3.1061 \(\int (a+b x)^{10} (A+B x) (d+e x)^{10} \, dx\)

Optimal. Leaf size=460 \[ \frac{e^9 (a+b x)^{21} (-11 a B e+A b e+10 b B d)}{21 b^{12}}+\frac{e^8 (a+b x)^{20} (b d-a e) (-11 a B e+2 A b e+9 b B d)}{4 b^{12}}+\frac{15 e^7 (a+b x)^{19} (b d-a e)^2 (-11 a B e+3 A b e+8 b B d)}{19 b^{12}}+\frac{5 e^6 (a+b x)^{18} (b d-a e)^3 (-11 a B e+4 A b e+7 b B d)}{3 b^{12}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^4 (-11 a B e+5 A b e+6 b B d)}{17 b^{12}}+\frac{21 e^4 (a+b x)^{16} (b d-a e)^5 (-11 a B e+6 A b e+5 b B d)}{8 b^{12}}+\frac{2 e^3 (a+b x)^{15} (b d-a e)^6 (-11 a B e+7 A b e+4 b B d)}{b^{12}}+\frac{15 e^2 (a+b x)^{14} (b d-a e)^7 (-11 a B e+8 A b e+3 b B d)}{14 b^{12}}+\frac{5 e (a+b x)^{13} (b d-a e)^8 (-11 a B e+9 A b e+2 b B d)}{13 b^{12}}+\frac{(a+b x)^{12} (b d-a e)^9 (-11 a B e+10 A b e+b B d)}{12 b^{12}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^{10}}{11 b^{12}}+\frac{B e^{10} (a+b x)^{22}}{22 b^{12}} \]

[Out]

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

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Rubi [A]  time = 15.8952, antiderivative size = 460, 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 \[ \frac{e^9 (a+b x)^{21} (-11 a B e+A b e+10 b B d)}{21 b^{12}}+\frac{e^8 (a+b x)^{20} (b d-a e) (-11 a B e+2 A b e+9 b B d)}{4 b^{12}}+\frac{15 e^7 (a+b x)^{19} (b d-a e)^2 (-11 a B e+3 A b e+8 b B d)}{19 b^{12}}+\frac{5 e^6 (a+b x)^{18} (b d-a e)^3 (-11 a B e+4 A b e+7 b B d)}{3 b^{12}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^4 (-11 a B e+5 A b e+6 b B d)}{17 b^{12}}+\frac{21 e^4 (a+b x)^{16} (b d-a e)^5 (-11 a B e+6 A b e+5 b B d)}{8 b^{12}}+\frac{2 e^3 (a+b x)^{15} (b d-a e)^6 (-11 a B e+7 A b e+4 b B d)}{b^{12}}+\frac{15 e^2 (a+b x)^{14} (b d-a e)^7 (-11 a B e+8 A b e+3 b B d)}{14 b^{12}}+\frac{5 e (a+b x)^{13} (b d-a e)^8 (-11 a B e+9 A b e+2 b B d)}{13 b^{12}}+\frac{(a+b x)^{12} (b d-a e)^9 (-11 a B e+10 A b e+b B d)}{12 b^{12}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^{10}}{11 b^{12}}+\frac{B e^{10} (a+b x)^{22}}{22 b^{12}} \]

Antiderivative was successfully verified.

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

[Out]

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

[Out]

Timed out

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Mathematica [B]  time = 2.36964, size = 2815, normalized size = 6.12 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

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

[Out]

