^7*d^5*b^4*a^6*B + 59400/13*x^13*e^8*d^4*b^3*a^7*B + 9900/13*x^13*e^9*d^3*b^2
*a^8*B + 660/13*x^13*e^10*d^2*b*a^9*B + 12/13*x^13*e^11*d*a^10*B + 66/13*x^13*e^
2*d^10*b^10*A + 2200/13*x^13*e^3*d^9*b^9*a*A + 22275/13*x^13*e^4*d^8*b^8*a^2*A +
95040/13*x^13*e^5*d^7*b^7*a^3*A + 194040/13*x^13*e^6*d^6*b^6*a^4*A + 199584/13*
x^13*e^7*d^5*b^5*a^5*A + 103950/13*x^13*e^8*d^4*b^4*a^6*A + 26400/13*x^13*e^9*d^
3*b^3*a^7*A + 2970/13*x^13*e^10*d^2*b^2*a^8*A + 120/13*x^13*e^11*d*b*a^9*A + 1/1
3*x^13*e^12*a^10*A + 1/12*x^12*d^12*b^10*B + 10*x^12*e*d^11*b^9*a*B + 495/2*x^12
*e^2*d^10*b^8*a^2*B + 2200*x^12*e^3*d^9*b^7*a^3*B + 17325/2*x^12*e^4*d^8*b^6*a^4
*B + 16632*x^12*e^5*d^7*b^5*a^5*B + 16170*x^12*e^6*d^6*b^4*a^6*B + 7920*x^12*e^7
*d^5*b^3*a^7*B + 7425/4*x^12*e^8*d^4*b^2*a^8*B + 550/3*x^12*e^9*d^3*b*a^9*B + 11
/2*x^12*e^10*d^2*a^10*B + x^12*e*d^11*b^10*A + 55*x^12*e^2*d^10*b^9*a*A + 825*x^
12*e^3*d^9*b^8*a^2*A + 4950*x^12*e^4*d^8*b^7*a^3*A + 13860*x^12*e^5*d^7*b^6*a^4*
A + 19404*x^12*e^6*d^6*b^5*a^5*A + 13860*x^12*e^7*d^5*b^4*a^6*A + 4950*x^12*e^8*
d^4*b^3*a^7*A + 825*x^12*e^9*d^3*b^2*a^8*A + 55*x^12*e^10*d^2*b*a^9*A + x^12*e^1
1*d*a^10*A + 10/11*x^11*d^12*b^9*a*B + 540/11*x^11*e*d^11*b^8*a^2*B + 720*x^11*e
^2*d^10*b^7*a^3*B + 4200*x^11*e^3*d^9*b^6*a^4*B + 11340*x^11*e^4*d^8*b^5*a^5*B +
15120*x^11*e^5*d^7*b^4*a^6*B + 10080*x^11*e^6*d^6*b^3*a^7*B + 3240*x^11*e^7*d^5
*b^2*a^8*B + 450*x^11*e^8*d^4*b*a^9*B + 20*x^11*e^9*d^3*a^10*B + 1/11*x^11*d^12*
b^10*A + 120/11*x^11*e*d^11*b^9*a*A + 270*x^11*e^2*d^10*b^8*a^2*A + 2400*x^11*e^
3*d^9*b^7*a^3*A + 9450*x^11*e^4*d^8*b^6*a^4*A + 18144*x^11*e^5*d^7*b^5*a^5*A + 1
7640*x^11*e^6*d^6*b^4*a^6*A + 8640*x^11*e^7*d^5*b^3*a^7*A + 2025*x^11*e^8*d^4*b^
2*a^8*A + 200*x^11*e^9*d^3*b*a^9*A + 6*x^11*e^10*d^2*a^10*A + 9/2*x^10*d^12*b^8*
a^2*B + 144*x^10*e*d^11*b^7*a^3*B + 1386*x^10*e^2*d^10*b^6*a^4*B + 5544*x^10*e^3
*d^9*b^5*a^5*B + 10395*x^10*e^4*d^8*b^4*a^6*B + 9504*x^10*e^5*d^7*b^3*a^7*B + 41
58*x^10*e^6*d^6*b^2*a^8*B + 792*x^10*e^7*d^5*b*a^9*B + 99/2*x^10*e^8*d^4*a^10*B
+ x^10*d^12*b^9*a*A + 54*x^10*e*d^11*b^8*a^2*A + 792*x^10*e^2*d^10*b^7*a^3*A + 4
620*x^10*e^3*d^9*b^6*a^4*A + 12474*x^10*e^4*d^8*b^5*a^5*A + 16632*x^10*e^5*d^7*b
