3.1058 \(\int (a+b x)^{10} (A+B x) (d+e x)^{13} \, dx\)

Optimal. Leaf size=464 \[ -\frac{b^9 (d+e x)^{24} (-10 a B e-A b e+11 b B d)}{24 e^{12}}+\frac{5 b^8 (d+e x)^{23} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{23 e^{12}}-\frac{15 b^7 (d+e x)^{22} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{22 e^{12}}+\frac{10 b^6 (d+e x)^{21} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{7 e^{12}}-\frac{21 b^5 (d+e x)^{20} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{10 e^{12}}+\frac{42 b^4 (d+e x)^{19} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{19 e^{12}}-\frac{5 b^3 (d+e x)^{18} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{3 e^{12}}+\frac{15 b^2 (d+e x)^{17} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{17 e^{12}}-\frac{5 b (d+e x)^{16} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{16 e^{12}}+\frac{(d+e x)^{15} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{15 e^{12}}-\frac{(d+e x)^{14} (b d-a e)^{10} (B d-A e)}{14 e^{12}}+\frac{b^{10} B (d+e x)^{25}}{25 e^{12}} \]

[Out]

-((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^14)/(14*e^12) + ((b*d - a*e)^9*(11*b*B*d
- 10*A*b*e - a*B*e)*(d + e*x)^15)/(15*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A
*b*e - 2*a*B*e)*(d + e*x)^16)/(16*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)^17)/(17*e^12) - (5*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*
e - 4*a*B*e)*(d + e*x)^18)/(3*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)^19)/(19*e^12) - (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e -
6*a*B*e)*(d + e*x)^20)/(10*e^12) + (10*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e -
7*a*B*e)*(d + e*x)^21)/(7*e^12) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*
a*B*e)*(d + e*x)^22)/(22*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*
e)*(d + e*x)^23)/(23*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^24)/(2
4*e^12) + (b^10*B*(d + e*x)^25)/(25*e^12)

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Rubi [A]  time = 23.7666, 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 \[ -\frac{b^9 (d+e x)^{24} (-10 a B e-A b e+11 b B d)}{24 e^{12}}+\frac{5 b^8 (d+e x)^{23} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{23 e^{12}}-\frac{15 b^7 (d+e x)^{22} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{22 e^{12}}+\frac{10 b^6 (d+e x)^{21} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{7 e^{12}}-\frac{21 b^5 (d+e x)^{20} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{10 e^{12}}+\frac{42 b^4 (d+e x)^{19} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{19 e^{12}}-\frac{5 b^3 (d+e x)^{18} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{3 e^{12}}+\frac{15 b^2 (d+e x)^{17} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{17 e^{12}}-\frac{5 b (d+e x)^{16} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{16 e^{12}}+\frac{(d+e x)^{15} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{15 e^{12}}-\frac{(d+e x)^{14} (b d-a e)^{10} (B d-A e)}{14 e^{12}}+\frac{b^{10} B (d+e x)^{25}}{25 e^{12}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^10*(A + B*x)*(d + e*x)^13,x]

[Out]

-((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^14)/(14*e^12) + ((b*d - a*e)^9*(11*b*B*d
- 10*A*b*e - a*B*e)*(d + e*x)^15)/(15*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A
*b*e - 2*a*B*e)*(d + e*x)^16)/(16*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)^17)/(17*e^12) - (5*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*
e - 4*a*B*e)*(d + e*x)^18)/(3*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)^19)/(19*e^12) - (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e -
6*a*B*e)*(d + e*x)^20)/(10*e^12) + (10*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e -
7*a*B*e)*(d + e*x)^21)/(7*e^12) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*
a*B*e)*(d + e*x)^22)/(22*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*
e)*(d + e*x)^23)/(23*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^24)/(2
4*e^12) + (b^10*B*(d + e*x)^25)/(25*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)**13,x)

[Out]

Timed out

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Mathematica [B]  time = 3.28137, size = 3532, normalized size = 7.61 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^13,x]

[Out]

