3.1060 \(\int (a+b x)^{10} (A+B x) (d+e x)^{11} \, dx\)

Optimal. Leaf size=461 \[ -\frac{b^9 (d+e x)^{22} (-10 a B e-A b e+11 b B d)}{22 e^{12}}+\frac{5 b^8 (d+e x)^{21} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{21 e^{12}}-\frac{3 b^7 (d+e x)^{20} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{4 e^{12}}+\frac{30 b^6 (d+e x)^{19} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{19 e^{12}}-\frac{7 b^5 (d+e x)^{18} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{3 e^{12}}+\frac{42 b^4 (d+e x)^{17} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{17 e^{12}}-\frac{15 b^3 (d+e x)^{16} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{8 e^{12}}+\frac{b^2 (d+e x)^{15} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12}}-\frac{5 b (d+e x)^{14} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{14 e^{12}}+\frac{(d+e x)^{13} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{13 e^{12}}-\frac{(d+e x)^{12} (b d-a e)^{10} (B d-A e)}{12 e^{12}}+\frac{b^{10} B (d+e x)^{23}}{23 e^{12}} \]

[Out]

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

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Rubi [A]  time = 18.3676, antiderivative size = 461, 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 \[ -\frac{b^9 (d+e x)^{22} (-10 a B e-A b e+11 b B d)}{22 e^{12}}+\frac{5 b^8 (d+e x)^{21} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{21 e^{12}}-\frac{3 b^7 (d+e x)^{20} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{4 e^{12}}+\frac{30 b^6 (d+e x)^{19} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{19 e^{12}}-\frac{7 b^5 (d+e x)^{18} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{3 e^{12}}+\frac{42 b^4 (d+e x)^{17} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{17 e^{12}}-\frac{15 b^3 (d+e x)^{16} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{8 e^{12}}+\frac{b^2 (d+e x)^{15} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12}}-\frac{5 b (d+e x)^{14} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{14 e^{12}}+\frac{(d+e x)^{13} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{13 e^{12}}-\frac{(d+e x)^{12} (b d-a e)^{10} (B d-A e)}{12 e^{12}}+\frac{b^{10} B (d+e x)^{23}}{23 e^{12}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^10*(A + B*x)*(d + e*x)^11,x]

[Out]

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

[Out]

Timed out

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Mathematica [B]  time = 2.67136, size = 3018, normalized size = 6.55 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^11,x]

[Out]