a^10*A*d^10*x + (a^9*d^9*(a*B*d + 10*A*(b*d + a*e))*x^2)/2 + (5*a^8*d^8*(2*a*B*d
*(b*d + a*e) + A*(9*b^2*d^2 + 20*a*b*d*e + 9*a^2*e^2))*x^3)/3 + (5*a^7*d^7*(a*B*
d*(9*b^2*d^2 + 20*a*b*d*e + 9*a^2*e^2) + 6*A*(4*b^3*d^3 + 15*a*b^2*d^2*e + 15*a^
2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + 3*a^6*d^6*(2*a*B*d*(4*b^3*d^3 + 15*a*b^2*d^2*e
+ 15*a^2*b*d*e^2 + 4*a^3*e^3) + A*(14*b^4*d^4 + 80*a*b^3*d^3*e + 135*a^2*b^2*d^2
*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4))*x^5 + (a^5*d^5*(5*a*B*d*(14*b^4*d^4 + 80*a*
b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4) + 4*A*(21*b^5*d^5
+ 175*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b*d*e^4
+ 21*a^5*e^5))*x^6)/2 + (6*a^4*d^4*(2*a*B*d*(21*b^5*d^5 + 175*a*b^4*d^4*e + 450
*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b*d*e^4 + 21*a^5*e^5) + 5*A*(7*
b^6*d^6 + 84*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b
^2*d^2*e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6))*x^7)/7 + (15*a^3*d^3*(a*B*d*(7*b^6*d^6
+ 84*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b^2*d^2*
e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6) + A*(4*b^7*d^7 + 70*a*b^6*d^6*e + 378*a^2*b^5*
d^5*e^2 + 840*a^3*b^4*d^4*e^3 + 840*a^4*b^3*d^3*e^4 + 378*a^5*b^2*d^2*e^5 + 70*a
^6*b*d*e^6 + 4*a^7*e^7))*x^8)/4 + (5*a^2*d^2*(4*a*B*d*(2*b^7*d^7 + 35*a*b^6*d^6*
e + 189*a^2*b^5*d^5*e^2 + 420*a^3*b^4*d^4*e^3 + 420*a^4*b^3*d^3*e^4 + 189*a^5*b^
2*d^2*e^5 + 35*a^6*b*d*e^6 + 2*a^7*e^7) + A*(3*b^8*d^8 + 80*a*b^7*d^7*e + 630*a^
2*b^6*d^6*e^2 + 2016*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e
^5 + 630*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + 3*a^8*e^8))*x^9)/3 + (a*d*(3*a*B*d*(
3*b^8*d^8 + 80*a*b^7*d^7*e + 630*a^2*b^6*d^6*e^2 + 2016*a^3*b^5*d^5*e^3 + 2940*a
^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e^5 + 630*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + 3
*a^8*e^8) + 2*A*(b^9*d^9 + 45*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d
^6*e^3 + 5292*a^4*b^5*d^5*e^4 + 5292*a^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 54
0*a^7*b^2*d^2*e^7 + 45*a^8*b*d*e^8 + a^9*e^9))*x^10)/2 + ((10*a*B*d*(b^9*d^9 + 4
5*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d^6*e^3 + 5292*a^4*b^5*d^5*e^
4 + 5292*a^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 540*a^7*b^2*d^2*e^7 + 45*a^8*b
*d*e^8 + a^9*e^9) + A*(b^10*d^10 + 100*a*b^9*d^9*e + 2025*a^2*b^8*d^8*e^2 + 1440
0*a^3*b^7*d^7*e^3 + 44100*a^4*b^6*d^6*e^4 + 63504*a^5*b^5*d^5*e^5 + 44100*a^6*b^
4*d^4*e^6 + 14400*a^7*b^3*d^3*e^7 + 2025*a^8*b^2*d^2*e^8 + 100*a^9*b*d*e^9 + a^1
0*e^10))*x^11)/11 + ((a^10*B*e^10 + 10*a^9*b*e^9*(10*B*d + A*e) + 225*a^8*b^2*d*
e^8*(9*B*d + 2*A*e) + 1800*a^7*b^3*d^2*e^7*(8*B*d + 3*A*e) + 6300*a^6*b^4*d^3*e^
6*(7*B*d + 4*A*e) + 10584*a^5*b^5*d^4*e^5*(6*B*d + 5*A*e) + 8820*a^4*b^6*d^5*e^4
*(5*B*d + 6*A*e) + 3600*a^3*b^7*d^6*e^3*(4*B*d + 7*A*e) + 675*a^2*b^8*d^7*e^2*(3
*B*d + 8*A*e) + 50*a*b^9*d^8*e*(2*B*d + 9*A*e) + b^10*d^9*(B*d + 10*A*e))*x^12)/
12 + (5*b*e*(2*a^9*B*e^9 + 9*a^8*b*e^8*(10*B*d + A*e) + 120*a^7*b^2*d*e^7*(9*B*d
+ 2*A*e) + 630*a^6*b^3*d^2*e^6*(8*B*d + 3*A*e) + 1512*a^5*b^4*d^3*e^5*(7*B*d +
4*A*e) + 1764*a^4*b^5*d^4*e^4*(6*B*d + 5*A*e) + 1008*a^3*b^6*d^5*e^3*(5*B*d + 6*
A*e) + 270*a^2*b^7*d^6*e^2*(4*B*d + 7*A*e) + 30*a*b^8*d^7*e*(3*B*d + 8*A*e) + b^
9*d^8*(2*B*d + 9*A*e))*x^13)/13 + (15*b^2*e^2*(3*a^8*B*e^8 + 8*a^7*b*e^7*(10*B*d
+ A*e) + 70*a^6*b^2*d*e^6*(9*B*d + 2*A*e) + 252*a^5*b^3*d^2*e^5*(8*B*d + 3*A*e)
+ 420*a^4*b^4*d^3*e^4*(7*B*d + 4*A*e) + 336*a^3*b^5*d^4*e^3*(6*B*d + 5*A*e) + 1
26*a^2*b^6*d^5*e^2*(5*B*d + 6*A*e) + 20*a*b^7*d^6*e*(4*B*d + 7*A*e) + b^8*d^7*(3
*B*d + 8*A*e))*x^14)/14 + 2*b^3*e^3*(4*a^7*B*e^7 + 7*a^6*b*e^6*(10*B*d + A*e) +
42*a^5*b^2*d*e^5*(9*B*d + 2*A*e) + 105*a^4*b^3*d^2*e^4*(8*B*d + 3*A*e) + 120*a^3
*b^4*d^3*e^3*(7*B*d + 4*A*e) + 63*a^2*b^5*d^4*e^2*(6*B*d + 5*A*e) + 14*a*b^6*d^5
*e*(5*B*d + 6*A*e) + b^7*d^6*(4*B*d + 7*A*e))*x^15 + (3*b^4*e^4*(35*a^6*B*e^6 +
42*a^5*b*e^5*(10*B*d + A*e) + 175*a^4*b^2*d*e^4*(9*B*d + 2*A*e) + 300*a^3*b^3*d^
2*e^3*(8*B*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(7*B*d + 4*A*e) + 70*a*b^5*d^4*e*(6*
B*d + 5*A*e) + 7*b^6*d^5*(5*B*d + 6*A*e))*x^16)/8 + (3*b^5*e^5*(84*a^5*B*e^5 + 7
0*a^4*b*e^4*(10*B*d + A*e) + 200*a^3*b^2*d*e^3*(9*B*d + 2*A*e) + 225*a^2*b^3*d^2
*e^2*(8*B*d + 3*A*e) + 100*a*b^4*d^3*e*(7*B*d + 4*A*e) + 14*b^5*d^4*(6*B*d + 5*A
*e))*x^17)/17 + (5*b^6*e^6*(14*a^4*B*e^4 + 8*a^3*b*e^3*(10*B*d + A*e) + 15*a^2*b
^2*d*e^2*(9*B*d + 2*A*e) + 10*a*b^3*d^2*e*(8*B*d + 3*A*e) + 2*b^4*d^3*(7*B*d + 4
*A*e))*x^18)/6 + (5*b^7*e^7*(24*a^3*B*e^3 + 9*a^2*b*e^2*(10*B*d + A*e) + 10*a*b^
2*d*e*(9*B*d + 2*A*e) + 3*b^3*d^2*(8*B*d + 3*A*e))*x^19)/19 + (b^8*e^8*(9*a^2*B*
e^2 + 2*a*b*e*(10*B*d + A*e) + b^2*d*(9*B*d + 2*A*e))*x^20)/4 + (b^9*e^9*(10*b*B
*d + A*b*e + 10*a*B*e)*x^21)/21 + (b^10*B*e^10*x^22)/22