a^10*A*d^13*x + (a^9*d^12*(10*A*b*d + a*B*d + 13*a*A*e)*x^2)/2 + (a^8*d^11*(a*B*
d*(10*b*d + 13*a*e) + A*(45*b^2*d^2 + 130*a*b*d*e + 78*a^2*e^2))*x^3)/3 + (a^7*d
^10*(a*B*d*(45*b^2*d^2 + 130*a*b*d*e + 78*a^2*e^2) + A*(120*b^3*d^3 + 585*a*b^2*
d^2*e + 780*a^2*b*d*e^2 + 286*a^3*e^3))*x^4)/4 + (a^6*d^9*(a*B*d*(120*b^3*d^3 +
585*a*b^2*d^2*e + 780*a^2*b*d*e^2 + 286*a^3*e^3) + 5*A*(42*b^4*d^4 + 312*a*b^3*d
^3*e + 702*a^2*b^2*d^2*e^2 + 572*a^3*b*d*e^3 + 143*a^4*e^4))*x^5)/5 + (a^5*d^8*(
5*a*B*d*(42*b^4*d^4 + 312*a*b^3*d^3*e + 702*a^2*b^2*d^2*e^2 + 572*a^3*b*d*e^3 +
143*a^4*e^4) + A*(252*b^5*d^5 + 2730*a*b^4*d^4*e + 9360*a^2*b^3*d^3*e^2 + 12870*
a^3*b^2*d^2*e^3 + 7150*a^4*b*d*e^4 + 1287*a^5*e^5))*x^6)/6 + (a^4*d^7*(a*B*d*(25
2*b^5*d^5 + 2730*a*b^4*d^4*e + 9360*a^2*b^3*d^3*e^2 + 12870*a^3*b^2*d^2*e^3 + 71
50*a^4*b*d*e^4 + 1287*a^5*e^5) + 3*A*(70*b^6*d^6 + 1092*a*b^5*d^5*e + 5460*a^2*b
^4*d^4*e^2 + 11440*a^3*b^3*d^3*e^3 + 10725*a^4*b^2*d^2*e^4 + 4290*a^5*b*d*e^5 +
572*a^6*e^6))*x^7)/7 + (3*a^3*d^6*(a*B*d*(70*b^6*d^6 + 1092*a*b^5*d^5*e + 5460*a
^2*b^4*d^4*e^2 + 11440*a^3*b^3*d^3*e^3 + 10725*a^4*b^2*d^2*e^4 + 4290*a^5*b*d*e^
5 + 572*a^6*e^6) + A*(40*b^7*d^7 + 910*a*b^6*d^6*e + 6552*a^2*b^5*d^5*e^2 + 2002
0*a^3*b^4*d^4*e^3 + 28600*a^4*b^3*d^3*e^4 + 19305*a^5*b^2*d^2*e^5 + 5720*a^6*b*d
*e^6 + 572*a^7*e^7))*x^8)/8 + (a^2*d^5*(a*B*d*(40*b^7*d^7 + 910*a*b^6*d^6*e + 65
52*a^2*b^5*d^5*e^2 + 20020*a^3*b^4*d^4*e^3 + 28600*a^4*b^3*d^3*e^4 + 19305*a^5*b
^2*d^2*e^5 + 5720*a^6*b*d*e^6 + 572*a^7*e^7) + A*(15*b^8*d^8 + 520*a*b^7*d^7*e +
5460*a^2*b^6*d^6*e^2 + 24024*a^3*b^5*d^5*e^3 + 50050*a^4*b^4*d^4*e^4 + 51480*a^
5*b^3*d^3*e^5 + 25740*a^6*b^2*d^2*e^6 + 5720*a^7*b*d*e^7 + 429*a^8*e^8))*x^9)/3
+ (a*d^4*(3*a*B*d*(15*b^8*d^8 + 520*a*b^7*d^7*e + 5460*a^2*b^6*d^6*e^2 + 24024*a
^3*b^5*d^5*e^3 + 50050*a^4*b^4*d^4*e^4 + 51480*a^5*b^3*d^3*e^5 + 25740*a^6*b^2*d
^2*e^6 + 5720*a^7*b*d*e^7 + 429*a^8*e^8) + 5*A*(2*b^9*d^9 + 117*a*b^8*d^8*e + 18
72*a^2*b^7*d^7*e^2 + 12012*a^3*b^6*d^6*e^3 + 36036*a^4*b^5*d^5*e^4 + 54054*a^5*b
^4*d^4*e^5 + 41184*a^6*b^3*d^3*e^6 + 15444*a^7*b^2*d^2*e^7 + 2574*a^8*b*d*e^8 +
143*a^9*e^9))*x^10)/10 + (d^3*(5*a*B*d*(2*b^9*d^9 + 117*a*b^8*d^8*e + 1872*a^2*b
^7*d^7*e^2 + 12012*a^3*b^6*d^6*e^3 + 36036*a^4*b^5*d^5*e^4 + 54054*a^5*b^4*d^4*e
^5 + 41184*a^6*b^3*d^3*e^6 + 15444*a^7*b^2*d^2*e^7 + 2574*a^8*b*d*e^8 + 143*a^9*
e^9) + A*(b^10*d^10 + 130*a*b^9*d^9*e + 3510*a^2*b^8*d^8*e^2 + 34320*a^3*b^7*d^7
*e^3 + 150150*a^4*b^6*d^6*e^4 + 324324*a^5*b^5*d^5*e^5 + 360360*a^6*b^4*d^4*e^6
+ 205920*a^7*b^3*d^3*e^7 + 57915*a^8*b^2*d^2*e^8 + 7150*a^9*b*d*e^9 + 286*a^10*e
^10))*x^11)/11 + (d^2*(360360*a^6*b^4*d^4*e^6*(B*d + A*e) + 1430*a^9*b*d*e^9*(5*
B*d + 2*A*e) + 51480*a^7*b^3*d^3*e^7*(4*B*d + 3*A*e) + 26*a^10*e^10*(11*B*d + 3*
A*e) + 108108*a^5*b^5*d^5*e^5*(3*B*d + 4*A*e) + 17160*a^3*b^7*d^7*e^3*(2*B*d + 5
*A*e) + 6435*a^8*b^2*d^2*e^8*(9*B*d + 5*A*e) + 130*a*b^9*d^9*e*(B*d + 6*A*e) + 3
0030*a^4*b^6*d^6*e^4*(5*B*d + 9*A*e) + 1170*a^2*b^8*d^8*e^2*(3*B*d + 11*A*e) + b
^10*d^10*(B*d + 13*A*e))*x^12)/12 + d*e*(33264*a^5*b^5*d^5*e^5*(B*d + A*e) + a^1