a^10*A*d^11*x + (a^9*d^10*(10*A*b*d + a*B*d + 11*a*A*e)*x^2)/2 + (a^8*d^9*(a*B*d
*(10*b*d + 11*a*e) + 5*A*(9*b^2*d^2 + 22*a*b*d*e + 11*a^2*e^2))*x^3)/3 + (5*a^7*
d^8*(a*B*d*(9*b^2*d^2 + 22*a*b*d*e + 11*a^2*e^2) + A*(24*b^3*d^3 + 99*a*b^2*d^2*
e + 110*a^2*b*d*e^2 + 33*a^3*e^3))*x^4)/4 + a^6*d^7*(a*B*d*(24*b^3*d^3 + 99*a*b^
2*d^2*e + 110*a^2*b*d*e^2 + 33*a^3*e^3) + 3*A*(14*b^4*d^4 + 88*a*b^3*d^3*e + 165
*a^2*b^2*d^2*e^2 + 110*a^3*b*d*e^3 + 22*a^4*e^4))*x^5 + (a^5*d^6*(5*a*B*d*(14*b^
4*d^4 + 88*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 110*a^3*b*d*e^3 + 22*a^4*e^4) + A
*(84*b^5*d^5 + 770*a*b^4*d^4*e + 2200*a^2*b^3*d^3*e^2 + 2475*a^3*b^2*d^2*e^3 + 1
100*a^4*b*d*e^4 + 154*a^5*e^5))*x^6)/2 + (3*a^4*d^5*(a*B*d*(84*b^5*d^5 + 770*a*b
^4*d^4*e + 2200*a^2*b^3*d^3*e^2 + 2475*a^3*b^2*d^2*e^3 + 1100*a^4*b*d*e^4 + 154*
a^5*e^5) + 2*A*(35*b^6*d^6 + 462*a*b^5*d^5*e + 1925*a^2*b^4*d^4*e^2 + 3300*a^3*b
^3*d^3*e^3 + 2475*a^4*b^2*d^2*e^4 + 770*a^5*b*d*e^5 + 77*a^6*e^6))*x^7)/7 + (3*a
^3*d^4*(a*B*d*(35*b^6*d^6 + 462*a*b^5*d^5*e + 1925*a^2*b^4*d^4*e^2 + 3300*a^3*b^
3*d^3*e^3 + 2475*a^4*b^2*d^2*e^4 + 770*a^5*b*d*e^5 + 77*a^6*e^6) + 5*A*(4*b^7*d^
7 + 77*a*b^6*d^6*e + 462*a^2*b^5*d^5*e^2 + 1155*a^3*b^4*d^4*e^3 + 1320*a^4*b^3*d
^3*e^4 + 693*a^5*b^2*d^2*e^5 + 154*a^6*b*d*e^6 + 11*a^7*e^7))*x^8)/4 + (5*a^2*d^
3*(2*a*B*d*(4*b^7*d^7 + 77*a*b^6*d^6*e + 462*a^2*b^5*d^5*e^2 + 1155*a^3*b^4*d^4*
e^3 + 1320*a^4*b^3*d^3*e^4 + 693*a^5*b^2*d^2*e^5 + 154*a^6*b*d*e^6 + 11*a^7*e^7)
+ A*(3*b^8*d^8 + 88*a*b^7*d^7*e + 770*a^2*b^6*d^6*e^2 + 2772*a^3*b^5*d^5*e^3 +
4620*a^4*b^4*d^4*e^4 + 3696*a^5*b^3*d^3*e^5 + 1386*a^6*b^2*d^2*e^6 + 220*a^7*b*d
*e^7 + 11*a^8*e^8))*x^9)/3 + (a*d^2*(3*a*B*d*(3*b^8*d^8 + 88*a*b^7*d^7*e + 770*a
^2*b^6*d^6*e^2 + 2772*a^3*b^5*d^5*e^3 + 4620*a^4*b^4*d^4*e^4 + 3696*a^5*b^3*d^3*
e^5 + 1386*a^6*b^2*d^2*e^6 + 220*a^7*b*d*e^7 + 11*a^8*e^8) + A*(2*b^9*d^9 + 99*a
*b^8*d^8*e + 1320*a^2*b^7*d^7*e^2 + 6930*a^3*b^6*d^6*e^3 + 16632*a^4*b^5*d^5*e^4
+ 19404*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 2970*a^7*b^2*d^2*e^7 + 330*a^
8*b*d*e^8 + 11*a^9*e^9))*x^10)/2 + (d*(5*a*B*d*(2*b^9*d^9 + 99*a*b^8*d^8*e + 132
0*a^2*b^7*d^7*e^2 + 6930*a^3*b^6*d^6*e^3 + 16632*a^4*b^5*d^5*e^4 + 19404*a^5*b^4
*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 2970*a^7*b^2*d^2*e^7 + 330*a^8*b*d*e^8 + 11*a
^9*e^9) + A*(b^10*d^10 + 110*a*b^9*d^9*e + 2475*a^2*b^8*d^8*e^2 + 19800*a^3*b^7*
d^7*e^3 + 69300*a^4*b^6*d^6*e^4 + 116424*a^5*b^5*d^5*e^5 + 97020*a^6*b^4*d^4*e^6
+ 39600*a^7*b^3*d^3*e^7 + 7425*a^8*b^2*d^2*e^8 + 550*a^9*b*d*e^9 + 11*a^10*e^10
))*x^11)/11 + ((116424*a^5*b^5*d^5*e^5*(B*d + A*e) + 19800*a^7*b^3*d^3*e^7*(2*B*
d + A*e) + 2475*a^8*b^2*d^2*e^8*(3*B*d + A*e) + 110*a^9*b*d*e^9*(5*B*d + A*e) +
a^10*e^10*(11*B*d + A*e) + 19800*a^3*b^7*d^7*e^3*(B*d + 2*A*e) + 2475*a^2*b^8*d^
8*e^2*(B*d + 3*A*e) + 110*a*b^9*d^9*e*(B*d + 5*A*e) + 13860*a^6*b^4*d^4*e^6*(7*B
*d + 5*A*e) + 13860*a^4*b^6*d^6*e^4*(5*B*d + 7*A*e) + b^10*d^10*(B*d + 11*A*e))*
x^12)/12 + (e*(a^10*B*e^10 + 97020*a^4*b^6*d^5*e^4*(B*d + A*e) + 34650*a^6*b^4*d
^3*e^6*(2*B*d + A*e) + 6600*a^7*b^3*d^2*e^7*(3*B*d + A*e) + 495*a^8*b^2*d*e^8*(5
*B*d + A*e) + 10*a^9*b*e^9*(11*B*d + A*e) + 7425*a^2*b^8*d^7*e^2*(B*d + 2*A*e) +
550*a*b^9*d^8*e*(B*d + 3*A*e) + 11*b^10*d^9*(B*d + 5*A*e) + 16632*a^5*b^5*d^4*e
^5*(7*B*d + 5*A*e) + 7920*a^3*b^7*d^6*e^3*(5*B*d + 7*A*e))*x^13)/13 + (5*b*e^2*(
2*a^9*B*e^9 + 11088*a^3*b^6*d^5*e^3*(B*d + A*e) + 8316*a^5*b^4*d^3*e^5*(2*B*d +
A*e) + 2310*a^6*b^3*d^2*e^6*(3*B*d + A*e) + 264*a^7*b^2*d*e^7*(5*B*d + A*e) + 9*
a^8*b*e^8*(11*B*d + A*e) + 330*a*b^8*d^7*e*(B*d + 2*A*e) + 11*b^9*d^8*(B*d + 3*A
*e) + 2772*a^4*b^5*d^4*e^4*(7*B*d + 5*A*e) + 594*a^2*b^7*d^6*e^2*(5*B*d + 7*A*e)
)*x^14)/14 + b^2*e^3*(3*a^8*B*e^8 + 1386*a^2*b^6*d^5*e^2*(B*d + A*e) + 2310*a^4*
b^4*d^3*e^4*(2*B*d + A*e) + 924*a^5*b^3*d^2*e^5*(3*B*d + A*e) + 154*a^6*b^2*d*e^
6*(5*B*d + A*e) + 8*a^7*b*e^7*(11*B*d + A*e) + 11*b^8*d^7*(B*d + 2*A*e) + 528*a^
3*b^5*d^4*e^3*(7*B*d + 5*A*e) + 44*a*b^7*d^6*e*(5*B*d + 7*A*e))*x^15 + (3*b^3*e^
4*(20*a^7*B*e^7 + 770*a*b^6*d^5*e*(B*d + A*e) + 3300*a^3*b^4*d^3*e^3*(2*B*d + A*
e) + 1925*a^4*b^3*d^2*e^4*(3*B*d + A*e) + 462*a^5*b^2*d*e^5*(5*B*d + A*e) + 35*a
^6*b*e^6*(11*B*d + A*e) + 495*a^2*b^5*d^4*e^2*(7*B*d + 5*A*e) + 11*b^7*d^6*(5*B*
d + 7*A*e))*x^16)/8 + (3*b^4*e^5*(70*a^6*B*e^6 + 154*b^6*d^5*(B*d + A*e) + 2475*
a^2*b^4*d^3*e^2*(2*B*d + A*e) + 2200*a^3*b^3*d^2*e^3*(3*B*d + A*e) + 770*a^4*b^2
*d*e^4*(5*B*d + A*e) + 84*a^5*b*e^5*(11*B*d + A*e) + 220*a*b^5*d^4*e*(7*B*d + 5*
A*e))*x^17)/17 + (b^5*e^6*(84*a^5*B*e^5 + 550*a*b^4*d^3*e*(2*B*d + A*e) + 825*a^
2*b^3*d^2*e^2*(3*B*d + A*e) + 440*a^3*b^2*d*e^3*(5*B*d + A*e) + 70*a^4*b*e^4*(11
*B*d + A*e) + 22*b^5*d^4*(7*B*d + 5*A*e))*x^18)/6 + (5*b^6*e^7*(42*a^4*B*e^4 + 3
3*b^4*d^3*(2*B*d + A*e) + 110*a*b^3*d^2*e*(3*B*d + A*e) + 99*a^2*b^2*d*e^2*(5*B*
d + A*e) + 24*a^3*b*e^3*(11*B*d + A*e))*x^19)/19 + (b^7*e^8*(24*a^3*B*e^3 + 11*b
^3*d^2*(3*B*d + A*e) + 22*a*b^2*d*e*(5*B*d + A*e) + 9*a^2*b*e^2*(11*B*d + A*e))*
x^20)/4 + (b^8*e^9*(45*a^2*B*e^2 + 11*b^2*d*(5*B*d + A*e) + 10*a*b*e*(11*B*d + A
*e))*x^21)/21 + (b^9*e^10*(11*b*B*d + A*b*e + 10*a*B*e)*x^22)/22 + (b^10*B*e^11*
x^23)/23

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Maple [B]  time = 0.004, size = 3325, normalized size = 7.2 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^10*(B*x+A)*(e*x+d)^11,x)

[Out]