^4*a^6*A + 11088*x^10*e^6*d^6*b^3*a^7*A + 3564*x^10*e^7*d^5*b^2*a^8*A + 495*x^10
*e^8*d^4*b*a^9*A + 22*x^10*e^9*d^3*a^10*A + 40/3*x^9*d^12*b^7*a^3*B + 280*x^9*e*
d^11*b^6*a^4*B + 1848*x^9*e^2*d^10*b^5*a^5*B + 15400/3*x^9*e^3*d^9*b^4*a^6*B + 6
600*x^9*e^4*d^8*b^3*a^7*B + 3960*x^9*e^5*d^7*b^2*a^8*B + 3080/3*x^9*e^6*d^6*b*a^
9*B + 88*x^9*e^7*d^5*a^10*B + 5*x^9*d^12*b^8*a^2*A + 160*x^9*e*d^11*b^7*a^3*A +
1540*x^9*e^2*d^10*b^6*a^4*A + 6160*x^9*e^3*d^9*b^5*a^5*A + 11550*x^9*e^4*d^8*b^4
*a^6*A + 10560*x^9*e^5*d^7*b^3*a^7*A + 4620*x^9*e^6*d^6*b^2*a^8*A + 880*x^9*e^7*
d^5*b*a^9*A + 55*x^9*e^8*d^4*a^10*A + 105/4*x^8*d^12*b^6*a^4*B + 378*x^8*e*d^11*
b^5*a^5*B + 3465/2*x^8*e^2*d^10*b^4*a^6*B + 3300*x^8*e^3*d^9*b^3*a^7*B + 22275/8
*x^8*e^4*d^8*b^2*a^8*B + 990*x^8*e^5*d^7*b*a^9*B + 231/2*x^8*e^6*d^6*a^10*B + 15
*x^8*d^12*b^7*a^3*A + 315*x^8*e*d^11*b^6*a^4*A + 2079*x^8*e^2*d^10*b^5*a^5*A + 5
775*x^8*e^3*d^9*b^4*a^6*A + 7425*x^8*e^4*d^8*b^3*a^7*A + 4455*x^8*e^5*d^7*b^2*a^
8*A + 1155*x^8*e^6*d^6*b*a^9*A + 99*x^8*e^7*d^5*a^10*A + 36*x^7*d^12*b^5*a^5*B +
360*x^7*e*d^11*b^4*a^6*B + 7920/7*x^7*e^2*d^10*b^3*a^7*B + 9900/7*x^7*e^3*d^9*b
^2*a^8*B + 4950/7*x^7*e^4*d^8*b*a^9*B + 792/7*x^7*e^5*d^7*a^10*B + 30*x^7*d^12*b
^6*a^4*A + 432*x^7*e*d^11*b^5*a^5*A + 1980*x^7*e^2*d^10*b^4*a^6*A + 26400/7*x^7*
e^3*d^9*b^3*a^7*A + 22275/7*x^7*e^4*d^8*b^2*a^8*A + 7920/7*x^7*e^5*d^7*b*a^9*A +
132*x^7*e^6*d^6*a^10*A + 35*x^6*d^12*b^4*a^6*B + 240*x^6*e*d^11*b^3*a^7*B + 495
*x^6*e^2*d^10*b^2*a^8*B + 1100/3*x^6*e^3*d^9*b*a^9*B + 165/2*x^6*e^4*d^8*a^10*B
+ 42*x^6*d^12*b^5*a^5*A + 420*x^6*e*d^11*b^4*a^6*A + 1320*x^6*e^2*d^10*b^3*a^7*A
+ 1650*x^6*e^3*d^9*b^2*a^8*A + 825*x^6*e^4*d^8*b*a^9*A + 132*x^6*e^5*d^7*a^10*A
+ 24*x^5*d^12*b^3*a^7*B + 108*x^5*e*d^11*b^2*a^8*B + 132*x^5*e^2*d^10*b*a^9*B +
44*x^5*e^3*d^9*a^10*B + 42*x^5*d^12*b^4*a^6*A + 288*x^5*e*d^11*b^3*a^7*A + 594*
x^5*e^2*d^10*b^2*a^8*A + 440*x^5*e^3*d^9*b*a^9*A + 99*x^5*e^4*d^8*a^10*A + 45/4*
x^4*d^12*b^2*a^8*B + 30*x^4*e*d^11*b*a^9*B + 33/2*x^4*e^2*d^10*a^10*B + 30*x^4*d
^12*b^3*a^7*A + 135*x^4*e*d^11*b^2*a^8*A + 165*x^4*e^2*d^10*b*a^9*A + 55*x^4*e^3