0*e^10*(6*B*d + A*e) + 495*a^8*b^2*d^2*e^8*(5*B*d + 2*A*e) + 6930*a^6*b^4*d^4*e^
6*(4*B*d + 3*A*e) + 20*a^9*b*d*e^9*(11*B*d + 3*A*e) + 6930*a^4*b^6*d^6*e^4*(3*B*
d + 4*A*e) + 495*a^2*b^8*d^8*e^2*(2*B*d + 5*A*e) + 1320*a^7*b^3*d^3*e^7*(9*B*d +
5*A*e) + b^10*d^10*(B*d + 6*A*e) + 1320*a^3*b^7*d^7*e^3*(5*B*d + 9*A*e) + 20*a*
b^9*d^9*e*(3*B*d + 11*A*e))*x^13 + (e^2*(360360*a^4*b^6*d^6*e^4*(B*d + A*e) + 13
0*a^9*b*d*e^9*(6*B*d + A*e) + a^10*e^10*(13*B*d + A*e) + 17160*a^7*b^3*d^3*e^7*(
5*B*d + 2*A*e) + 108108*a^5*b^5*d^5*e^5*(4*B*d + 3*A*e) + 1170*a^8*b^2*d^2*e^8*(
11*B*d + 3*A*e) + 51480*a^3*b^7*d^7*e^3*(3*B*d + 4*A*e) + 1430*a*b^9*d^9*e*(2*B*
d + 5*A*e) + 30030*a^6*b^4*d^4*e^6*(9*B*d + 5*A*e) + 6435*a^2*b^8*d^8*e^2*(5*B*d
+ 9*A*e) + 26*b^10*d^10*(3*B*d + 11*A*e))*x^14)/14 + (e^3*(a^10*B*e^10 + 205920
*a^3*b^7*d^6*e^3*(B*d + A*e) + 585*a^8*b^2*d*e^8*(6*B*d + A*e) + 10*a^9*b*e^9*(1
3*B*d + A*e) + 30030*a^6*b^4*d^3*e^6*(5*B*d + 2*A*e) + 90090*a^4*b^6*d^5*e^4*(4*
B*d + 3*A*e) + 3120*a^7*b^3*d^2*e^7*(11*B*d + 3*A*e) + 19305*a^2*b^8*d^7*e^2*(3*
B*d + 4*A*e) + 143*b^10*d^9*(2*B*d + 5*A*e) + 36036*a^5*b^5*d^4*e^5*(9*B*d + 5*A
*e) + 1430*a*b^9*d^8*e*(5*B*d + 9*A*e))*x^15)/15 + (b*e^4*(10*a^9*B*e^9 + 77220*
a^2*b^7*d^6*e^2*(B*d + A*e) + 1560*a^7*b^2*d*e^7*(6*B*d + A*e) + 45*a^8*b*e^8*(1
3*B*d + A*e) + 36036*a^5*b^4*d^3*e^5*(5*B*d + 2*A*e) + 51480*a^3*b^6*d^5*e^3*(4*
B*d + 3*A*e) + 5460*a^6*b^3*d^2*e^6*(11*B*d + 3*A*e) + 4290*a*b^8*d^7*e*(3*B*d +
4*A*e) + 30030*a^4*b^5*d^4*e^4*(9*B*d + 5*A*e) + 143*b^9*d^8*(5*B*d + 9*A*e))*x
^16)/16 + (3*b^2*e^5*(15*a^8*B*e^8 + 5720*a*b^7*d^6*e*(B*d + A*e) + 910*a^6*b^2*
d*e^6*(6*B*d + A*e) + 40*a^7*b*e^7*(13*B*d + A*e) + 10010*a^4*b^4*d^3*e^4*(5*B*d
+ 2*A*e) + 6435*a^2*b^6*d^5*e^2*(4*B*d + 3*A*e) + 2184*a^5*b^3*d^2*e^5*(11*B*d
+ 3*A*e) + 143*b^8*d^7*(3*B*d + 4*A*e) + 5720*a^3*b^5*d^4*e^3*(9*B*d + 5*A*e))*x
^17)/17 + (b^3*e^6*(40*a^7*B*e^7 + 572*b^7*d^6*(B*d + A*e) + 1092*a^5*b^2*d*e^5*
(6*B*d + A*e) + 70*a^6*b*e^6*(13*B*d + A*e) + 5720*a^3*b^4*d^3*e^3*(5*B*d + 2*A*
e) + 1430*a*b^6*d^5*e*(4*B*d + 3*A*e) + 1820*a^4*b^3*d^2*e^4*(11*B*d + 3*A*e) +
2145*a^2*b^5*d^4*e^2*(9*B*d + 5*A*e))*x^18)/6 + (b^4*e^7*(210*a^6*B*e^6 + 2730*a
^4*b^2*d*e^4*(6*B*d + A*e) + 252*a^5*b*e^5*(13*B*d + A*e) + 6435*a^2*b^4*d^3*e^2
*(5*B*d + 2*A*e) + 429*b^6*d^5*(4*B*d + 3*A*e) + 3120*a^3*b^3*d^2*e^3*(11*B*d +
3*A*e) + 1430*a*b^5*d^4*e*(9*B*d + 5*A*e))*x^19)/19 + (b^5*e^8*(252*a^5*B*e^5 +
1560*a^3*b^2*d*e^3*(6*B*d + A*e) + 210*a^4*b*e^4*(13*B*d + A*e) + 1430*a*b^4*d^3
*e*(5*B*d + 2*A*e) + 1170*a^2*b^3*d^2*e^2*(11*B*d + 3*A*e) + 143*b^5*d^4*(9*B*d
+ 5*A*e))*x^20)/20 + (b^6*e^9*(210*a^4*B*e^4 + 585*a^2*b^2*d*e^2*(6*B*d + A*e) +
120*a^3*b*e^3*(13*B*d + A*e) + 143*b^4*d^3*(5*B*d + 2*A*e) + 260*a*b^3*d^2*e*(1
1*B*d + 3*A*e))*x^21)/21 + (b^7*e^10*(120*a^3*B*e^3 + 130*a*b^2*d*e*(6*B*d + A*e
) + 45*a^2*b*e^2*(13*B*d + A*e) + 26*b^3*d^2*(11*B*d + 3*A*e))*x^22)/22 + (b^8*e
^11*(45*a^2*B*e^2 + 13*b^2*d*(6*B*d + A*e) + 10*a*b*e*(13*B*d + A*e))*x^23)/23 +
(b^9*e^12*(13*b*B*d + A*b*e + 10*a*B*e)*x^24)/24 + (b^10*B*e^13*x^25)/25