1/23*b^10*B*e^11*x^23+1/22*((A*b^10+10*B*a*b^9)*e^11+11*b^10*B*d*e^10)*x^22+1/21
*((10*A*a*b^9+45*B*a^2*b^8)*e^11+11*(A*b^10+10*B*a*b^9)*d*e^10+55*b^10*B*d^2*e^9
)*x^21+1/20*((45*A*a^2*b^8+120*B*a^3*b^7)*e^11+11*(10*A*a*b^9+45*B*a^2*b^8)*d*e^
10+55*(A*b^10+10*B*a*b^9)*d^2*e^9+165*b^10*B*d^3*e^8)*x^20+1/19*((120*A*a^3*b^7+
210*B*a^4*b^6)*e^11+11*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^10+55*(10*A*a*b^9+45*B*a
^2*b^8)*d^2*e^9+165*(A*b^10+10*B*a*b^9)*d^3*e^8+330*b^10*B*d^4*e^7)*x^19+1/18*((
210*A*a^4*b^6+252*B*a^5*b^5)*e^11+11*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^10+55*(45
*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^9+165*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^8+330*(A*b
^10+10*B*a*b^9)*d^4*e^7+462*b^10*B*d^5*e^6)*x^18+1/17*((252*A*a^5*b^5+210*B*a^6*
b^4)*e^11+11*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^10+55*(120*A*a^3*b^7+210*B*a^4*b^
6)*d^2*e^9+165*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^8+330*(10*A*a*b^9+45*B*a^2*b^8
)*d^4*e^7+462*(A*b^10+10*B*a*b^9)*d^5*e^6+462*b^10*B*d^6*e^5)*x^17+1/16*((210*A*
a^6*b^4+120*B*a^7*b^3)*e^11+11*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^10+55*(210*A*a^
4*b^6+252*B*a^5*b^5)*d^2*e^9+165*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*e^8+330*(45*A
*a^2*b^8+120*B*a^3*b^7)*d^4*e^7+462*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e^6+462*(A*b^1
0+10*B*a*b^9)*d^6*e^5+330*b^10*B*d^7*e^4)*x^16+1/15*((120*A*a^7*b^3+45*B*a^8*b^2
)*e^11+11*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^10+55*(252*A*a^5*b^5+210*B*a^6*b^4)*
d^2*e^9+165*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^8+330*(120*A*a^3*b^7+210*B*a^4*b
^6)*d^4*e^7+462*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e^6+462*(10*A*a*b^9+45*B*a^2*b^
8)*d^6*e^5+330*(A*b^10+10*B*a*b^9)*d^7*e^4+165*b^10*B*d^8*e^3)*x^15+1/14*((45*A*
a^8*b^2+10*B*a^9*b)*e^11+11*(120*A*a^7*b^3+45*B*a^8*b^2)*d*e^10+55*(210*A*a^6*b^
4+120*B*a^7*b^3)*d^2*e^9+165*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^8+330*(210*A*a^
4*b^6+252*B*a^5*b^5)*d^4*e^7+462*(120*A*a^3*b^7+210*B*a^4*b^6)*d^5*e^6+462*(45*A
*a^2*b^8+120*B*a^3*b^7)*d^6*e^5+330*(10*A*a*b^9+45*B*a^2*b^8)*d^7*e^4+165*(A*b^1
0+10*B*a*b^9)*d^8*e^3+55*b^10*B*d^9*e^2)*x^14+1/13*((10*A*a^9*b+B*a^10)*e^11+11*
(45*A*a^8*b^2+10*B*a^9*b)*d*e^10+55*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^9+165*(21
0*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^8+330*(252*A*a^5*b^5+210*B*a^6*b^4)*d^4*e^7+462
*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e^6+462*(120*A*a^3*b^7+210*B*a^4*b^6)*d^6*e^5
+330*(45*A*a^2*b^8+120*B*a^3*b^7)*d^7*e^4+165*(10*A*a*b^9+45*B*a^2*b^8)*d^8*e^3+
55*(A*b^10+10*B*a*b^9)*d^9*e^2+11*b^10*B*d^10*e)*x^13+1/12*(a^10*A*e^11+11*(10*A
*a^9*b+B*a^10)*d*e^10+55*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^9+165*(120*A*a^7*b^3+45
*B*a^8*b^2)*d^3*e^8+330*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^7+462*(252*A*a^5*b^5
+210*B*a^6*b^4)*d^5*e^6+462*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^5+330*(120*A*a^3
*b^7+210*B*a^4*b^6)*d^7*e^4+165*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e^3+55*(10*A*a*
b^9+45*B*a^2*b^8)*d^9*e^2+11*(A*b^10+10*B*a*b^9)*d^10*e+b^10*B*d^11)*x^12+1/11*(
11*a^10*A*d*e^10+55*(10*A*a^9*b+B*a^10)*d^2*e^9+165*(45*A*a^8*b^2+10*B*a^9*b)*d^
3*e^8+330*(120*A*a^7*b^3+45*B*a^8*b^2)*d^4*e^7+462*(210*A*a^6*b^4+120*B*a^7*b^3)
*d^5*e^6+462*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^5+330*(210*A*a^4*b^6+252*B*a^5*
b^5)*d^7*e^4+165*(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e^3+55*(45*A*a^2*b^8+120*B*a^
3*b^7)*d^9*e^2+11*(10*A*a*b^9+45*B*a^2*b^8)*d^10*e+(A*b^10+10*B*a*b^9)*d^11)*x^1
1+1/10*(55*a^10*A*d^2*e^9+165*(10*A*a^9*b+B*a^10)*d^3*e^8+330*(45*A*a^8*b^2+10*B
*a^9*b)*d^4*e^7+462*(120*A*a^7*b^3+45*B*a^8*b^2)*d^5*e^6+462*(210*A*a^6*b^4+120*
B*a^7*b^3)*d^6*e^5+330*(252*A*a^5*b^5+210*B*a^6*b^4)*d^7*e^4+165*(210*A*a^4*b^6+
252*B*a^5*b^5)*d^8*e^3+55*(120*A*a^3*b^7+210*B*a^4*b^6)*d^9*e^2+11*(45*A*a^2*b^8
+120*B*a^3*b^7)*d^10*e+(10*A*a*b^9+45*B*a^2*b^8)*d^11)*x^10+1/9*(165*a^10*A*d^3*
e^8+330*(10*A*a^9*b+B*a^10)*d^4*e^7+462*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e^6+462*(1
20*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^5+330*(210*A*a^6*b^4+120*B*a^7*b^3)*d^7*e^4+165
*(252*A*a^5*b^5+210*B*a^6*b^4)*d^8*e^3+55*(210*A*a^4*b^6+252*B*a^5*b^5)*d^9*e^2+
11*(120*A*a^3*b^7+210*B*a^4*b^6)*d^10*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^11)*x^9+1
/8*(330*a^10*A*d^4*e^7+462*(10*A*a^9*b+B*a^10)*d^5*e^6+462*(45*A*a^8*b^2+10*B*a^
9*b)*d^6*e^5+330*(120*A*a^7*b^3+45*B*a^8*b^2)*d^7*e^4+165*(210*A*a^6*b^4+120*B*a
^7*b^3)*d^8*e^3+55*(252*A*a^5*b^5+210*B*a^6*b^4)*d^9*e^2+11*(210*A*a^4*b^6+252*B
*a^5*b^5)*d^10*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^11)*x^8+1/7*(462*a^10*A*d^5*e^6
+462*(10*A*a^9*b+B*a^10)*d^6*e^5+330*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^4+165*(120*
A*a^7*b^3+45*B*a^8*b^2)*d^8*e^3+55*(210*A*a^6*b^4+120*B*a^7*b^3)*d^9*e^2+11*(252
*A*a^5*b^5+210*B*a^6*b^4)*d^10*e+(210*A*a^4*b^6+252*B*a^5*b^5)*d^11)*x^7+1/6*(46
2*a^10*A*d^6*e^5+330*(10*A*a^9*b+B*a^10)*d^7*e^4+165*(45*A*a^8*b^2+10*B*a^9*b)*d
^8*e^3+55*(120*A*a^7*b^3+45*B*a^8*b^2)*d^9*e^2+11*(210*A*a^6*b^4+120*B*a^7*b^3)*
d^10*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^11)*x^6+1/5*(330*a^10*A*d^7*e^4+165*(10*A
*a^9*b+B*a^10)*d^8*e^3+55*(45*A*a^8*b^2+10*B*a^9*b)*d^9*e^2+11*(120*A*a^7*b^3+45
*B*a^8*b^2)*d^10*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^11)*x^5+1/4*(165*a^10*A*d^8*e
^3+55*(10*A*a^9*b+B*a^10)*d^9*e^2+11*(45*A*a^8*b^2+10*B*a^9*b)*d^10*e+(120*A*a^7
*b^3+45*B*a^8*b^2)*d^11)*x^4+1/3*(55*a^10*A*d^9*e^2+11*(10*A*a^9*b+B*a^10)*d^10*
e+(45*A*a^8*b^2+10*B*a^9*b)*d^11)*x^3+1/2*(11*a^10*A*d^10*e+(10*A*a^9*b+B*a^10)*
d^11)*x^2+a^10*A*d^11*x

_______________________________________________________________________________________

Maxima [A]  time = 1.42884, size = 4501, normalized size = 9.76 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^11,x, algorithm="maxima")

[Out]