*d^9*a^10*A + 10/3*x^3*d^12*b*a^9*B + 4*x^3*e*d^11*a^10*B + 15*x^3*d^12*b^2*a^8*
A + 40*x^3*e*d^11*b*a^9*A + 22*x^3*e^2*d^10*a^10*A + 1/2*x^2*d^12*a^10*B + 5*x^2
*d^12*b*a^9*A + 6*x^2*e*d^11*a^10*A + x*d^12*a^10*A

_______________________________________________________________________________________

Sympy [A]  time = 1.87995, size = 4655, normalized size = 10.03 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**10*(B*x+A)*(e*x+d)**12,x)

[Out]

A*a**10*d**12*x + B*b**10*e**12*x**24/24 + x**23*(A*b**10*e**12/23 + 10*B*a*b**9
*e**12/23 + 12*B*b**10*d*e**11/23) + x**22*(5*A*a*b**9*e**12/11 + 6*A*b**10*d*e*
*11/11 + 45*B*a**2*b**8*e**12/22 + 60*B*a*b**9*d*e**11/11 + 3*B*b**10*d**2*e**10
) + x**21*(15*A*a**2*b**8*e**12/7 + 40*A*a*b**9*d*e**11/7 + 22*A*b**10*d**2*e**1
0/7 + 40*B*a**3*b**7*e**12/7 + 180*B*a**2*b**8*d*e**11/7 + 220*B*a*b**9*d**2*e**
10/7 + 220*B*b**10*d**3*e**9/21) + x**20*(6*A*a**3*b**7*e**12 + 27*A*a**2*b**8*d
*e**11 + 33*A*a*b**9*d**2*e**10 + 11*A*b**10*d**3*e**9 + 21*B*a**4*b**6*e**12/2
+ 72*B*a**3*b**7*d*e**11 + 297*B*a**2*b**8*d**2*e**10/2 + 110*B*a*b**9*d**3*e**9
+ 99*B*b**10*d**4*e**8/4) + x**19*(210*A*a**4*b**6*e**12/19 + 1440*A*a**3*b**7*
d*e**11/19 + 2970*A*a**2*b**8*d**2*e**10/19 + 2200*A*a*b**9*d**3*e**9/19 + 495*A
*b**10*d**4*e**8/19 + 252*B*a**5*b**5*e**12/19 + 2520*B*a**4*b**6*d*e**11/19 + 7
920*B*a**3*b**7*d**2*e**10/19 + 9900*B*a**2*b**8*d**3*e**9/19 + 4950*B*a*b**9*d*
*4*e**8/19 + 792*B*b**10*d**5*e**7/19) + x**18*(14*A*a**5*b**5*e**12 + 140*A*a**
4*b**6*d*e**11 + 440*A*a**3*b**7*d**2*e**10 + 550*A*a**2*b**8*d**3*e**9 + 275*A*
a*b**9*d**4*e**8 + 44*A*b**10*d**5*e**7 + 35*B*a**6*b**4*e**12/3 + 168*B*a**5*b*
*5*d*e**11 + 770*B*a**4*b**6*d**2*e**10 + 4400*B*a**3*b**7*d**3*e**9/3 + 2475*B*
a**2*b**8*d**4*e**8/2 + 440*B*a*b**9*d**5*e**7 + 154*B*b**10*d**6*e**6/3) + x**1
7*(210*A*a**6*b**4*e**12/17 + 3024*A*a**5*b**5*d*e**11/17 + 13860*A*a**4*b**6*d*
*2*e**10/17 + 26400*A*a**3*b**7*d**3*e**9/17 + 22275*A*a**2*b**8*d**4*e**8/17 +
7920*A*a*b**9*d**5*e**7/17 + 924*A*b**10*d**6*e**6/17 + 120*B*a**7*b**3*e**12/17
+ 2520*B*a**6*b**4*d*e**11/17 + 16632*B*a**5*b**5*d**2*e**10/17 + 46200*B*a**4*