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Maple [B]  time = 0.005, size = 3893, normalized size = 8.4 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^10*(B*x+A)*(e*x+d)^13,x)

[Out]

1/4*(286*a^10*A*d^10*e^3+78*(10*A*a^9*b+B*a^10)*d^11*e^2+13*(45*A*a^8*b^2+10*B*a
^9*b)*d^12*e+(120*A*a^7*b^3+45*B*a^8*b^2)*d^13)*x^4+1/3*(78*a^10*A*d^11*e^2+13*(
10*A*a^9*b+B*a^10)*d^12*e+(45*A*a^8*b^2+10*B*a^9*b)*d^13)*x^3+1/2*(13*a^10*A*d^1
2*e+(10*A*a^9*b+B*a^10)*d^13)*x^2+1/24*((A*b^10+10*B*a*b^9)*e^13+13*b^10*B*d*e^1
2)*x^24+1/23*((10*A*a*b^9+45*B*a^2*b^8)*e^13+13*(A*b^10+10*B*a*b^9)*d*e^12+78*b^
10*B*d^2*e^11)*x^23+1/22*((45*A*a^2*b^8+120*B*a^3*b^7)*e^13+13*(10*A*a*b^9+45*B*
a^2*b^8)*d*e^12+78*(A*b^10+10*B*a*b^9)*d^2*e^11+286*b^10*B*d^3*e^10)*x^22+1/21*(
(120*A*a^3*b^7+210*B*a^4*b^6)*e^13+13*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^12+78*(10
*A*a*b^9+45*B*a^2*b^8)*d^2*e^11+286*(A*b^10+10*B*a*b^9)*d^3*e^10+715*b^10*B*d^4*
e^9)*x^21+1/20*((210*A*a^4*b^6+252*B*a^5*b^5)*e^13+13*(120*A*a^3*b^7+210*B*a^4*b
^6)*d*e^12+78*(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^11+286*(10*A*a*b^9+45*B*a^2*b^8
)*d^3*e^10+715*(A*b^10+10*B*a*b^9)*d^4*e^9+1287*b^10*B*d^5*e^8)*x^20+1/19*((252*
A*a^5*b^5+210*B*a^6*b^4)*e^13+13*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^12+78*(120*A*
a^3*b^7+210*B*a^4*b^6)*d^2*e^11+286*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^10+715*(1
0*A*a*b^9+45*B*a^2*b^8)*d^4*e^9+1287*(A*b^10+10*B*a*b^9)*d^5*e^8+1716*b^10*B*d^6
*e^7)*x^19+1/18*((210*A*a^6*b^4+120*B*a^7*b^3)*e^13+13*(252*A*a^5*b^5+210*B*a^6*
b^4)*d*e^12+78*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^11+286*(120*A*a^3*b^7+210*B*a
^4*b^6)*d^3*e^10+715*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*e^9+1287*(10*A*a*b^9+45*B*
a^2*b^8)*d^5*e^8+1716*(A*b^10+10*B*a*b^9)*d^6*e^7+1716*b^10*B*d^7*e^6)*x^18+1/17
*((120*A*a^7*b^3+45*B*a^8*b^2)*e^13+13*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^12+78*(
252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^11+286*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^10
+715*(120*A*a^3*b^7+210*B*a^4*b^6)*d^4*e^9+1287*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5
*e^8+1716*(10*A*a*b^9+45*B*a^2*b^8)*d^6*e^7+1716*(A*b^10+10*B*a*b^9)*d^7*e^6+128
7*b^10*B*d^8*e^5)*x^17+1/16*((45*A*a^8*b^2+10*B*a^9*b)*e^13+13*(120*A*a^7*b^3+45
*B*a^8*b^2)*d*e^12+78*(210*A*a^6*b^4+120*B*a^7*b^3)*d^2*e^11+286*(252*A*a^5*b^5+
210*B*a^6*b^4)*d^3*e^10+715*(210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^9+1287*(120*A*a^
3*b^7+210*B*a^4*b^6)*d^5*e^8+1716*(45*A*a^2*b^8+120*B*a^3*b^7)*d^6*e^7+1716*(10*
A*a*b^9+45*B*a^2*b^8)*d^7*e^6+1287*(A*b^10+10*B*a*b^9)*d^8*e^5+715*b^10*B*d^9*e^
4)*x^16+1/15*((10*A*a^9*b+B*a^10)*e^13+13*(45*A*a^8*b^2+10*B*a^9*b)*d*e^12+78*(1
20*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^11+286*(210*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^10+7
15*(252*A*a^5*b^5+210*B*a^6*b^4)*d^4*e^9+1287*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*
e^8+1716*(120*A*a^3*b^7+210*B*a^4*b^6)*d^6*e^7+1716*(45*A*a^2*b^8+120*B*a^3*b^7)
*d^7*e^6+1287*(10*A*a*b^9+45*B*a^2*b^8)*d^8*e^5+715*(A*b^10+10*B*a*b^9)*d^9*e^4+
286*b^10*B*d^10*e^3)*x^15+1/14*(a^10*A*e^13+13*(10*A*a^9*b+B*a^10)*d*e^12+78*(45
*A*a^8*b^2+10*B*a^9*b)*d^2*e^11+286*(120*A*a^7*b^3+45*B*a^8*b^2)*d^3*e^10+715*(2
10*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^9+1287*(252*A*a^5*b^5+210*B*a^6*b^4)*d^5*e^8+1