1/23*B*b^10*e^11*x^23 + A*a^10*d^11*x + 1/22*(11*B*b^10*d*e^10 + (10*B*a*b^9 + A
*b^10)*e^11)*x^22 + 1/21*(55*B*b^10*d^2*e^9 + 11*(10*B*a*b^9 + A*b^10)*d*e^10 +
5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^21 + 1/4*(33*B*b^10*d^3*e^8 + 11*(10*B*a*b^9
+ A*b^10)*d^2*e^9 + 11*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 3*(8*B*a^3*b^7 + 3*A*
a^2*b^8)*e^11)*x^20 + 5/19*(66*B*b^10*d^4*e^7 + 33*(10*B*a*b^9 + A*b^10)*d^3*e^8
+ 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 33*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10
+ 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^19 + 1/6*(154*B*b^10*d^5*e^6 + 110*(10*B
*a*b^9 + A*b^10)*d^4*e^7 + 275*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 275*(8*B*a^3*
b^7 + 3*A*a^2*b^8)*d^2*e^9 + 110*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 14*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*e^11)*x^18 + 3/17*(154*B*b^10*d^6*e^5 + 154*(10*B*a*b^9 + A
*b^10)*d^5*e^6 + 550*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 825*(8*B*a^3*b^7 + 3*A*
a^2*b^8)*d^3*e^8 + 550*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 154*(6*B*a^5*b^5 +
5*A*a^4*b^6)*d*e^10 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^17 + 3/8*(55*B*b^10
*d^7*e^4 + 77*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 385*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*
e^6 + 825*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 825*(7*B*a^4*b^6 + 4*A*a^3*b^7)*
d^3*e^8 + 385*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 77*(5*B*a^6*b^4 + 6*A*a^5*b^
5)*d*e^10 + 5*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^16 + (11*B*b^10*d^8*e^3 + 22*(
10*B*a*b^9 + A*b^10)*d^7*e^4 + 154*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 462*(8*B*
a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 660*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 462*(
6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 154*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 2
2*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^15 +
5/14*(11*B*b^10*d^9*e^2 + 33*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 330*(9*B*a^2*b^8 +
2*A*a*b^9)*d^7*e^4 + 1386*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 2772*(7*B*a^4*b^
6 + 4*A*a^3*b^7)*d^5*e^6 + 2772*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 1386*(5*B*
a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 33*(3
*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + (2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^14 + 1/13*(
11*B*b^10*d^10*e + 55*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 825*(9*B*a^2*b^8 + 2*A*a*b
^9)*d^8*e^3 + 4950*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 13860*(7*B*a^4*b^6 + 4*
A*a^3*b^7)*d^6*e^5 + 19404*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 13860*(5*B*a^6*
b^4 + 6*A*a^5*b^5)*d^4*e^7 + 4950*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 825*(3*B
*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 55*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10
+ 10*A*a^9*b)*e^11)*x^13 + 1/12*(B*b^10*d^11 + A*a^10*e^11 + 11*(10*B*a*b^9 + A*
b^10)*d^10*e + 275*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 2475*(8*B*a^3*b^7 + 3*A*a
^2*b^8)*d^8*e^3 + 9900*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 19404*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d^6*e^5 + 19404*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 9900*(4*B*a
^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 2475*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 275*(
2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 11*(B*a^10 + 10*A*a^9*b)*d*e^10)*x^12 + 1/11*
(11*A*a^10*d*e^10 + (10*B*a*b^9 + A*b^10)*d^11 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^
10*e + 825*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^9*e^2 + 4950*(7*B*a^4*b^6 + 4*A*a^3*b^7
)*d^8*e^3 + 13860*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*e^4 + 19404*(5*B*a^6*b^4 + 6*A
*a^5*b^5)*d^6*e^5 + 13860*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^5*e^6 + 4950*(3*B*a^8*b^
2 + 8*A*a^7*b^3)*d^4*e^7 + 825*(2*B*a^9*b + 9*A*a^8*b^2)*d^3*e^8 + 55*(B*a^10 +
10*A*a^9*b)*d^2*e^9)*x^11 + 1/2*(11*A*a^10*d^2*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d
^11 + 33*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10*e + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^
9*e^2 + 1386*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^8*e^3 + 2772*(5*B*a^6*b^4 + 6*A*a^5*b
^5)*d^7*e^4 + 2772*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*e^5 + 1386*(3*B*a^8*b^2 + 8*A
*a^7*b^3)*d^5*e^6 + 330*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*e^7 + 33*(B*a^10 + 10*A*a^
9*b)*d^3*e^8)*x^10 + 5/3*(11*A*a^10*d^3*e^8 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^11 +
22*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^10*e + 154*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^9*e^2
+ 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*e^3 + 660*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^7
*e^4 + 462*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*e^5 + 154*(2*B*a^9*b + 9*A*a^8*b^2)*d
^5*e^6 + 22*(B*a^10 + 10*A*a^9*b)*d^4*e^7)*x^9 + 3/4*(55*A*a^10*d^4*e^7 + 5*(7*B
*a^4*b^6 + 4*A*a^3*b^7)*d^11 + 77*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^10*e + 385*(5*B*
a^6*b^4 + 6*A*a^5*b^5)*d^9*e^2 + 825*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*e^3 + 825*(
3*B*a^8*b^2 + 8*A*a^7*b^3)*d^7*e^4 + 385*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*e^5 + 77*
(B*a^10 + 10*A*a^9*b)*d^5*e^6)*x^8 + 3/7*(154*A*a^10*d^5*e^6 + 14*(6*B*a^5*b^5 +
5*A*a^4*b^6)*d^11 + 154*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^10*e + 550*(4*B*a^7*b^3 +
7*A*a^6*b^4)*d^9*e^2 + 825*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^8*e^3 + 550*(2*B*a^9*b
+ 9*A*a^8*b^2)*d^7*e^4 + 154*(B*a^10 + 10*A*a^9*b)*d^6*e^5)*x^7 + 1/2*(154*A*a^
10*d^6*e^5 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^11 + 110*(4*B*a^7*b^3 + 7*A*a^6*b^
4)*d^10*e + 275*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^9*e^2 + 275*(2*B*a^9*b + 9*A*a^8*b
^2)*d^8*e^3 + 110*(B*a^10 + 10*A*a^9*b)*d^7*e^4)*x^6 + (66*A*a^10*d^7*e^4 + 6*(4
*B*a^7*b^3 + 7*A*a^6*b^4)*d^11 + 33*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^10*e + 55*(2*B
*a^9*b + 9*A*a^8*b^2)*d^9*e^2 + 33*(B*a^10 + 10*A*a^9*b)*d^8*e^3)*x^5 + 5/4*(33*
A*a^10*d^8*e^3 + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^11 + 11*(2*B*a^9*b + 9*A*a^8*b^
2)*d^10*e + 11*(B*a^10 + 10*A*a^9*b)*d^9*e^2)*x^4 + 1/3*(55*A*a^10*d^9*e^2 + 5*(
2*B*a^9*b + 9*A*a^8*b^2)*d^11 + 11*(B*a^10 + 10*A*a^9*b)*d^10*e)*x^3 + 1/2*(11*A
*a^10*d^10*e + (B*a^10 + 10*A*a^9*b)*d^11)*x^2

_______________________________________________________________________________________

Fricas [A]  time = 0.195416, 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)^11,x, algorithm="fricas")

[Out]