b**6*d**3*e**9/17 + 59400*B*a**3*b**7*d**4*e**8/17 + 35640*B*a**2*b**8*d**5*e**7
/17 + 9240*B*a*b**9*d**6*e**6/17 + 792*B*b**10*d**7*e**5/17) + x**16*(15*A*a**7*
b**3*e**12/2 + 315*A*a**6*b**4*d*e**11/2 + 2079*A*a**5*b**5*d**2*e**10/2 + 5775*
A*a**4*b**6*d**3*e**9/2 + 7425*A*a**3*b**7*d**4*e**8/2 + 4455*A*a**2*b**8*d**5*e
**7/2 + 1155*A*a*b**9*d**6*e**6/2 + 99*A*b**10*d**7*e**5/2 + 45*B*a**8*b**2*e**1
2/16 + 90*B*a**7*b**3*d*e**11 + 3465*B*a**6*b**4*d**2*e**10/4 + 3465*B*a**5*b**5
*d**3*e**9 + 51975*B*a**4*b**6*d**4*e**8/8 + 5940*B*a**3*b**7*d**5*e**7 + 10395*
B*a**2*b**8*d**6*e**6/4 + 495*B*a*b**9*d**7*e**5 + 495*B*b**10*d**8*e**4/16) + x
**15*(3*A*a**8*b**2*e**12 + 96*A*a**7*b**3*d*e**11 + 924*A*a**6*b**4*d**2*e**10
+ 3696*A*a**5*b**5*d**3*e**9 + 6930*A*a**4*b**6*d**4*e**8 + 6336*A*a**3*b**7*d**
5*e**7 + 2772*A*a**2*b**8*d**6*e**6 + 528*A*a*b**9*d**7*e**5 + 33*A*b**10*d**8*e
**4 + 2*B*a**9*b*e**12/3 + 36*B*a**8*b**2*d*e**11 + 528*B*a**7*b**3*d**2*e**10 +
3080*B*a**6*b**4*d**3*e**9 + 8316*B*a**5*b**5*d**4*e**8 + 11088*B*a**4*b**6*d**
5*e**7 + 7392*B*a**3*b**7*d**6*e**6 + 2376*B*a**2*b**8*d**7*e**5 + 330*B*a*b**9*
d**8*e**4 + 44*B*b**10*d**9*e**3/3) + x**14*(5*A*a**9*b*e**12/7 + 270*A*a**8*b**
2*d*e**11/7 + 3960*A*a**7*b**3*d**2*e**10/7 + 3300*A*a**6*b**4*d**3*e**9 + 8910*
A*a**5*b**5*d**4*e**8 + 11880*A*a**4*b**6*d**5*e**7 + 7920*A*a**3*b**7*d**6*e**6
+ 17820*A*a**2*b**8*d**7*e**5/7 + 2475*A*a*b**9*d**8*e**4/7 + 110*A*b**10*d**9*
e**3/7 + B*a**10*e**12/14 + 60*B*a**9*b*d*e**11/7 + 1485*B*a**8*b**2*d**2*e**10/
7 + 13200*B*a**7*b**3*d**3*e**9/7 + 7425*B*a**6*b**4*d**4*e**8 + 14256*B*a**5*b*
*5*d**5*e**7 + 13860*B*a**4*b**6*d**6*e**6 + 47520*B*a**3*b**7*d**7*e**5/7 + 222
75*B*a**2*b**8*d**8*e**4/14 + 1100*B*a*b**9*d**9*e**3/7 + 33*B*b**10*d**10*e**2/
7) + x**13*(A*a**10*e**12/13 + 120*A*a**9*b*d*e**11/13 + 2970*A*a**8*b**2*d**2*e
**10/13 + 26400*A*a**7*b**3*d**3*e**9/13 + 103950*A*a**6*b**4*d**4*e**8/13 + 199
584*A*a**5*b**5*d**5*e**7/13 + 194040*A*a**4*b**6*d**6*e**6/13 + 95040*A*a**3*b*
*7*d**7*e**5/13 + 22275*A*a**2*b**8*d**8*e**4/13 + 2200*A*a*b**9*d**9*e**3/13 +
66*A*b**10*d**10*e**2/13 + 12*B*a**10*d*e**11/13 + 660*B*a**9*b*d**2*e**10/13 +