716*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^7+1716*(120*A*a^3*b^7+210*B*a^4*b^6)*d^7
*e^6+1287*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e^5+715*(10*A*a*b^9+45*B*a^2*b^8)*d^9
*e^4+286*(A*b^10+10*B*a*b^9)*d^10*e^3+78*b^10*B*d^11*e^2)*x^14+1/13*(13*a^10*A*d
*e^12+78*(10*A*a^9*b+B*a^10)*d^2*e^11+286*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e^10+715
*(120*A*a^7*b^3+45*B*a^8*b^2)*d^4*e^9+1287*(210*A*a^6*b^4+120*B*a^7*b^3)*d^5*e^8
+1716*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^7+1716*(210*A*a^4*b^6+252*B*a^5*b^5)*d
^7*e^6+1287*(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e^5+715*(45*A*a^2*b^8+120*B*a^3*b^
7)*d^9*e^4+286*(10*A*a*b^9+45*B*a^2*b^8)*d^10*e^3+78*(A*b^10+10*B*a*b^9)*d^11*e^
2+13*b^10*B*d^12*e)*x^13+1/12*(78*a^10*A*d^2*e^11+286*(10*A*a^9*b+B*a^10)*d^3*e^
10+715*(45*A*a^8*b^2+10*B*a^9*b)*d^4*e^9+1287*(120*A*a^7*b^3+45*B*a^8*b^2)*d^5*e
^8+1716*(210*A*a^6*b^4+120*B*a^7*b^3)*d^6*e^7+1716*(252*A*a^5*b^5+210*B*a^6*b^4)
*d^7*e^6+1287*(210*A*a^4*b^6+252*B*a^5*b^5)*d^8*e^5+715*(120*A*a^3*b^7+210*B*a^4
*b^6)*d^9*e^4+286*(45*A*a^2*b^8+120*B*a^3*b^7)*d^10*e^3+78*(10*A*a*b^9+45*B*a^2*
b^8)*d^11*e^2+13*(A*b^10+10*B*a*b^9)*d^12*e+b^10*B*d^13)*x^12+1/11*(286*a^10*A*d
^3*e^10+715*(10*A*a^9*b+B*a^10)*d^4*e^9+1287*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e^8+1
716*(120*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^7+1716*(210*A*a^6*b^4+120*B*a^7*b^3)*d^7*
e^6+1287*(252*A*a^5*b^5+210*B*a^6*b^4)*d^8*e^5+715*(210*A*a^4*b^6+252*B*a^5*b^5)
*d^9*e^4+286*(120*A*a^3*b^7+210*B*a^4*b^6)*d^10*e^3+78*(45*A*a^2*b^8+120*B*a^3*b
^7)*d^11*e^2+13*(10*A*a*b^9+45*B*a^2*b^8)*d^12*e+(A*b^10+10*B*a*b^9)*d^13)*x^11+
1/10*(715*a^10*A*d^4*e^9+1287*(10*A*a^9*b+B*a^10)*d^5*e^8+1716*(45*A*a^8*b^2+10*
B*a^9*b)*d^6*e^7+1716*(120*A*a^7*b^3+45*B*a^8*b^2)*d^7*e^6+1287*(210*A*a^6*b^4+1
20*B*a^7*b^3)*d^8*e^5+715*(252*A*a^5*b^5+210*B*a^6*b^4)*d^9*e^4+286*(210*A*a^4*b
^6+252*B*a^5*b^5)*d^10*e^3+78*(120*A*a^3*b^7+210*B*a^4*b^6)*d^11*e^2+13*(45*A*a^
2*b^8+120*B*a^3*b^7)*d^12*e+(10*A*a*b^9+45*B*a^2*b^8)*d^13)*x^10+1/9*(1287*a^10*
A*d^5*e^8+1716*(10*A*a^9*b+B*a^10)*d^6*e^7+1716*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^
6+1287*(120*A*a^7*b^3+45*B*a^8*b^2)*d^8*e^5+715*(210*A*a^6*b^4+120*B*a^7*b^3)*d^
9*e^4+286*(252*A*a^5*b^5+210*B*a^6*b^4)*d^10*e^3+78*(210*A*a^4*b^6+252*B*a^5*b^5
)*d^11*e^2+13*(120*A*a^3*b^7+210*B*a^4*b^6)*d^12*e+(45*A*a^2*b^8+120*B*a^3*b^7)*
d^13)*x^9+1/8*(1716*a^10*A*d^6*e^7+1716*(10*A*a^9*b+B*a^10)*d^7*e^6+1287*(45*A*a
^8*b^2+10*B*a^9*b)*d^8*e^5+715*(120*A*a^7*b^3+45*B*a^8*b^2)*d^9*e^4+286*(210*A*a
^6*b^4+120*B*a^7*b^3)*d^10*e^3+78*(252*A*a^5*b^5+210*B*a^6*b^4)*d^11*e^2+13*(210
*A*a^4*b^6+252*B*a^5*b^5)*d^12*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^13)*x^8+1/7*(17
16*a^10*A*d^7*e^6+1287*(10*A*a^9*b+B*a^10)*d^8*e^5+715*(45*A*a^8*b^2+10*B*a^9*b)
*d^9*e^4+286*(120*A*a^7*b^3+45*B*a^8*b^2)*d^10*e^3+78*(210*A*a^6*b^4+120*B*a^7*b
^3)*d^11*e^2+13*(252*A*a^5*b^5+210*B*a^6*b^4)*d^12*e+(210*A*a^4*b^6+252*B*a^5*b^
5)*d^13)*x^7+1/6*(1287*a^10*A*d^8*e^5+715*(10*A*a^9*b+B*a^10)*d^9*e^4+286*(45*A*
a^8*b^2+10*B*a^9*b)*d^10*e^3+78*(120*A*a^7*b^3+45*B*a^8*b^2)*d^11*e^2+13*(210*A*
a^6*b^4+120*B*a^7*b^3)*d^12*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^13)*x^6+1/5*(715*a
^10*A*d^9*e^4+286*(10*A*a^9*b+B*a^10)*d^10*e^3+78*(45*A*a^8*b^2+10*B*a^9*b)*d^11
*e^2+13*(120*A*a^7*b^3+45*B*a^8*b^2)*d^12*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^13)*
x^5+1/25*b^10*B*e^13*x^25+a^10*A*d^13*x