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Maple [B]  time = 0.006, size = 3041, normalized size = 6.6 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Maxima [A]  time = 1.41395, size = 4115, normalized size = 8.95 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/22*B*b^10*e^10*x^22 + A*a^10*d^10*x + 1/21*(10*B*b^10*d*e^9 + (10*B*a*b^9 + A*
b^10)*e^10)*x^21 + 1/4*(9*B*b^10*d^2*e^8 + 2*(10*B*a*b^9 + A*b^10)*d*e^9 + (9*B*
a^2*b^8 + 2*A*a*b^9)*e^10)*x^20 + 5/19*(24*B*b^10*d^3*e^7 + 9*(10*B*a*b^9 + A*b^
10)*d^2*e^8 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^9 + 3*(8*B*a^3*b^7 + 3*A*a^2*b^8)
*e^10)*x^19 + 5/6*(14*B*b^10*d^4*e^6 + 8*(10*B*a*b^9 + A*b^10)*d^3*e^7 + 15*(9*B
*a^2*b^8 + 2*A*a*b^9)*d^2*e^8 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^9 + 2*(7*B*a^
4*b^6 + 4*A*a^3*b^7)*e^10)*x^18 + 3/17*(84*B*b^10*d^5*e^5 + 70*(10*B*a*b^9 + A*b
^10)*d^4*e^6 + 200*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^7 + 225*(8*B*a^3*b^7 + 3*A*a^
2*b^8)*d^2*e^8 + 100*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^9 + 14*(6*B*a^5*b^5 + 5*A*a
^4*b^6)*e^10)*x^17 + 3/8*(35*B*b^10*d^6*e^4 + 42*(10*B*a*b^9 + A*b^10)*d^5*e^5 +
175*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^6 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^7
+ 225*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^8 + 70*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^
9 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^10)*x^16 + 2*(4*B*b^10*d^7*e^3 + 7*(10*B*a*b
^9 + A*b^10)*d^6*e^4 + 42*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^5 + 105*(8*B*a^3*b^7 +
3*A*a^2*b^8)*d^4*e^6 + 120*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^7 + 63*(6*B*a^5*b^
5 + 5*A*a^4*b^6)*d^2*e^8 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^9 + (4*B*a^7*b^3 +
7*A*a^6*b^4)*e^10)*x^15 + 15/14*(3*B*b^10*d^8*e^2 + 8*(10*B*a*b^9 + A*b^10)*d^7
*e^3 + 70*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^4 + 252*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^
5*e^5 + 420*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^6 + 336*(6*B*a^5*b^5 + 5*A*a^4*b^6
)*d^3*e^7 + 126*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^8 + 20*(4*B*a^7*b^3 + 7*A*a^6*
b^4)*d*e^9 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*e^10)*x^14 + 5/13*(2*B*b^10*d^9*e + 9*(
10*B*a*b^9 + A*b^10)*d^8*e^2 + 120*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^3 + 630*(8*B*
a^3*b^7 + 3*A*a^2*b^8)*d^6*e^4 + 1512*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^5 + 1764
*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^6 + 1008*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^7
+ 270*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^8 + 30*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^9
+ (2*B*a^9*b + 9*A*a^8*b^2)*e^10)*x^13 + 1/12*(B*b^10*d^10 + 10*(10*B*a*b^9 + A
*b^10)*d^9*e + 225*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^2 + 1800*(8*B*a^3*b^7 + 3*A*a
^2*b^8)*d^7*e^3 + 6300*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^4 + 10584*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d^5*e^5 + 8820*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^6 + 3600*(4*B*a^
7*b^3 + 7*A*a^6*b^4)*d^3*e^7 + 675*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^8 + 50*(2*B
*a^9*b + 9*A*a^8*b^2)*d*e^9 + (B*a^10 + 10*A*a^9*b)*e^10)*x^12 + 1/11*(A*a^10*e^
10 + (10*B*a*b^9 + A*b^10)*d^10 + 50*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e + 675*(8*B*
a^3*b^7 + 3*A*a^2*b^8)*d^8*e^2 + 3600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^3 + 8820
*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^4 + 10584*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^5
+ 6300*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^6 + 1800*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d
^3*e^7 + 225*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^8 + 10*(B*a^10 + 10*A*a^9*b)*d*e^9)
*x^11 + 1/2*(2*A*a^10*d*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^10 + 30*(8*B*a^3*b^7 +
3*A*a^2*b^8)*d^9*e + 270*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*e^2 + 1008*(6*B*a^5*b^
5 + 5*A*a^4*b^6)*d^7*e^3 + 1764*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*e^4 + 1512*(4*B*
a^7*b^3 + 7*A*a^6*b^4)*d^5*e^5 + 630*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*e^6 + 120*(
2*B*a^9*b + 9*A*a^8*b^2)*d^3*e^7 + 9*(B*a^10 + 10*A*a^9*b)*d^2*e^8)*x^10 + 5/3*(
3*A*a^10*d^2*e^8 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10 + 20*(7*B*a^4*b^6 + 4*A*a^3*
b^7)*d^9*e + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^8*e^2 + 336*(5*B*a^6*b^4 + 6*A*a^
5*b^5)*d^7*e^3 + 420*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*e^4 + 252*(3*B*a^8*b^2 + 8*
A*a^7*b^3)*d^5*e^5 + 70*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*e^6 + 8*(B*a^10 + 10*A*a^9
*b)*d^3*e^7)*x^9 + 15/4*(4*A*a^10*d^3*e^7 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^10 + 1
4*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^9*e + 63*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*e^2 + 1
20*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^7*e^3 + 105*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*e^4
+ 42*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*e^5 + 7*(B*a^10 + 10*A*a^9*b)*d^4*e^6)*x^8 +
6/7*(35*A*a^10*d^4*e^6 + 7*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^10 + 70*(5*B*a^6*b^4 +
6*A*a^5*b^5)*d^9*e + 225*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*e^2 + 300*(3*B*a^8*b^2
+ 8*A*a^7*b^3)*d^7*e^3 + 175*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*e^4 + 42*(B*a^10 + 1
0*A*a^9*b)*d^5*e^5)*x^7 + 1/2*(84*A*a^10*d^5*e^5 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5
)*d^10 + 100*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^9*e + 225*(3*B*a^8*b^2 + 8*A*a^7*b^3)
*d^8*e^2 + 200*(2*B*a^9*b + 9*A*a^8*b^2)*d^7*e^3 + 70*(B*a^10 + 10*A*a^9*b)*d^6*
e^4)*x^6 + 3*(14*A*a^10*d^6*e^4 + 2*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^10 + 10*(3*B*a
^8*b^2 + 8*A*a^7*b^3)*d^9*e + 15*(2*B*a^9*b + 9*A*a^8*b^2)*d^8*e^2 + 8*(B*a^10 +
10*A*a^9*b)*d^7*e^3)*x^5 + 5/4*(24*A*a^10*d^7*e^3 + 3*(3*B*a^8*b^2 + 8*A*a^7*b^
3)*d^10 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^9*e + 9*(B*a^10 + 10*A*a^9*b)*d^8*e^2)*
x^4 + 5/3*(9*A*a^10*d^8*e^2 + (2*B*a^9*b + 9*A*a^8*b^2)*d^10 + 2*(B*a^10 + 10*A*
a^9*b)*d^9*e)*x^3 + 1/2*(10*A*a^10*d^9*e + (B*a^10 + 10*A*a^9*b)*d^10)*x^2