1/23*x^23*e^11*b^10*B + 1/2*x^22*e^10*d*b^10*B + 5/11*x^22*e^11*b^9*a*B + 1/22*x
^22*e^11*b^10*A + 55/21*x^21*e^9*d^2*b^10*B + 110/21*x^21*e^10*d*b^9*a*B + 15/7*
x^21*e^11*b^8*a^2*B + 11/21*x^21*e^10*d*b^10*A + 10/21*x^21*e^11*b^9*a*A + 33/4*
x^20*e^8*d^3*b^10*B + 55/2*x^20*e^9*d^2*b^9*a*B + 99/4*x^20*e^10*d*b^8*a^2*B + 6
*x^20*e^11*b^7*a^3*B + 11/4*x^20*e^9*d^2*b^10*A + 11/2*x^20*e^10*d*b^9*a*A + 9/4
*x^20*e^11*b^8*a^2*A + 330/19*x^19*e^7*d^4*b^10*B + 1650/19*x^19*e^8*d^3*b^9*a*B
+ 2475/19*x^19*e^9*d^2*b^8*a^2*B + 1320/19*x^19*e^10*d*b^7*a^3*B + 210/19*x^19*
e^11*b^6*a^4*B + 165/19*x^19*e^8*d^3*b^10*A + 550/19*x^19*e^9*d^2*b^9*a*A + 495/
19*x^19*e^10*d*b^8*a^2*A + 120/19*x^19*e^11*b^7*a^3*A + 77/3*x^18*e^6*d^5*b^10*B
+ 550/3*x^18*e^7*d^4*b^9*a*B + 825/2*x^18*e^8*d^3*b^8*a^2*B + 1100/3*x^18*e^9*d
^2*b^7*a^3*B + 385/3*x^18*e^10*d*b^6*a^4*B + 14*x^18*e^11*b^5*a^5*B + 55/3*x^18*
e^7*d^4*b^10*A + 275/3*x^18*e^8*d^3*b^9*a*A + 275/2*x^18*e^9*d^2*b^8*a^2*A + 220
/3*x^18*e^10*d*b^7*a^3*A + 35/3*x^18*e^11*b^6*a^4*A + 462/17*x^17*e^5*d^6*b^10*B
+ 4620/17*x^17*e^6*d^5*b^9*a*B + 14850/17*x^17*e^7*d^4*b^8*a^2*B + 19800/17*x^1
7*e^8*d^3*b^7*a^3*B + 11550/17*x^17*e^9*d^2*b^6*a^4*B + 2772/17*x^17*e^10*d*b^5*
a^5*B + 210/17*x^17*e^11*b^4*a^6*B + 462/17*x^17*e^6*d^5*b^10*A + 3300/17*x^17*e
^7*d^4*b^9*a*A + 7425/17*x^17*e^8*d^3*b^8*a^2*A + 6600/17*x^17*e^9*d^2*b^7*a^3*A
+ 2310/17*x^17*e^10*d*b^6*a^4*A + 252/17*x^17*e^11*b^5*a^5*A + 165/8*x^16*e^4*d
^7*b^10*B + 1155/4*x^16*e^5*d^6*b^9*a*B + 10395/8*x^16*e^6*d^5*b^8*a^2*B + 2475*
x^16*e^7*d^4*b^7*a^3*B + 17325/8*x^16*e^8*d^3*b^6*a^4*B + 3465/4*x^16*e^9*d^2*b^
5*a^5*B + 1155/8*x^16*e^10*d*b^4*a^6*B + 15/2*x^16*e^11*b^3*a^7*B + 231/8*x^16*e
^5*d^6*b^10*A + 1155/4*x^16*e^6*d^5*b^9*a*A + 7425/8*x^16*e^7*d^4*b^8*a^2*A + 24
75/2*x^16*e^8*d^3*b^7*a^3*A + 5775/8*x^16*e^9*d^2*b^6*a^4*A + 693/4*x^16*e^10*d*
b^5*a^5*A + 105/8*x^16*e^11*b^4*a^6*A + 11*x^15*e^3*d^8*b^10*B + 220*x^15*e^4*d^
7*b^9*a*B + 1386*x^15*e^5*d^6*b^8*a^2*B + 3696*x^15*e^6*d^5*b^7*a^3*B + 4620*x^1
5*e^7*d^4*b^6*a^4*B + 2772*x^15*e^8*d^3*b^5*a^5*B + 770*x^15*e^9*d^2*b^4*a^6*B +
88*x^15*e^10*d*b^3*a^7*B + 3*x^15*e^11*b^2*a^8*B + 22*x^15*e^4*d^7*b^10*A + 308
*x^15*e^5*d^6*b^9*a*A + 1386*x^15*e^6*d^5*b^8*a^2*A + 2640*x^15*e^7*d^4*b^7*a^3*
A + 2310*x^15*e^8*d^3*b^6*a^4*A + 924*x^15*e^9*d^2*b^5*a^5*A + 154*x^15*e^10*d*b
^4*a^6*A + 8*x^15*e^11*b^3*a^7*A + 55/14*x^14*e^2*d^9*b^10*B + 825/7*x^14*e^3*d^
8*b^9*a*B + 7425/7*x^14*e^4*d^7*b^8*a^2*B + 3960*x^14*e^5*d^6*b^7*a^3*B + 6930*x
^14*e^6*d^5*b^6*a^4*B + 5940*x^14*e^7*d^4*b^5*a^5*B + 2475*x^14*e^8*d^3*b^4*a^6*
B + 3300/7*x^14*e^9*d^2*b^3*a^7*B + 495/14*x^14*e^10*d*b^2*a^8*B + 5/7*x^14*e^11
*b*a^9*B + 165/14*x^14*e^3*d^8*b^10*A + 1650/7*x^14*e^4*d^7*b^9*a*A + 1485*x^14*
e^5*d^6*b^8*a^2*A + 3960*x^14*e^6*d^5*b^7*a^3*A + 4950*x^14*e^7*d^4*b^6*a^4*A +
2970*x^14*e^8*d^3*b^5*a^5*A + 825*x^14*e^9*d^2*b^4*a^6*A + 660/7*x^14*e^10*d*b^3
*a^7*A + 45/14*x^14*e^11*b^2*a^8*A + 11/13*x^13*e*d^10*b^10*B + 550/13*x^13*e^2*
d^9*b^9*a*B + 7425/13*x^13*e^3*d^8*b^8*a^2*B + 39600/13*x^13*e^4*d^7*b^7*a^3*B +
97020/13*x^13*e^5*d^6*b^6*a^4*B + 116424/13*x^13*e^6*d^5*b^5*a^5*B + 69300/13*x
^13*e^7*d^4*b^4*a^6*B + 19800/13*x^13*e^8*d^3*b^3*a^7*B + 2475/13*x^13*e^9*d^2*b
^2*a^8*B + 110/13*x^13*e^10*d*b*a^9*B + 1/13*x^13*e^11*a^10*B + 55/13*x^13*e^2*d
^9*b^10*A + 1650/13*x^13*e^3*d^8*b^9*a*A + 14850/13*x^13*e^4*d^7*b^8*a^2*A + 554
40/13*x^13*e^5*d^6*b^7*a^3*A + 97020/13*x^13*e^6*d^5*b^6*a^4*A + 83160/13*x^13*e
^7*d^4*b^5*a^5*A + 34650/13*x^13*e^8*d^3*b^4*a^6*A + 6600/13*x^13*e^9*d^2*b^3*a^
7*A + 495/13*x^13*e^10*d*b^2*a^8*A + 10/13*x^13*e^11*b*a^9*A + 1/12*x^12*d^11*b^
10*B + 55/6*x^12*e*d^10*b^9*a*B + 825/4*x^12*e^2*d^9*b^8*a^2*B + 1650*x^12*e^3*d
^8*b^7*a^3*B + 5775*x^12*e^4*d^7*b^6*a^4*B + 9702*x^12*e^5*d^6*b^5*a^5*B + 8085*