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Maxima [A]  time = 1.43361, size = 5272, normalized size = 11.36 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^13,x, algorithm="maxima")

[Out]

1/25*B*b^10*e^13*x^25 + A*a^10*d^13*x + 1/24*(13*B*b^10*d*e^12 + (10*B*a*b^9 + A
*b^10)*e^13)*x^24 + 1/23*(78*B*b^10*d^2*e^11 + 13*(10*B*a*b^9 + A*b^10)*d*e^12 +
5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^13)*x^23 + 1/22*(286*B*b^10*d^3*e^10 + 78*(10*B*a
*b^9 + A*b^10)*d^2*e^11 + 65*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^12 + 15*(8*B*a^3*b^7
+ 3*A*a^2*b^8)*e^13)*x^22 + 1/21*(715*B*b^10*d^4*e^9 + 286*(10*B*a*b^9 + A*b^10)
*d^3*e^10 + 390*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^11 + 195*(8*B*a^3*b^7 + 3*A*a^2*
b^8)*d*e^12 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^13)*x^21 + 1/20*(1287*B*b^10*d^5*
e^8 + 715*(10*B*a*b^9 + A*b^10)*d^4*e^9 + 1430*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^1
0 + 1170*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^11 + 390*(7*B*a^4*b^6 + 4*A*a^3*b^7)*
d*e^12 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^13)*x^20 + 1/19*(1716*B*b^10*d^6*e^7 +
1287*(10*B*a*b^9 + A*b^10)*d^5*e^8 + 3575*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^9 + 4
290*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^10 + 2340*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*
e^11 + 546*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^12 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e
^13)*x^19 + 1/6*(572*B*b^10*d^7*e^6 + 572*(10*B*a*b^9 + A*b^10)*d^6*e^7 + 2145*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^8 + 3575*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^9 + 28
60*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^10 + 1092*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e
^11 + 182*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^12 + 10*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^
13)*x^18 + 3/17*(429*B*b^10*d^8*e^5 + 572*(10*B*a*b^9 + A*b^10)*d^7*e^6 + 2860*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^7 + 6435*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^8 + 71
50*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^9 + 4004*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^
10 + 1092*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^11 + 130*(4*B*a^7*b^3 + 7*A*a^6*b^4)
*d*e^12 + 5*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^13)*x^17 + 1/16*(715*B*b^10*d^9*e^4 +
1287*(10*B*a*b^9 + A*b^10)*d^8*e^5 + 8580*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^6 + 25
740*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^7 + 38610*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*
e^8 + 30030*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^9 + 12012*(5*B*a^6*b^4 + 6*A*a^5*b
^5)*d^3*e^10 + 2340*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^11 + 195*(3*B*a^8*b^2 + 8*
A*a^7*b^3)*d*e^12 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^13)*x^16 + 1/15*(286*B*b^10*d^
10*e^3 + 715*(10*B*a*b^9 + A*b^10)*d^9*e^4 + 6435*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*
e^5 + 25740*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^6 + 51480*(7*B*a^4*b^6 + 4*A*a^3*b
^7)*d^6*e^7 + 54054*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^8 + 30030*(5*B*a^6*b^4 + 6
*A*a^5*b^5)*d^4*e^9 + 8580*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^10 + 1170*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d^2*e^11 + 65*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^12 + (B*a^10 + 10
*A*a^9*b)*e^13)*x^15 + 1/14*(78*B*b^10*d^11*e^2 + A*a^10*e^13 + 286*(10*B*a*b^9
+ A*b^10)*d^10*e^3 + 3575*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^4 + 19305*(8*B*a^3*b^7
+ 3*A*a^2*b^8)*d^8*e^5 + 51480*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^6 + 72072*(6*B
*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^7 + 54054*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^8 + 21
450*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^9 + 4290*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e
^10 + 390*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^11 + 13*(B*a^10 + 10*A*a^9*b)*d*e^12)*
x^14 + (B*b^10*d^12*e + A*a^10*d*e^12 + 6*(10*B*a*b^9 + A*b^10)*d^11*e^2 + 110*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^10*e^3 + 825*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^9*e^4 + 29
70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*e^5 + 5544*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*e^
6 + 5544*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*e^7 + 2970*(4*B*a^7*b^3 + 7*A*a^6*b^4)*
d^5*e^8 + 825*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*e^9 + 110*(2*B*a^9*b + 9*A*a^8*b^2
)*d^3*e^10 + 6*(B*a^10 + 10*A*a^9*b)*d^2*e^11)*x^13 + 1/12*(B*b^10*d^13 + 78*A*a
^10*d^2*e^11 + 13*(10*B*a*b^9 + A*b^10)*d^12*e + 390*(9*B*a^2*b^8 + 2*A*a*b^9)*d
^11*e^2 + 4290*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10*e^3 + 21450*(7*B*a^4*b^6 + 4*A*a
^3*b^7)*d^9*e^4 + 54054*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^8*e^5 + 72072*(5*B*a^6*b^4
+ 6*A*a^5*b^5)*d^7*e^6 + 51480*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*e^7 + 19305*(3*B
*a^8*b^2 + 8*A*a^7*b^3)*d^5*e^8 + 3575*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*e^9 + 286*(
B*a^10 + 10*A*a^9*b)*d^3*e^10)*x^12 + 1/11*(286*A*a^10*d^3*e^10 + (10*B*a*b^9 +
A*b^10)*d^13 + 65*(9*B*a^2*b^8 + 2*A*a*b^9)*d^12*e + 1170*(8*B*a^3*b^7 + 3*A*a^2
*b^8)*d^11*e^2 + 8580*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^10*e^3 + 30030*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d^9*e^4 + 54054*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*e^5 + 51480*(4*B*
a^7*b^3 + 7*A*a^6*b^4)*d^7*e^6 + 25740*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*e^7 + 643
5*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*e^8 + 715*(B*a^10 + 10*A*a^9*b)*d^4*e^9)*x^11 +
1/10*(715*A*a^10*d^4*e^9 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^13 + 195*(8*B*a^3*b^7 +
3*A*a^2*b^8)*d^12*e + 2340*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^11*e^2 + 12012*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*d^10*e^3 + 30030*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^9*e^4 + 3861
0*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*e^5 + 25740*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^7*e^
6 + 8580*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*e^7 + 1287*(B*a^10 + 10*A*a^9*b)*d^5*e^8)
*x^10 + 1/3*(429*A*a^10*d^5*e^8 + 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^13 + 130*(7*B*
a^4*b^6 + 4*A*a^3*b^7)*d^12*e + 1092*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^11*e^2 + 4004
*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^10*e^3 + 7150*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^9*e^4
+ 6435*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^8*e^5 + 2860*(2*B*a^9*b + 9*A*a^8*b^2)*d^7
*e^6 + 572*(B*a^10 + 10*A*a^9*b)*d^6*e^7)*x^9 + 3/8*(572*A*a^10*d^6*e^7 + 10*(7*
B*a^4*b^6 + 4*A*a^3*b^7)*d^13 + 182*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^12*e + 1092*(5
*B*a^6*b^4 + 6*A*a^5*b^5)*d^11*e^2 + 2860*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^10*e^3 +
3575*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^9*e^4 + 2145*(2*B*a^9*b + 9*A*a^8*b^2)*d^8*e
^5 + 572*(B*a^10 + 10*A*a^9*b)*d^7*e^6)*x^8 + 1/7*(1716*A*a^10*d^7*e^6 + 42*(6*B
*a^5*b^5 + 5*A*a^4*b^6)*d^13 + 546*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^12*e + 2340*(4*
B*a^7*b^3 + 7*A*a^6*b^4)*d^11*e^2 + 4290*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^10*e^3 +
3575*(2*B*a^9*b + 9*A*a^8*b^2)*d^9*e^4 + 1287*(B*a^10 + 10*A*a^9*b)*d^8*e^5)*x^7
+ 1/6*(1287*A*a^10*d^8*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^13 + 390*(4*B*a^7
*b^3 + 7*A*a^6*b^4)*d^12*e + 1170*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^11*e^2 + 1430*(2
*B*a^9*b + 9*A*a^8*b^2)*d^10*e^3 + 715*(B*a^10 + 10*A*a^9*b)*d^9*e^4)*x^6 + 1/5*
(715*A*a^10*d^9*e^4 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^13 + 195*(3*B*a^8*b^2 + 8
*A*a^7*b^3)*d^12*e + 390*(2*B*a^9*b + 9*A*a^8*b^2)*d^11*e^2 + 286*(B*a^10 + 10*A
*a^9*b)*d^10*e^3)*x^5 + 1/4*(286*A*a^10*d^10*e^3 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3
)*d^13 + 65*(2*B*a^9*b + 9*A*a^8*b^2)*d^12*e + 78*(B*a^10 + 10*A*a^9*b)*d^11*e^2
)*x^4 + 1/3*(78*A*a^10*d^11*e^2 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^13 + 13*(B*a^10
+ 10*A*a^9*b)*d^12*e)*x^3 + 1/2*(13*A*a^10*d^12*e + (B*a^10 + 10*A*a^9*b)*d^13)*
x^2

_______________________________________________________________________________________

Fricas [A]  time = 0.196357, 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)^13,x, algorithm="fricas")

[Out]