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Fricas [A]  time = 0.19901, 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)^10,x, algorithm="fricas")

[Out]

1/22*x^22*e^10*b^10*B + 10/21*x^21*e^9*d*b^10*B + 10/21*x^21*e^10*b^9*a*B + 1/21
*x^21*e^10*b^10*A + 9/4*x^20*e^8*d^2*b^10*B + 5*x^20*e^9*d*b^9*a*B + 9/4*x^20*e^
10*b^8*a^2*B + 1/2*x^20*e^9*d*b^10*A + 1/2*x^20*e^10*b^9*a*A + 120/19*x^19*e^7*d
^3*b^10*B + 450/19*x^19*e^8*d^2*b^9*a*B + 450/19*x^19*e^9*d*b^8*a^2*B + 120/19*x
^19*e^10*b^7*a^3*B + 45/19*x^19*e^8*d^2*b^10*A + 100/19*x^19*e^9*d*b^9*a*A + 45/
19*x^19*e^10*b^8*a^2*A + 35/3*x^18*e^6*d^4*b^10*B + 200/3*x^18*e^7*d^3*b^9*a*B +
225/2*x^18*e^8*d^2*b^8*a^2*B + 200/3*x^18*e^9*d*b^7*a^3*B + 35/3*x^18*e^10*b^6*
a^4*B + 20/3*x^18*e^7*d^3*b^10*A + 25*x^18*e^8*d^2*b^9*a*A + 25*x^18*e^9*d*b^8*a
^2*A + 20/3*x^18*e^10*b^7*a^3*A + 252/17*x^17*e^5*d^5*b^10*B + 2100/17*x^17*e^6*
d^4*b^9*a*B + 5400/17*x^17*e^7*d^3*b^8*a^2*B + 5400/17*x^17*e^8*d^2*b^7*a^3*B +
2100/17*x^17*e^9*d*b^6*a^4*B + 252/17*x^17*e^10*b^5*a^5*B + 210/17*x^17*e^6*d^4*
b^10*A + 1200/17*x^17*e^7*d^3*b^9*a*A + 2025/17*x^17*e^8*d^2*b^8*a^2*A + 1200/17
*x^17*e^9*d*b^7*a^3*A + 210/17*x^17*e^10*b^6*a^4*A + 105/8*x^16*e^4*d^6*b^10*B +
315/2*x^16*e^5*d^5*b^9*a*B + 4725/8*x^16*e^6*d^4*b^8*a^2*B + 900*x^16*e^7*d^3*b
^7*a^3*B + 4725/8*x^16*e^8*d^2*b^6*a^4*B + 315/2*x^16*e^9*d*b^5*a^5*B + 105/8*x^
16*e^10*b^4*a^6*B + 63/4*x^16*e^5*d^5*b^10*A + 525/4*x^16*e^6*d^4*b^9*a*A + 675/
2*x^16*e^7*d^3*b^8*a^2*A + 675/2*x^16*e^8*d^2*b^7*a^3*A + 525/4*x^16*e^9*d*b^6*a
^4*A + 63/4*x^16*e^10*b^5*a^5*A + 8*x^15*e^3*d^7*b^10*B + 140*x^15*e^4*d^6*b^9*a
*B + 756*x^15*e^5*d^5*b^8*a^2*B + 1680*x^15*e^6*d^4*b^7*a^3*B + 1680*x^15*e^7*d^
3*b^6*a^4*B + 756*x^15*e^8*d^2*b^5*a^5*B + 140*x^15*e^9*d*b^4*a^6*B + 8*x^15*e^1
0*b^3*a^7*B + 14*x^15*e^4*d^6*b^10*A + 168*x^15*e^5*d^5*b^9*a*A + 630*x^15*e^6*d
^4*b^8*a^2*A + 960*x^15*e^7*d^3*b^7*a^3*A + 630*x^15*e^8*d^2*b^6*a^4*A + 168*x^1
5*e^9*d*b^5*a^5*A + 14*x^15*e^10*b^4*a^6*A + 45/14*x^14*e^2*d^8*b^10*B + 600/7*x
^14*e^3*d^7*b^9*a*B + 675*x^14*e^4*d^6*b^8*a^2*B + 2160*x^14*e^5*d^5*b^7*a^3*B +
3150*x^14*e^6*d^4*b^6*a^4*B + 2160*x^14*e^7*d^3*b^5*a^5*B + 675*x^14*e^8*d^2*b^
4*a^6*B + 600/7*x^14*e^9*d*b^3*a^7*B + 45/14*x^14*e^10*b^2*a^8*B + 60/7*x^14*e^3
*d^7*b^10*A + 150*x^14*e^4*d^6*b^9*a*A + 810*x^14*e^5*d^5*b^8*a^2*A + 1800*x^14*