x^12*e^6*d^5*b^4*a^6*B + 3300*x^12*e^7*d^4*b^3*a^7*B + 2475/4*x^12*e^8*d^3*b^2*a
^8*B + 275/6*x^12*e^9*d^2*b*a^9*B + 11/12*x^12*e^10*d*a^10*B + 11/12*x^12*e*d^10
*b^10*A + 275/6*x^12*e^2*d^9*b^9*a*A + 2475/4*x^12*e^3*d^8*b^8*a^2*A + 3300*x^12
*e^4*d^7*b^7*a^3*A + 8085*x^12*e^5*d^6*b^6*a^4*A + 9702*x^12*e^6*d^5*b^5*a^5*A +
5775*x^12*e^7*d^4*b^4*a^6*A + 1650*x^12*e^8*d^3*b^3*a^7*A + 825/4*x^12*e^9*d^2*
b^2*a^8*A + 55/6*x^12*e^10*d*b*a^9*A + 1/12*x^12*e^11*a^10*A + 10/11*x^11*d^11*b
^9*a*B + 45*x^11*e*d^10*b^8*a^2*B + 600*x^11*e^2*d^9*b^7*a^3*B + 3150*x^11*e^3*d
^8*b^6*a^4*B + 7560*x^11*e^4*d^7*b^5*a^5*B + 8820*x^11*e^5*d^6*b^4*a^6*B + 5040*
x^11*e^6*d^5*b^3*a^7*B + 1350*x^11*e^7*d^4*b^2*a^8*B + 150*x^11*e^8*d^3*b*a^9*B
+ 5*x^11*e^9*d^2*a^10*B + 1/11*x^11*d^11*b^10*A + 10*x^11*e*d^10*b^9*a*A + 225*x
^11*e^2*d^9*b^8*a^2*A + 1800*x^11*e^3*d^8*b^7*a^3*A + 6300*x^11*e^4*d^7*b^6*a^4*
A + 10584*x^11*e^5*d^6*b^5*a^5*A + 8820*x^11*e^6*d^5*b^4*a^6*A + 3600*x^11*e^7*d
^4*b^3*a^7*A + 675*x^11*e^8*d^3*b^2*a^8*A + 50*x^11*e^9*d^2*b*a^9*A + x^11*e^10*
d*a^10*A + 9/2*x^10*d^11*b^8*a^2*B + 132*x^10*e*d^10*b^7*a^3*B + 1155*x^10*e^2*d
^9*b^6*a^4*B + 4158*x^10*e^3*d^8*b^5*a^5*B + 6930*x^10*e^4*d^7*b^4*a^6*B + 5544*
x^10*e^5*d^6*b^3*a^7*B + 2079*x^10*e^6*d^5*b^2*a^8*B + 330*x^10*e^7*d^4*b*a^9*B
+ 33/2*x^10*e^8*d^3*a^10*B + x^10*d^11*b^9*a*A + 99/2*x^10*e*d^10*b^8*a^2*A + 66
0*x^10*e^2*d^9*b^7*a^3*A + 3465*x^10*e^3*d^8*b^6*a^4*A + 8316*x^10*e^4*d^7*b^5*a
^5*A + 9702*x^10*e^5*d^6*b^4*a^6*A + 5544*x^10*e^6*d^5*b^3*a^7*A + 1485*x^10*e^7
*d^4*b^2*a^8*A + 165*x^10*e^8*d^3*b*a^9*A + 11/2*x^10*e^9*d^2*a^10*A + 40/3*x^9*
d^11*b^7*a^3*B + 770/3*x^9*e*d^10*b^6*a^4*B + 1540*x^9*e^2*d^9*b^5*a^5*B + 3850*
x^9*e^3*d^8*b^4*a^6*B + 4400*x^9*e^4*d^7*b^3*a^7*B + 2310*x^9*e^5*d^6*b^2*a^8*B
+ 1540/3*x^9*e^6*d^5*b*a^9*B + 110/3*x^9*e^7*d^4*a^10*B + 5*x^9*d^11*b^8*a^2*A +
440/3*x^9*e*d^10*b^7*a^3*A + 3850/3*x^9*e^2*d^9*b^6*a^4*A + 4620*x^9*e^3*d^8*b^
5*a^5*A + 7700*x^9*e^4*d^7*b^4*a^6*A + 6160*x^9*e^5*d^6*b^3*a^7*A + 2310*x^9*e^6
*d^5*b^2*a^8*A + 1100/3*x^9*e^7*d^4*b*a^9*A + 55/3*x^9*e^8*d^3*a^10*A + 105/4*x^
8*d^11*b^6*a^4*B + 693/2*x^8*e*d^10*b^5*a^5*B + 5775/4*x^8*e^2*d^9*b^4*a^6*B + 2
475*x^8*e^3*d^8*b^3*a^7*B + 7425/4*x^8*e^4*d^7*b^2*a^8*B + 1155/2*x^8*e^5*d^6*b*
a^9*B + 231/4*x^8*e^6*d^5*a^10*B + 15*x^8*d^11*b^7*a^3*A + 1155/4*x^8*e*d^10*b^6
*a^4*A + 3465/2*x^8*e^2*d^9*b^5*a^5*A + 17325/4*x^8*e^3*d^8*b^4*a^6*A + 4950*x^8
*e^4*d^7*b^3*a^7*A + 10395/4*x^8*e^5*d^6*b^2*a^8*A + 1155/2*x^8*e^6*d^5*b*a^9*A
+ 165/4*x^8*e^7*d^4*a^10*A + 36*x^7*d^11*b^5*a^5*B + 330*x^7*e*d^10*b^4*a^6*B +
6600/7*x^7*e^2*d^9*b^3*a^7*B + 7425/7*x^7*e^3*d^8*b^2*a^8*B + 3300/7*x^7*e^4*d^7
*b*a^9*B + 66*x^7*e^5*d^6*a^10*B + 30*x^7*d^11*b^6*a^4*A + 396*x^7*e*d^10*b^5*a^
5*A + 1650*x^7*e^2*d^9*b^4*a^6*A + 19800/7*x^7*e^3*d^8*b^3*a^7*A + 14850/7*x^7*e
^4*d^7*b^2*a^8*A + 660*x^7*e^5*d^6*b*a^9*A + 66*x^7*e^6*d^5*a^10*A + 35*x^6*d^11
*b^4*a^6*B + 220*x^6*e*d^10*b^3*a^7*B + 825/2*x^6*e^2*d^9*b^2*a^8*B + 275*x^6*e^
3*d^8*b*a^9*B + 55*x^6*e^4*d^7*a^10*B + 42*x^6*d^11*b^5*a^5*A + 385*x^6*e*d^10*b
^4*a^6*A + 1100*x^6*e^2*d^9*b^3*a^7*A + 2475/2*x^6*e^3*d^8*b^2*a^8*A + 550*x^6*e
^4*d^7*b*a^9*A + 77*x^6*e^5*d^6*a^10*A + 24*x^5*d^11*b^3*a^7*B + 99*x^5*e*d^10*b
^2*a^8*B + 110*x^5*e^2*d^9*b*a^9*B + 33*x^5*e^3*d^8*a^10*B + 42*x^5*d^11*b^4*a^6
*A + 264*x^5*e*d^10*b^3*a^7*A + 495*x^5*e^2*d^9*b^2*a^8*A + 330*x^5*e^3*d^8*b*a^
9*A + 66*x^5*e^4*d^7*a^10*A + 45/4*x^4*d^11*b^2*a^8*B + 55/2*x^4*e*d^10*b*a^9*B
+ 55/4*x^4*e^2*d^9*a^10*B + 30*x^4*d^11*b^3*a^7*A + 495/4*x^4*e*d^10*b^2*a^8*A +
275/2*x^4*e^2*d^9*b*a^9*A + 165/4*x^4*e^3*d^8*a^10*A + 10/3*x^3*d^11*b*a^9*B +
11/3*x^3*e*d^10*a^10*B + 15*x^3*d^11*b^2*a^8*A + 110/3*x^3*e*d^10*b*a^9*A + 55/3
*x^3*e^2*d^9*a^10*A + 1/2*x^2*d^11*a^10*B + 5*x^2*d^11*b*a^9*A + 11/2*x^2*e*d^10
*a^10*A + x*d^11*a^10*A