9900*B*a**8*b**2*d**3*e**9/13 + 59400*B*a**7*b**3*d**4*e**8/13 + 166320*B*a**6*b
**4*d**5*e**7/13 + 232848*B*a**5*b**5*d**6*e**6/13 + 166320*B*a**4*b**6*d**7*e**
5/13 + 59400*B*a**3*b**7*d**8*e**4/13 + 9900*B*a**2*b**8*d**9*e**3/13 + 660*B*a*
b**9*d**10*e**2/13 + 12*B*b**10*d**11*e/13) + x**12*(A*a**10*d*e**11 + 55*A*a**9
*b*d**2*e**10 + 825*A*a**8*b**2*d**3*e**9 + 4950*A*a**7*b**3*d**4*e**8 + 13860*A
*a**6*b**4*d**5*e**7 + 19404*A*a**5*b**5*d**6*e**6 + 13860*A*a**4*b**6*d**7*e**5
+ 4950*A*a**3*b**7*d**8*e**4 + 825*A*a**2*b**8*d**9*e**3 + 55*A*a*b**9*d**10*e*
*2 + A*b**10*d**11*e + 11*B*a**10*d**2*e**10/2 + 550*B*a**9*b*d**3*e**9/3 + 7425
*B*a**8*b**2*d**4*e**8/4 + 7920*B*a**7*b**3*d**5*e**7 + 16170*B*a**6*b**4*d**6*e
**6 + 16632*B*a**5*b**5*d**7*e**5 + 17325*B*a**4*b**6*d**8*e**4/2 + 2200*B*a**3*
b**7*d**9*e**3 + 495*B*a**2*b**8*d**10*e**2/2 + 10*B*a*b**9*d**11*e + B*b**10*d*
*12/12) + x**11*(6*A*a**10*d**2*e**10 + 200*A*a**9*b*d**3*e**9 + 2025*A*a**8*b**
2*d**4*e**8 + 8640*A*a**7*b**3*d**5*e**7 + 17640*A*a**6*b**4*d**6*e**6 + 18144*A
*a**5*b**5*d**7*e**5 + 9450*A*a**4*b**6*d**8*e**4 + 2400*A*a**3*b**7*d**9*e**3 +
270*A*a**2*b**8*d**10*e**2 + 120*A*a*b**9*d**11*e/11 + A*b**10*d**12/11 + 20*B*
a**10*d**3*e**9 + 450*B*a**9*b*d**4*e**8 + 3240*B*a**8*b**2*d**5*e**7 + 10080*B*
a**7*b**3*d**6*e**6 + 15120*B*a**6*b**4*d**7*e**5 + 11340*B*a**5*b**5*d**8*e**4
+ 4200*B*a**4*b**6*d**9*e**3 + 720*B*a**3*b**7*d**10*e**2 + 540*B*a**2*b**8*d**1
1*e/11 + 10*B*a*b**9*d**12/11) + x**10*(22*A*a**10*d**3*e**9 + 495*A*a**9*b*d**4
*e**8 + 3564*A*a**8*b**2*d**5*e**7 + 11088*A*a**7*b**3*d**6*e**6 + 16632*A*a**6*
b**4*d**7*e**5 + 12474*A*a**5*b**5*d**8*e**4 + 4620*A*a**4*b**6*d**9*e**3 + 792*
A*a**3*b**7*d**10*e**2 + 54*A*a**2*b**8*d**11*e + A*a*b**9*d**12 + 99*B*a**10*d*
*4*e**8/2 + 792*B*a**9*b*d**5*e**7 + 4158*B*a**8*b**2*d**6*e**6 + 9504*B*a**7*b*
*3*d**7*e**5 + 10395*B*a**6*b**4*d**8*e**4 + 5544*B*a**5*b**5*d**9*e**3 + 1386*B
*a**4*b**6*d**10*e**2 + 144*B*a**3*b**7*d**11*e + 9*B*a**2*b**8*d**12/2) + x**9*
(55*A*a**10*d**4*e**8 + 880*A*a**9*b*d**5*e**7 + 4620*A*a**8*b**2*d**6*e**6 + 10
560*A*a**7*b**3*d**7*e**5 + 11550*A*a**6*b**4*d**8*e**4 + 6160*A*a**5*b**5*d**9*