1/25*x^25*e^13*b^10*B + 13/24*x^24*e^12*d*b^10*B + 5/12*x^24*e^13*b^9*a*B + 1/24
*x^24*e^13*b^10*A + 78/23*x^23*e^11*d^2*b^10*B + 130/23*x^23*e^12*d*b^9*a*B + 45
/23*x^23*e^13*b^8*a^2*B + 13/23*x^23*e^12*d*b^10*A + 10/23*x^23*e^13*b^9*a*A + 1
3*x^22*e^10*d^3*b^10*B + 390/11*x^22*e^11*d^2*b^9*a*B + 585/22*x^22*e^12*d*b^8*a
^2*B + 60/11*x^22*e^13*b^7*a^3*B + 39/11*x^22*e^11*d^2*b^10*A + 65/11*x^22*e^12*
d*b^9*a*A + 45/22*x^22*e^13*b^8*a^2*A + 715/21*x^21*e^9*d^4*b^10*B + 2860/21*x^2
1*e^10*d^3*b^9*a*B + 1170/7*x^21*e^11*d^2*b^8*a^2*B + 520/7*x^21*e^12*d*b^7*a^3*
B + 10*x^21*e^13*b^6*a^4*B + 286/21*x^21*e^10*d^3*b^10*A + 260/7*x^21*e^11*d^2*b
^9*a*A + 195/7*x^21*e^12*d*b^8*a^2*A + 40/7*x^21*e^13*b^7*a^3*A + 1287/20*x^20*e
^8*d^5*b^10*B + 715/2*x^20*e^9*d^4*b^9*a*B + 1287/2*x^20*e^10*d^3*b^8*a^2*B + 46
8*x^20*e^11*d^2*b^7*a^3*B + 273/2*x^20*e^12*d*b^6*a^4*B + 63/5*x^20*e^13*b^5*a^5
*B + 143/4*x^20*e^9*d^4*b^10*A + 143*x^20*e^10*d^3*b^9*a*A + 351/2*x^20*e^11*d^2
*b^8*a^2*A + 78*x^20*e^12*d*b^7*a^3*A + 21/2*x^20*e^13*b^6*a^4*A + 1716/19*x^19*
e^7*d^6*b^10*B + 12870/19*x^19*e^8*d^5*b^9*a*B + 32175/19*x^19*e^9*d^4*b^8*a^2*B
+ 34320/19*x^19*e^10*d^3*b^7*a^3*B + 16380/19*x^19*e^11*d^2*b^6*a^4*B + 3276/19
*x^19*e^12*d*b^5*a^5*B + 210/19*x^19*e^13*b^4*a^6*B + 1287/19*x^19*e^8*d^5*b^10*
A + 7150/19*x^19*e^9*d^4*b^9*a*A + 12870/19*x^19*e^10*d^3*b^8*a^2*A + 9360/19*x^
19*e^11*d^2*b^7*a^3*A + 2730/19*x^19*e^12*d*b^6*a^4*A + 252/19*x^19*e^13*b^5*a^5
*A + 286/3*x^18*e^6*d^7*b^10*B + 2860/3*x^18*e^7*d^6*b^9*a*B + 6435/2*x^18*e^8*d
^5*b^8*a^2*B + 14300/3*x^18*e^9*d^4*b^7*a^3*B + 10010/3*x^18*e^10*d^3*b^6*a^4*B
+ 1092*x^18*e^11*d^2*b^5*a^5*B + 455/3*x^18*e^12*d*b^4*a^6*B + 20/3*x^18*e^13*b^
3*a^7*B + 286/3*x^18*e^7*d^6*b^10*A + 715*x^18*e^8*d^5*b^9*a*A + 3575/2*x^18*e^9
*d^4*b^8*a^2*A + 5720/3*x^18*e^10*d^3*b^7*a^3*A + 910*x^18*e^11*d^2*b^6*a^4*A +
182*x^18*e^12*d*b^5*a^5*A + 35/3*x^18*e^13*b^4*a^6*A + 1287/17*x^17*e^5*d^8*b^10
*B + 17160/17*x^17*e^6*d^7*b^9*a*B + 77220/17*x^17*e^7*d^6*b^8*a^2*B + 154440/17
*x^17*e^8*d^5*b^7*a^3*B + 150150/17*x^17*e^9*d^4*b^6*a^4*B + 72072/17*x^17*e^10*
d^3*b^5*a^5*B + 16380/17*x^17*e^11*d^2*b^4*a^6*B + 1560/17*x^17*e^12*d*b^3*a^7*B
+ 45/17*x^17*e^13*b^2*a^8*B + 1716/17*x^17*e^6*d^7*b^10*A + 17160/17*x^17*e^7*d
^6*b^9*a*A + 57915/17*x^17*e^8*d^5*b^8*a^2*A + 85800/17*x^17*e^9*d^4*b^7*a^3*A +
60060/17*x^17*e^10*d^3*b^6*a^4*A + 19656/17*x^17*e^11*d^2*b^5*a^5*A + 2730/17*x
^17*e^12*d*b^4*a^6*A + 120/17*x^17*e^13*b^3*a^7*A + 715/16*x^16*e^4*d^9*b^10*B +
6435/8*x^16*e^5*d^8*b^9*a*B + 19305/4*x^16*e^6*d^7*b^8*a^2*B + 12870*x^16*e^7*d
^6*b^7*a^3*B + 135135/8*x^16*e^8*d^5*b^6*a^4*B + 45045/4*x^16*e^9*d^4*b^5*a^5*B
+ 15015/4*x^16*e^10*d^3*b^4*a^6*B + 585*x^16*e^11*d^2*b^3*a^7*B + 585/16*x^16*e^
12*d*b^2*a^8*B + 5/8*x^16*e^13*b*a^9*B + 1287/16*x^16*e^5*d^8*b^10*A + 2145/2*x^
16*e^6*d^7*b^9*a*A + 19305/4*x^16*e^7*d^6*b^8*a^2*A + 19305/2*x^16*e^8*d^5*b^7*a
^3*A + 75075/8*x^16*e^9*d^4*b^6*a^4*A + 9009/2*x^16*e^10*d^3*b^5*a^5*A + 4095/4*
x^16*e^11*d^2*b^4*a^6*A + 195/2*x^16*e^12*d*b^3*a^7*A + 45/16*x^16*e^13*b^2*a^8*
A + 286/15*x^15*e^3*d^10*b^10*B + 1430/3*x^15*e^4*d^9*b^9*a*B + 3861*x^15*e^5*d^
8*b^8*a^2*B + 13728*x^15*e^6*d^7*b^7*a^3*B + 24024*x^15*e^7*d^6*b^6*a^4*B + 1081