_______________________________________________________________________________________

Sympy [A]  time = 1.75521, size = 4328, normalized size = 9.39 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**10*(B*x+A)*(e*x+d)**11,x)

[Out]

A*a**10*d**11*x + B*b**10*e**11*x**23/23 + x**22*(A*b**10*e**11/22 + 5*B*a*b**9*
e**11/11 + B*b**10*d*e**10/2) + x**21*(10*A*a*b**9*e**11/21 + 11*A*b**10*d*e**10
/21 + 15*B*a**2*b**8*e**11/7 + 110*B*a*b**9*d*e**10/21 + 55*B*b**10*d**2*e**9/21
) + x**20*(9*A*a**2*b**8*e**11/4 + 11*A*a*b**9*d*e**10/2 + 11*A*b**10*d**2*e**9/
4 + 6*B*a**3*b**7*e**11 + 99*B*a**2*b**8*d*e**10/4 + 55*B*a*b**9*d**2*e**9/2 + 3
3*B*b**10*d**3*e**8/4) + x**19*(120*A*a**3*b**7*e**11/19 + 495*A*a**2*b**8*d*e**
10/19 + 550*A*a*b**9*d**2*e**9/19 + 165*A*b**10*d**3*e**8/19 + 210*B*a**4*b**6*e
**11/19 + 1320*B*a**3*b**7*d*e**10/19 + 2475*B*a**2*b**8*d**2*e**9/19 + 1650*B*a
*b**9*d**3*e**8/19 + 330*B*b**10*d**4*e**7/19) + x**18*(35*A*a**4*b**6*e**11/3 +
220*A*a**3*b**7*d*e**10/3 + 275*A*a**2*b**8*d**2*e**9/2 + 275*A*a*b**9*d**3*e**
8/3 + 55*A*b**10*d**4*e**7/3 + 14*B*a**5*b**5*e**11 + 385*B*a**4*b**6*d*e**10/3
+ 1100*B*a**3*b**7*d**2*e**9/3 + 825*B*a**2*b**8*d**3*e**8/2 + 550*B*a*b**9*d**4
*e**7/3 + 77*B*b**10*d**5*e**6/3) + x**17*(252*A*a**5*b**5*e**11/17 + 2310*A*a**
4*b**6*d*e**10/17 + 6600*A*a**3*b**7*d**2*e**9/17 + 7425*A*a**2*b**8*d**3*e**8/1
7 + 3300*A*a*b**9*d**4*e**7/17 + 462*A*b**10*d**5*e**6/17 + 210*B*a**6*b**4*e**1
1/17 + 2772*B*a**5*b**5*d*e**10/17 + 11550*B*a**4*b**6*d**2*e**9/17 + 19800*B*a*
*3*b**7*d**3*e**8/17 + 14850*B*a**2*b**8*d**4*e**7/17 + 4620*B*a*b**9*d**5*e**6/
17 + 462*B*b**10*d**6*e**5/17) + x**16*(105*A*a**6*b**4*e**11/8 + 693*A*a**5*b**
5*d*e**10/4 + 5775*A*a**4*b**6*d**2*e**9/8 + 2475*A*a**3*b**7*d**3*e**8/2 + 7425
*A*a**2*b**8*d**4*e**7/8 + 1155*A*a*b**9*d**5*e**6/4 + 231*A*b**10*d**6*e**5/8 +
15*B*a**7*b**3*e**11/2 + 1155*B*a**6*b**4*d*e**10/8 + 3465*B*a**5*b**5*d**2*e**
9/4 + 17325*B*a**4*b**6*d**3*e**8/8 + 2475*B*a**3*b**7*d**4*e**7 + 10395*B*a**2*
b**8*d**5*e**6/8 + 1155*B*a*b**9*d**6*e**5/4 + 165*B*b**10*d**7*e**4/8) + x**15*
(8*A*a**7*b**3*e**11 + 154*A*a**6*b**4*d*e**10 + 924*A*a**5*b**5*d**2*e**9 + 231
0*A*a**4*b**6*d**3*e**8 + 2640*A*a**3*b**7*d**4*e**7 + 1386*A*a**2*b**8*d**5*e**
6 + 308*A*a*b**9*d**6*e**5 + 22*A*b**10*d**7*e**4 + 3*B*a**8*b**2*e**11 + 88*B*a
**7*b**3*d*e**10 + 770*B*a**6*b**4*d**2*e**9 + 2772*B*a**5*b**5*d**3*e**8 + 4620
*B*a**4*b**6*d**4*e**7 + 3696*B*a**3*b**7*d**5*e**6 + 1386*B*a**2*b**8*d**6*e**5
+ 220*B*a*b**9*d**7*e**4 + 11*B*b**10*d**8*e**3) + x**14*(45*A*a**8*b**2*e**11/
14 + 660*A*a**7*b**3*d*e**10/7 + 825*A*a**6*b**4*d**2*e**9 + 2970*A*a**5*b**5*d*
*3*e**8 + 4950*A*a**4*b**6*d**4*e**7 + 3960*A*a**3*b**7*d**5*e**6 + 1485*A*a**2*
b**8*d**6*e**5 + 1650*A*a*b**9*d**7*e**4/7 + 165*A*b**10*d**8*e**3/14 + 5*B*a**9
*b*e**11/7 + 495*B*a**8*b**2*d*e**10/14 + 3300*B*a**7*b**3*d**2*e**9/7 + 2475*B*
a**6*b**4*d**3*e**8 + 5940*B*a**5*b**5*d**4*e**7 + 6930*B*a**4*b**6*d**5*e**6 +
3960*B*a**3*b**7*d**6*e**5 + 7425*B*a**2*b**8*d**7*e**4/7 + 825*B*a*b**9*d**8*e*
*3/7 + 55*B*b**10*d**9*e**2/14) + x**13*(10*A*a**9*b*e**11/13 + 495*A*a**8*b**2*
d*e**10/13 + 6600*A*a**7*b**3*d**2*e**9/13 + 34650*A*a**6*b**4*d**3*e**8/13 + 83
160*A*a**5*b**5*d**4*e**7/13 + 97020*A*a**4*b**6*d**5*e**6/13 + 55440*A*a**3*b**
7*d**6*e**5/13 + 14850*A*a**2*b**8*d**7*e**4/13 + 1650*A*a*b**9*d**8*e**3/13 + 5
5*A*b**10*d**9*e**2/13 + B*a**10*e**11/13 + 110*B*a**9*b*d*e**10/13 + 2475*B*a**
8*b**2*d**2*e**9/13 + 19800*B*a**7*b**3*d**3*e**8/13 + 69300*B*a**6*b**4*d**4*e*
*7/13 + 116424*B*a**5*b**5*d**5*e**6/13 + 97020*B*a**4*b**6*d**6*e**5/13 + 39600
*B*a**3*b**7*d**7*e**4/13 + 7425*B*a**2*b**8*d**8*e**3/13 + 550*B*a*b**9*d**9*e*
*2/13 + 11*B*b**10*d**10*e/13) + x**12*(A*a**10*e**11/12 + 55*A*a**9*b*d*e**10/6
+ 825*A*a**8*b**2*d**2*e**9/4 + 1650*A*a**7*b**3*d**3*e**8 + 5775*A*a**6*b**4*d