e^6*d^4*b^7*a^3*A + 1800*x^14*e^7*d^3*b^6*a^4*A + 810*x^14*e^8*d^2*b^5*a^5*A + 1
50*x^14*e^9*d*b^4*a^6*A + 60/7*x^14*e^10*b^3*a^7*A + 10/13*x^13*e*d^9*b^10*B + 4
50/13*x^13*e^2*d^8*b^9*a*B + 5400/13*x^13*e^3*d^7*b^8*a^2*B + 25200/13*x^13*e^4*
d^6*b^7*a^3*B + 52920/13*x^13*e^5*d^5*b^6*a^4*B + 52920/13*x^13*e^6*d^4*b^5*a^5*
B + 25200/13*x^13*e^7*d^3*b^4*a^6*B + 5400/13*x^13*e^8*d^2*b^3*a^7*B + 450/13*x^
13*e^9*d*b^2*a^8*B + 10/13*x^13*e^10*b*a^9*B + 45/13*x^13*e^2*d^8*b^10*A + 1200/
13*x^13*e^3*d^7*b^9*a*A + 9450/13*x^13*e^4*d^6*b^8*a^2*A + 30240/13*x^13*e^5*d^5
*b^7*a^3*A + 44100/13*x^13*e^6*d^4*b^6*a^4*A + 30240/13*x^13*e^7*d^3*b^5*a^5*A +
9450/13*x^13*e^8*d^2*b^4*a^6*A + 1200/13*x^13*e^9*d*b^3*a^7*A + 45/13*x^13*e^10
*b^2*a^8*A + 1/12*x^12*d^10*b^10*B + 25/3*x^12*e*d^9*b^9*a*B + 675/4*x^12*e^2*d^
8*b^8*a^2*B + 1200*x^12*e^3*d^7*b^7*a^3*B + 3675*x^12*e^4*d^6*b^6*a^4*B + 5292*x
^12*e^5*d^5*b^5*a^5*B + 3675*x^12*e^6*d^4*b^4*a^6*B + 1200*x^12*e^7*d^3*b^3*a^7*
B + 675/4*x^12*e^8*d^2*b^2*a^8*B + 25/3*x^12*e^9*d*b*a^9*B + 1/12*x^12*e^10*a^10
*B + 5/6*x^12*e*d^9*b^10*A + 75/2*x^12*e^2*d^8*b^9*a*A + 450*x^12*e^3*d^7*b^8*a^
2*A + 2100*x^12*e^4*d^6*b^7*a^3*A + 4410*x^12*e^5*d^5*b^6*a^4*A + 4410*x^12*e^6*
d^4*b^5*a^5*A + 2100*x^12*e^7*d^3*b^4*a^6*A + 450*x^12*e^8*d^2*b^3*a^7*A + 75/2*
x^12*e^9*d*b^2*a^8*A + 5/6*x^12*e^10*b*a^9*A + 10/11*x^11*d^10*b^9*a*B + 450/11*
x^11*e*d^9*b^8*a^2*B + 5400/11*x^11*e^2*d^8*b^7*a^3*B + 25200/11*x^11*e^3*d^7*b^
6*a^4*B + 52920/11*x^11*e^4*d^6*b^5*a^5*B + 52920/11*x^11*e^5*d^5*b^4*a^6*B + 25
200/11*x^11*e^6*d^4*b^3*a^7*B + 5400/11*x^11*e^7*d^3*b^2*a^8*B + 450/11*x^11*e^8
*d^2*b*a^9*B + 10/11*x^11*e^9*d*a^10*B + 1/11*x^11*d^10*b^10*A + 100/11*x^11*e*d
^9*b^9*a*A + 2025/11*x^11*e^2*d^8*b^8*a^2*A + 14400/11*x^11*e^3*d^7*b^7*a^3*A +
44100/11*x^11*e^4*d^6*b^6*a^4*A + 63504/11*x^11*e^5*d^5*b^5*a^5*A + 44100/11*x^1
1*e^6*d^4*b^4*a^6*A + 14400/11*x^11*e^7*d^3*b^3*a^7*A + 2025/11*x^11*e^8*d^2*b^2
*a^8*A + 100/11*x^11*e^9*d*b*a^9*A + 1/11*x^11*e^10*a^10*A + 9/2*x^10*d^10*b^8*a
^2*B + 120*x^10*e*d^9*b^7*a^3*B + 945*x^10*e^2*d^8*b^6*a^4*B + 3024*x^10*e^3*d^7
*b^5*a^5*B + 4410*x^10*e^4*d^6*b^4*a^6*B + 3024*x^10*e^5*d^5*b^3*a^7*B + 945*x^1
0*e^6*d^4*b^2*a^8*B + 120*x^10*e^7*d^3*b*a^9*B + 9/2*x^10*e^8*d^2*a^10*B + x^10*
d^10*b^9*a*A + 45*x^10*e*d^9*b^8*a^2*A + 540*x^10*e^2*d^8*b^7*a^3*A + 2520*x^10*