e**3 + 1540*A*a**4*b**6*d**10*e**2 + 160*A*a**3*b**7*d**11*e + 5*A*a**2*b**8*d**
12 + 88*B*a**10*d**5*e**7 + 3080*B*a**9*b*d**6*e**6/3 + 3960*B*a**8*b**2*d**7*e*
*5 + 6600*B*a**7*b**3*d**8*e**4 + 15400*B*a**6*b**4*d**9*e**3/3 + 1848*B*a**5*b*
*5*d**10*e**2 + 280*B*a**4*b**6*d**11*e + 40*B*a**3*b**7*d**12/3) + x**8*(99*A*a
**10*d**5*e**7 + 1155*A*a**9*b*d**6*e**6 + 4455*A*a**8*b**2*d**7*e**5 + 7425*A*a
**7*b**3*d**8*e**4 + 5775*A*a**6*b**4*d**9*e**3 + 2079*A*a**5*b**5*d**10*e**2 +
315*A*a**4*b**6*d**11*e + 15*A*a**3*b**7*d**12 + 231*B*a**10*d**6*e**6/2 + 990*B
*a**9*b*d**7*e**5 + 22275*B*a**8*b**2*d**8*e**4/8 + 3300*B*a**7*b**3*d**9*e**3 +
3465*B*a**6*b**4*d**10*e**2/2 + 378*B*a**5*b**5*d**11*e + 105*B*a**4*b**6*d**12
/4) + x**7*(132*A*a**10*d**6*e**6 + 7920*A*a**9*b*d**7*e**5/7 + 22275*A*a**8*b**
2*d**8*e**4/7 + 26400*A*a**7*b**3*d**9*e**3/7 + 1980*A*a**6*b**4*d**10*e**2 + 43
2*A*a**5*b**5*d**11*e + 30*A*a**4*b**6*d**12 + 792*B*a**10*d**7*e**5/7 + 4950*B*
a**9*b*d**8*e**4/7 + 9900*B*a**8*b**2*d**9*e**3/7 + 7920*B*a**7*b**3*d**10*e**2/
7 + 360*B*a**6*b**4*d**11*e + 36*B*a**5*b**5*d**12) + x**6*(132*A*a**10*d**7*e**
5 + 825*A*a**9*b*d**8*e**4 + 1650*A*a**8*b**2*d**9*e**3 + 1320*A*a**7*b**3*d**10
*e**2 + 420*A*a**6*b**4*d**11*e + 42*A*a**5*b**5*d**12 + 165*B*a**10*d**8*e**4/2
+ 1100*B*a**9*b*d**9*e**3/3 + 495*B*a**8*b**2*d**10*e**2 + 240*B*a**7*b**3*d**1
1*e + 35*B*a**6*b**4*d**12) + x**5*(99*A*a**10*d**8*e**4 + 440*A*a**9*b*d**9*e**
3 + 594*A*a**8*b**2*d**10*e**2 + 288*A*a**7*b**3*d**11*e + 42*A*a**6*b**4*d**12
+ 44*B*a**10*d**9*e**3 + 132*B*a**9*b*d**10*e**2 + 108*B*a**8*b**2*d**11*e + 24*
B*a**7*b**3*d**12) + x**4*(55*A*a**10*d**9*e**3 + 165*A*a**9*b*d**10*e**2 + 135*
A*a**8*b**2*d**11*e + 30*A*a**7*b**3*d**12 + 33*B*a**10*d**10*e**2/2 + 30*B*a**9
*b*d**11*e + 45*B*a**8*b**2*d**12/4) + x**3*(22*A*a**10*d**10*e**2 + 40*A*a**9*b
*d**11*e + 15*A*a**8*b**2*d**12 + 4*B*a**10*d**11*e + 10*B*a**9*b*d**12/3) + x**
2*(6*A*a**10*d**11*e + 5*A*a**9*b*d**12 + B*a**10*d**12/2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.215134, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^12,x, algorithm="giac")

[Out]

Done