**4*e**7 + 9702*A*a**5*b**5*d**5*e**6 + 8085*A*a**4*b**6*d**6*e**5 + 3300*A*a**3
*b**7*d**7*e**4 + 2475*A*a**2*b**8*d**8*e**3/4 + 275*A*a*b**9*d**9*e**2/6 + 11*A
*b**10*d**10*e/12 + 11*B*a**10*d*e**10/12 + 275*B*a**9*b*d**2*e**9/6 + 2475*B*a*
*8*b**2*d**3*e**8/4 + 3300*B*a**7*b**3*d**4*e**7 + 8085*B*a**6*b**4*d**5*e**6 +
9702*B*a**5*b**5*d**6*e**5 + 5775*B*a**4*b**6*d**7*e**4 + 1650*B*a**3*b**7*d**8*
e**3 + 825*B*a**2*b**8*d**9*e**2/4 + 55*B*a*b**9*d**10*e/6 + B*b**10*d**11/12) +
x**11*(A*a**10*d*e**10 + 50*A*a**9*b*d**2*e**9 + 675*A*a**8*b**2*d**3*e**8 + 36
00*A*a**7*b**3*d**4*e**7 + 8820*A*a**6*b**4*d**5*e**6 + 10584*A*a**5*b**5*d**6*e
**5 + 6300*A*a**4*b**6*d**7*e**4 + 1800*A*a**3*b**7*d**8*e**3 + 225*A*a**2*b**8*
d**9*e**2 + 10*A*a*b**9*d**10*e + A*b**10*d**11/11 + 5*B*a**10*d**2*e**9 + 150*B
*a**9*b*d**3*e**8 + 1350*B*a**8*b**2*d**4*e**7 + 5040*B*a**7*b**3*d**5*e**6 + 88
20*B*a**6*b**4*d**6*e**5 + 7560*B*a**5*b**5*d**7*e**4 + 3150*B*a**4*b**6*d**8*e*
*3 + 600*B*a**3*b**7*d**9*e**2 + 45*B*a**2*b**8*d**10*e + 10*B*a*b**9*d**11/11)
+ x**10*(11*A*a**10*d**2*e**9/2 + 165*A*a**9*b*d**3*e**8 + 1485*A*a**8*b**2*d**4
*e**7 + 5544*A*a**7*b**3*d**5*e**6 + 9702*A*a**6*b**4*d**6*e**5 + 8316*A*a**5*b*
*5*d**7*e**4 + 3465*A*a**4*b**6*d**8*e**3 + 660*A*a**3*b**7*d**9*e**2 + 99*A*a**
2*b**8*d**10*e/2 + A*a*b**9*d**11 + 33*B*a**10*d**3*e**8/2 + 330*B*a**9*b*d**4*e
**7 + 2079*B*a**8*b**2*d**5*e**6 + 5544*B*a**7*b**3*d**6*e**5 + 6930*B*a**6*b**4
*d**7*e**4 + 4158*B*a**5*b**5*d**8*e**3 + 1155*B*a**4*b**6*d**9*e**2 + 132*B*a**
3*b**7*d**10*e + 9*B*a**2*b**8*d**11/2) + x**9*(55*A*a**10*d**3*e**8/3 + 1100*A*
a**9*b*d**4*e**7/3 + 2310*A*a**8*b**2*d**5*e**6 + 6160*A*a**7*b**3*d**6*e**5 + 7
700*A*a**6*b**4*d**7*e**4 + 4620*A*a**5*b**5*d**8*e**3 + 3850*A*a**4*b**6*d**9*e
**2/3 + 440*A*a**3*b**7*d**10*e/3 + 5*A*a**2*b**8*d**11 + 110*B*a**10*d**4*e**7/
3 + 1540*B*a**9*b*d**5*e**6/3 + 2310*B*a**8*b**2*d**6*e**5 + 4400*B*a**7*b**3*d*
*7*e**4 + 3850*B*a**6*b**4*d**8*e**3 + 1540*B*a**5*b**5*d**9*e**2 + 770*B*a**4*b
**6*d**10*e/3 + 40*B*a**3*b**7*d**11/3) + x**8*(165*A*a**10*d**4*e**7/4 + 1155*A
*a**9*b*d**5*e**6/2 + 10395*A*a**8*b**2*d**6*e**5/4 + 4950*A*a**7*b**3*d**7*e**4
+ 17325*A*a**6*b**4*d**8*e**3/4 + 3465*A*a**5*b**5*d**9*e**2/2 + 1155*A*a**4*b*
*6*d**10*e/4 + 15*A*a**3*b**7*d**11 + 231*B*a**10*d**5*e**6/4 + 1155*B*a**9*b*d*
*6*e**5/2 + 7425*B*a**8*b**2*d**7*e**4/4 + 2475*B*a**7*b**3*d**8*e**3 + 5775*B*a
**6*b**4*d**9*e**2/4 + 693*B*a**5*b**5*d**10*e/2 + 105*B*a**4*b**6*d**11/4) + x*
*7*(66*A*a**10*d**5*e**6 + 660*A*a**9*b*d**6*e**5 + 14850*A*a**8*b**2*d**7*e**4/
7 + 19800*A*a**7*b**3*d**8*e**3/7 + 1650*A*a**6*b**4*d**9*e**2 + 396*A*a**5*b**5
*d**10*e + 30*A*a**4*b**6*d**11 + 66*B*a**10*d**6*e**5 + 3300*B*a**9*b*d**7*e**4
/7 + 7425*B*a**8*b**2*d**8*e**3/7 + 6600*B*a**7*b**3*d**9*e**2/7 + 330*B*a**6*b*
*4*d**10*e + 36*B*a**5*b**5*d**11) + x**6*(77*A*a**10*d**6*e**5 + 550*A*a**9*b*d
**7*e**4 + 2475*A*a**8*b**2*d**8*e**3/2 + 1100*A*a**7*b**3*d**9*e**2 + 385*A*a**
6*b**4*d**10*e + 42*A*a**5*b**5*d**11 + 55*B*a**10*d**7*e**4 + 275*B*a**9*b*d**8
*e**3 + 825*B*a**8*b**2*d**9*e**2/2 + 220*B*a**7*b**3*d**10*e + 35*B*a**6*b**4*d
**11) + x**5*(66*A*a**10*d**7*e**4 + 330*A*a**9*b*d**8*e**3 + 495*A*a**8*b**2*d*
*9*e**2 + 264*A*a**7*b**3*d**10*e + 42*A*a**6*b**4*d**11 + 33*B*a**10*d**8*e**3
+ 110*B*a**9*b*d**9*e**2 + 99*B*a**8*b**2*d**10*e + 24*B*a**7*b**3*d**11) + x**4
*(165*A*a**10*d**8*e**3/4 + 275*A*a**9*b*d**9*e**2/2 + 495*A*a**8*b**2*d**10*e/4
+ 30*A*a**7*b**3*d**11 + 55*B*a**10*d**9*e**2/4 + 55*B*a**9*b*d**10*e/2 + 45*B*
a**8*b**2*d**11/4) + x**3*(55*A*a**10*d**9*e**2/3 + 110*A*a**9*b*d**10*e/3 + 15*
A*a**8*b**2*d**11 + 11*B*a**10*d**10*e/3 + 10*B*a**9*b*d**11/3) + x**2*(11*A*a**
10*d**10*e/2 + 5*A*a**9*b*d**11 + B*a**10*d**11/2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21873, 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)^11,x, algorithm="giac")

[Out]

Done