e^3*d^7*b^6*a^4*A + 5292*x^10*e^4*d^6*b^5*a^5*A + 5292*x^10*e^5*d^5*b^4*a^6*A +
2520*x^10*e^6*d^4*b^3*a^7*A + 540*x^10*e^7*d^3*b^2*a^8*A + 45*x^10*e^8*d^2*b*a^9
*A + x^10*e^9*d*a^10*A + 40/3*x^9*d^10*b^7*a^3*B + 700/3*x^9*e*d^9*b^6*a^4*B + 1
260*x^9*e^2*d^8*b^5*a^5*B + 2800*x^9*e^3*d^7*b^4*a^6*B + 2800*x^9*e^4*d^6*b^3*a^
7*B + 1260*x^9*e^5*d^5*b^2*a^8*B + 700/3*x^9*e^6*d^4*b*a^9*B + 40/3*x^9*e^7*d^3*
a^10*B + 5*x^9*d^10*b^8*a^2*A + 400/3*x^9*e*d^9*b^7*a^3*A + 1050*x^9*e^2*d^8*b^6
*a^4*A + 3360*x^9*e^3*d^7*b^5*a^5*A + 4900*x^9*e^4*d^6*b^4*a^6*A + 3360*x^9*e^5*
d^5*b^3*a^7*A + 1050*x^9*e^6*d^4*b^2*a^8*A + 400/3*x^9*e^7*d^3*b*a^9*A + 5*x^9*e
^8*d^2*a^10*A + 105/4*x^8*d^10*b^6*a^4*B + 315*x^8*e*d^9*b^5*a^5*B + 4725/4*x^8*
e^2*d^8*b^4*a^6*B + 1800*x^8*e^3*d^7*b^3*a^7*B + 4725/4*x^8*e^4*d^6*b^2*a^8*B +
315*x^8*e^5*d^5*b*a^9*B + 105/4*x^8*e^6*d^4*a^10*B + 15*x^8*d^10*b^7*a^3*A + 525
/2*x^8*e*d^9*b^6*a^4*A + 2835/2*x^8*e^2*d^8*b^5*a^5*A + 3150*x^8*e^3*d^7*b^4*a^6
*A + 3150*x^8*e^4*d^6*b^3*a^7*A + 2835/2*x^8*e^5*d^5*b^2*a^8*A + 525/2*x^8*e^6*d
^4*b*a^9*A + 15*x^8*e^7*d^3*a^10*A + 36*x^7*d^10*b^5*a^5*B + 300*x^7*e*d^9*b^4*a
^6*B + 5400/7*x^7*e^2*d^8*b^3*a^7*B + 5400/7*x^7*e^3*d^7*b^2*a^8*B + 300*x^7*e^4
*d^6*b*a^9*B + 36*x^7*e^5*d^5*a^10*B + 30*x^7*d^10*b^6*a^4*A + 360*x^7*e*d^9*b^5
*a^5*A + 1350*x^7*e^2*d^8*b^4*a^6*A + 14400/7*x^7*e^3*d^7*b^3*a^7*A + 1350*x^7*e
^4*d^6*b^2*a^8*A + 360*x^7*e^5*d^5*b*a^9*A + 30*x^7*e^6*d^4*a^10*A + 35*x^6*d^10
*b^4*a^6*B + 200*x^6*e*d^9*b^3*a^7*B + 675/2*x^6*e^2*d^8*b^2*a^8*B + 200*x^6*e^3
*d^7*b*a^9*B + 35*x^6*e^4*d^6*a^10*B + 42*x^6*d^10*b^5*a^5*A + 350*x^6*e*d^9*b^4
*a^6*A + 900*x^6*e^2*d^8*b^3*a^7*A + 900*x^6*e^3*d^7*b^2*a^8*A + 350*x^6*e^4*d^6
*b*a^9*A + 42*x^6*e^5*d^5*a^10*A + 24*x^5*d^10*b^3*a^7*B + 90*x^5*e*d^9*b^2*a^8*
B + 90*x^5*e^2*d^8*b*a^9*B + 24*x^5*e^3*d^7*a^10*B + 42*x^5*d^10*b^4*a^6*A + 240
*x^5*e*d^9*b^3*a^7*A + 405*x^5*e^2*d^8*b^2*a^8*A + 240*x^5*e^3*d^7*b*a^9*A + 42*
x^5*e^4*d^6*a^10*A + 45/4*x^4*d^10*b^2*a^8*B + 25*x^4*e*d^9*b*a^9*B + 45/4*x^4*e
^2*d^8*a^10*B + 30*x^4*d^10*b^3*a^7*A + 225/2*x^4*e*d^9*b^2*a^8*A + 225/2*x^4*e^
2*d^8*b*a^9*A + 30*x^4*e^3*d^7*a^10*A + 10/3*x^3*d^10*b*a^9*B + 10/3*x^3*e*d^9*a
^10*B + 15*x^3*d^10*b^2*a^8*A + 100/3*x^3*e*d^9*b*a^9*A + 15*x^3*e^2*d^8*a^10*A
+ 1/2*x^2*d^10*a^10*B + 5*x^2*d^10*b*a^9*A + 5*x^2*e*d^9*a^10*A + x*d^10*a^10*A

_______________________________________________________________________________________

Sympy [A]  time = 1.62988, size = 3936, normalized size = 8.56 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

A*a**10*d**10*x + B*b**10*e**10*x**22/22 + x**21*(A*b**10*e**10/21 + 10*B*a*b**9
*e**10/21 + 10*B*b**10*d*e**9/21) + x**20*(A*a*b**9*e**10/2 + A*b**10*d*e**9/2 +
9*B*a**2*b**8*e**10/4 + 5*B*a*b**9*d*e**9 + 9*B*b**10*d**2*e**8/4) + x**19*(45*
A*a**2*b**8*e**10/19 + 100*A*a*b**9*d*e**9/19 + 45*A*b**10*d**2*e**8/19 + 120*B*
a**3*b**7*e**10/19 + 450*B*a**2*b**8*d*e**9/19 + 450*B*a*b**9*d**2*e**8/19 + 120
*B*b**10*d**3*e**7/19) + x**18*(20*A*a**3*b**7*e**10/3 + 25*A*a**2*b**8*d*e**9 +
25*A*a*b**9*d**2*e**8 + 20*A*b**10*d**3*e**7/3 + 35*B*a**4*b**6*e**10/3 + 200*B
*a**3*b**7*d*e**9/3 + 225*B*a**2*b**8*d**2*e**8/2 + 200*B*a*b**9*d**3*e**7/3 + 3
5*B*b**10*d**4*e**6/3) + x**17*(210*A*a**4*b**6*e**10/17 + 1200*A*a**3*b**7*d*e*
*9/17 + 2025*A*a**2*b**8*d**2*e**8/17 + 1200*A*a*b**9*d**3*e**7/17 + 210*A*b**10
*d**4*e**6/17 + 252*B*a**5*b**5*e**10/17 + 2100*B*a**4*b**6*d*e**9/17 + 5400*B*a
**3*b**7*d**2*e**8/17 + 5400*B*a**2*b**8*d**3*e**7/17 + 2100*B*a*b**9*d**4*e**6/
17 + 252*B*b**10*d**5*e**5/17) + x**16*(63*A*a**5*b**5*e**10/4 + 525*A*a**4*b**6
*d*e**9/4 + 675*A*a**3*b**7*d**2*e**8/2 + 675*A*a**2*b**8*d**3*e**7/2 + 525*A*a*
b**9*d**4*e**6/4 + 63*A*b**10*d**5*e**5/4 + 105*B*a**6*b**4*e**10/8 + 315*B*a**5
*b**5*d*e**9/2 + 4725*B*a**4*b**6*d**2*e**8/8 + 900*B*a**3*b**7*d**3*e**7 + 4725
*B*a**2*b**8*d**4*e**6/8 + 315*B*a*b**9*d**5*e**5/2 + 105*B*b**10*d**6*e**4/8) +
x**15*(14*A*a**6*b**4*e**10 + 168*A*a**5*b**5*d*e**9 + 630*A*a**4*b**6*d**2*e**
8 + 960*A*a**3*b**7*d**3*e**7 + 630*A*a**2*b**8*d**4*e**6 + 168*A*a*b**9*d**5*e*
*5 + 14*A*b**10*d**6*e**4 + 8*B*a**7*b**3*e**10 + 140*B*a**6*b**4*d*e**9 + 756*B
*a**5*b**5*d**2*e**8 + 1680*B*a**4*b**6*d**3*e**7 + 1680*B*a**3*b**7*d**4*e**6 +
756*B*a**2*b**8*d**5*e**5 + 140*B*a*b**9*d**6*e**4 + 8*B*b**10*d**7*e**3) + x**
14*(60*A*a**7*b**3*e**10/7 + 150*A*a**6*b**4*d*e**9 + 810*A*a**5*b**5*d**2*e**8
+ 1800*A*a**4*b**6*d**3*e**7 + 1800*A*a**3*b**7*d**4*e**6 + 810*A*a**2*b**8*d**5
*e**5 + 150*A*a*b**9*d**6*e**4 + 60*A*b**10*d**7*e**3/7 + 45*B*a**8*b**2*e**10/1
4 + 600*B*a**7*b**3*d*e**9/7 + 675*B*a**6*b**4*d**2*e**8 + 2160*B*a**5*b**5*d**3
*e**7 + 3150*B*a**4*b**6*d**4*e**6 + 2160*B*a**3*b**7*d**5*e**5 + 675*B*a**2*b**
8*d**6*e**4 + 600*B*a*b**9*d**7*e**3/7 + 45*B*b**10*d**8*e**2/14) + x**13*(45*A*
a**8*b**2*e**10/13 + 1200*A*a**7*b**3*d*e**9/13 + 9450*A*a**6*b**4*d**2*e**8/13
+ 30240*A*a**5*b**5*d**3*e**7/13 + 44100*A*a**4*b**6*d**4*e**6/13 + 30240*A*a**3
*b**7*d**5*e**5/13 + 9450*A*a**2*b**8*d**6*e**4/13 + 1200*A*a*b**9*d**7*e**3/13
+ 45*A*b**10*d**8*e**2/13 + 10*B*a**9*b*e**10/13 + 450*B*a**8*b**2*d*e**9/13 + 5
400*B*a**7*b**3*d**2*e**8/13 + 25200*B*a**6*b**4*d**3*e**7/13 + 52920*B*a**5*b**
5*d**4*e**6/13 + 52920*B*a**4*b**6*d**5*e**5/13 + 25200*B*a**3*b**7*d**6*e**4/13
+ 5400*B*a**2*b**8*d**7*e**3/13 + 450*B*a*b**9*d**8*e**2/13 + 10*B*b**10*d**9*e
/13) + x**12*(5*A*a**9*b*e**10/6 + 75*A*a**8*b**2*d*e**9/2 + 450*A*a**7*b**3*d**
2*e**8 + 2100*A*a**6*b**4*d**3*e**7 + 4410*A*a**5*b**5*d**4*e**6 + 4410*A*a**4*b
**6*d**5*e**5 + 2100*A*a**3*b**7*d**6*e**4 + 450*A*a**2*b**8*d**7*e**3 + 75*A*a*
b**9*d**8*e**2/2 + 5*A*b**10*d**9*e/6 + B*a**10*e**10/12 + 25*B*a**9*b*d*e**9/3
+ 675*B*a**8*b**2*d**2*e**8/4 + 1200*B*a**7*b**3*d**3*e**7 + 3675*B*a**6*b**4*d*
*4*e**6 + 5292*B*a**5*b**5*d**5*e**5 + 3675*B*a**4*b**6*d**6*e**4 + 1200*B*a**3*
b**7*d**7*e**3 + 675*B*a**2*b**8*d**8*e**2/4 + 25*B*a*b**9*d**9*e/3 + B*b**10*d*
*10/12) + x**11*(A*a**10*e**10/11 + 100*A*a**9*b*d*e**9/11 + 2025*A*a**8*b**2*d*
*2*e**8/11 + 14400*A*a**7*b**3*d**3*e**7/11 + 44100*A*a**6*b**4*d**4*e**6/11 + 6
3504*A*a**5*b**5*d**5*e**5/11 + 44100*A*a**4*b**6*d**6*e**4/11 + 14400*A*a**3*b*
*7*d**7*e**3/11 + 2025*A*a**2*b**8*d**8*e**2/11 + 100*A*a*b**9*d**9*e/11 + A*b**
10*d**10/11 + 10*B*a**10*d*e**9/11 + 450*B*a**9*b*d**2*e**8/11 + 5400*B*a**8*b**
2*d**3*e**7/11 + 25200*B*a**7*b**3*d**4*e**6/11 + 52920*B*a**6*b**4*d**5*e**5/11
+ 52920*B*a**5*b**5*d**6*e**4/11 + 25200*B*a**4*b**6*d**7*e**3/11 + 5400*B*a**3
*b**7*d**8*e**2/11 + 450*B*a**2*b**8*d**9*e/11 + 10*B*a*b**9*d**10/11) + x**10*(
A*a**10*d*e**9 + 45*A*a**9*b*d**2*e**8 + 540*A*a**8*b**2*d**3*e**7 + 2520*A*a**7
*b**3*d**4*e**6 + 5292*A*a**6*b**4*d**5*e**5 + 5292*A*a**5*b**5*d**6*e**4 + 2520
*A*a**4*b**6*d**7*e**3 + 540*A*a**3*b**7*d**8*e**2 + 45*A*a**2*b**8*d**9*e + A*a
*b**9*d**10 + 9*B*a**10*d**2*e**8/2 + 120*B*a**9*b*d**3*e**7 + 945*B*a**8*b**2*d
**4*e**6 + 3024*B*a**7*b**3*d**5*e**5 + 4410*B*a**6*b**4*d**6*e**4 + 3024*B*a**5
*b**5*d**7*e**3 + 945*B*a**4*b**6*d**8*e**2 + 120*B*a**3*b**7*d**9*e + 9*B*a**2*
b**8*d**10/2) + x**9*(5*A*a**10*d**2*e**8 + 400*A*a**9*b*d**3*e**7/3 + 1050*A*a*
*8*b**2*d**4*e**6 + 3360*A*a**7*b**3*d**5*e**5 + 4900*A*a**6*b**4*d**6*e**4 + 33
60*A*a**5*b**5*d**7*e**3 + 1050*A*a**4*b**6*d**8*e**2 + 400*A*a**3*b**7*d**9*e/3
+ 5*A*a**2*b**8*d**10 + 40*B*a**10*d**3*e**7/3 + 700*B*a**9*b*d**4*e**6/3 + 126
0*B*a**8*b**2*d**5*e**5 + 2800*B*a**7*b**3*d**6*e**4 + 2800*B*a**6*b**4*d**7*e**
3 + 1260*B*a**5*b**5*d**8*e**2 + 700*B*a**4*b**6*d**9*e/3 + 40*B*a**3*b**7*d**10
/3) + x**8*(15*A*a**10*d**3*e**7 + 525*A*a**9*b*d**4*e**6/2 + 2835*A*a**8*b**2*d
**5*e**5/2 + 3150*A*a**7*b**3*d**6*e**4 + 3150*A*a**6*b**4*d**7*e**3 + 2835*A*a*
*5*b**5*d**8*e**2/2 + 525*A*a**4*b**6*d**9*e/2 + 15*A*a**3*b**7*d**10 + 105*B*a*
*10*d**4*e**6/4 + 315*B*a**9*b*d**5*e**5 + 4725*B*a**8*b**2*d**6*e**4/4 + 1800*B
*a**7*b**3*d**7*e**3 + 4725*B*a**6*b**4*d**8*e**2/4 + 315*B*a**5*b**5*d**9*e + 1
05*B*a**4*b**6*d**10/4) + x**7*(30*A*a**10*d**4*e**6 + 360*A*a**9*b*d**5*e**5 +
1350*A*a**8*b**2*d**6*e**4 + 14400*A*a**7*b**3*d**7*e**3/7 + 1350*A*a**6*b**4*d*
*8*e**2 + 360*A*a**5*b**5*d**9*e + 30*A*a**4*b**6*d**10 + 36*B*a**10*d**5*e**5 +
300*B*a**9*b*d**6*e**4 + 5400*B*a**8*b**2*d**7*e**3/7 + 5400*B*a**7*b**3*d**8*e
**2/7 + 300*B*a**6*b**4*d**9*e + 36*B*a**5*b**5*d**10) + x**6*(42*A*a**10*d**5*e
**5 + 350*A*a**9*b*d**6*e**4 + 900*A*a**8*b**2*d**7*e**3 + 900*A*a**7*b**3*d**8*
e**2 + 350*A*a**6*b**4*d**9*e + 42*A*a**5*b**5*d**10 + 35*B*a**10*d**6*e**4 + 20
0*B*a**9*b*d**7*e**3 + 675*B*a**8*b**2*d**8*e**2/2 + 200*B*a**7*b**3*d**9*e + 35
*B*a**6*b**4*d**10) + x**5*(42*A*a**10*d**6*e**4 + 240*A*a**9*b*d**7*e**3 + 405*
A*a**8*b**2*d**8*e**2 + 240*A*a**7*b**3*d**9*e + 42*A*a**6*b**4*d**10 + 24*B*a**
10*d**7*e**3 + 90*B*a**9*b*d**8*e**2 + 90*B*a**8*b**2*d**9*e + 24*B*a**7*b**3*d*
*10) + x**4*(30*A*a**10*d**7*e**3 + 225*A*a**9*b*d**8*e**2/2 + 225*A*a**8*b**2*d
**9*e/2 + 30*A*a**7*b**3*d**10 + 45*B*a**10*d**8*e**2/4 + 25*B*a**9*b*d**9*e + 4
5*B*a**8*b**2*d**10/4) + x**3*(15*A*a**10*d**8*e**2 + 100*A*a**9*b*d**9*e/3 + 15
*A*a**8*b**2*d**10 + 10*B*a**10*d**9*e/3 + 10*B*a**9*b*d**10/3) + x**2*(5*A*a**1
0*d**9*e + 5*A*a**9*b*d**10 + B*a**10*d**10/2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21111, 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)^10,x, algorithm="giac")

[Out]

Done