08/5*x^15*e^8*d^5*b^5*a^5*B + 10010*x^15*e^9*d^4*b^4*a^6*B + 2288*x^15*e^10*d^3*
b^3*a^7*B + 234*x^15*e^11*d^2*b^2*a^8*B + 26/3*x^15*e^12*d*b*a^9*B + 1/15*x^15*e
^13*a^10*B + 143/3*x^15*e^4*d^9*b^10*A + 858*x^15*e^5*d^8*b^9*a*A + 5148*x^15*e^
6*d^7*b^8*a^2*A + 13728*x^15*e^7*d^6*b^7*a^3*A + 18018*x^15*e^8*d^5*b^6*a^4*A +
12012*x^15*e^9*d^4*b^5*a^5*A + 4004*x^15*e^10*d^3*b^4*a^6*A + 624*x^15*e^11*d^2*
b^3*a^7*A + 39*x^15*e^12*d*b^2*a^8*A + 2/3*x^15*e^13*b*a^9*A + 39/7*x^14*e^2*d^1
1*b^10*B + 1430/7*x^14*e^3*d^10*b^9*a*B + 32175/14*x^14*e^4*d^9*b^8*a^2*B + 7722
0/7*x^14*e^5*d^8*b^7*a^3*B + 25740*x^14*e^6*d^7*b^6*a^4*B + 30888*x^14*e^7*d^6*b
^5*a^5*B + 19305*x^14*e^8*d^5*b^4*a^6*B + 42900/7*x^14*e^9*d^4*b^3*a^7*B + 6435/
7*x^14*e^10*d^3*b^2*a^8*B + 390/7*x^14*e^11*d^2*b*a^9*B + 13/14*x^14*e^12*d*a^10
*B + 143/7*x^14*e^3*d^10*b^10*A + 3575/7*x^14*e^4*d^9*b^9*a*A + 57915/14*x^14*e^
5*d^8*b^8*a^2*A + 102960/7*x^14*e^6*d^7*b^7*a^3*A + 25740*x^14*e^7*d^6*b^6*a^4*A
+ 23166*x^14*e^8*d^5*b^5*a^5*A + 10725*x^14*e^9*d^4*b^4*a^6*A + 17160/7*x^14*e^
10*d^3*b^3*a^7*A + 1755/7*x^14*e^11*d^2*b^2*a^8*A + 65/7*x^14*e^12*d*b*a^9*A + 1
/14*x^14*e^13*a^10*A + x^13*e*d^12*b^10*B + 60*x^13*e^2*d^11*b^9*a*B + 990*x^13*
e^3*d^10*b^8*a^2*B + 6600*x^13*e^4*d^9*b^7*a^3*B + 20790*x^13*e^5*d^8*b^6*a^4*B
+ 33264*x^13*e^6*d^7*b^5*a^5*B + 27720*x^13*e^7*d^6*b^4*a^6*B + 11880*x^13*e^8*d
^5*b^3*a^7*B + 2475*x^13*e^9*d^4*b^2*a^8*B + 220*x^13*e^10*d^3*b*a^9*B + 6*x^13*
e^11*d^2*a^10*B + 6*x^13*e^2*d^11*b^10*A + 220*x^13*e^3*d^10*b^9*a*A + 2475*x^13
*e^4*d^9*b^8*a^2*A + 11880*x^13*e^5*d^8*b^7*a^3*A + 27720*x^13*e^6*d^7*b^6*a^4*A
+ 33264*x^13*e^7*d^6*b^5*a^5*A + 20790*x^13*e^8*d^5*b^4*a^6*A + 6600*x^13*e^9*d
^4*b^3*a^7*A + 990*x^13*e^10*d^3*b^2*a^8*A + 60*x^13*e^11*d^2*b*a^9*A + x^13*e^1
2*d*a^10*A + 1/12*x^12*d^13*b^10*B + 65/6*x^12*e*d^12*b^9*a*B + 585/2*x^12*e^2*d
^11*b^8*a^2*B + 2860*x^12*e^3*d^10*b^7*a^3*B + 25025/2*x^12*e^4*d^9*b^6*a^4*B +
27027*x^12*e^5*d^8*b^5*a^5*B + 30030*x^12*e^6*d^7*b^4*a^6*B + 17160*x^12*e^7*d^6
*b^3*a^7*B + 19305/4*x^12*e^8*d^5*b^2*a^8*B + 3575/6*x^12*e^9*d^4*b*a^9*B + 143/
6*x^12*e^10*d^3*a^10*B + 13/12*x^12*e*d^12*b^10*A + 65*x^12*e^2*d^11*b^9*a*A + 2
145/2*x^12*e^3*d^10*b^8*a^2*A + 7150*x^12*e^4*d^9*b^7*a^3*A + 45045/2*x^12*e^5*d
^8*b^6*a^4*A + 36036*x^12*e^6*d^7*b^5*a^5*A + 30030*x^12*e^7*d^6*b^4*a^6*A + 128
70*x^12*e^8*d^5*b^3*a^7*A + 10725/4*x^12*e^9*d^4*b^2*a^8*A + 715/3*x^12*e^10*d^3
*b*a^9*A + 13/2*x^12*e^11*d^2*a^10*A + 10/11*x^11*d^13*b^9*a*B + 585/11*x^11*e*d
^12*b^8*a^2*B + 9360/11*x^11*e^2*d^11*b^7*a^3*B + 5460*x^11*e^3*d^10*b^6*a^4*B +
16380*x^11*e^4*d^9*b^5*a^5*B + 24570*x^11*e^5*d^8*b^4*a^6*B + 18720*x^11*e^6*d^
7*b^3*a^7*B + 7020*x^11*e^7*d^6*b^2*a^8*B + 1170*x^11*e^8*d^5*b*a^9*B + 65*x^11*
e^9*d^4*a^10*B + 1/11*x^11*d^13*b^10*A + 130/11*x^11*e*d^12*b^9*a*A + 3510/11*x^
11*e^2*d^11*b^8*a^2*A + 3120*x^11*e^3*d^10*b^7*a^3*A + 13650*x^11*e^4*d^9*b^6*a^
4*A + 29484*x^11*e^5*d^8*b^5*a^5*A + 32760*x^11*e^6*d^7*b^4*a^6*A + 18720*x^11*e
^7*d^6*b^3*a^7*A + 5265*x^11*e^8*d^5*b^2*a^8*A + 650*x^11*e^9*d^4*b*a^9*A + 26*x
^11*e^10*d^3*a^10*A + 9/2*x^10*d^13*b^8*a^2*B + 156*x^10*e*d^12*b^7*a^3*B + 1638
*x^10*e^2*d^11*b^6*a^4*B + 36036/5*x^10*e^3*d^10*b^5*a^5*B + 15015*x^10*e^4*d^9*
b^4*a^6*B + 15444*x^10*e^5*d^8*b^3*a^7*B + 7722*x^10*e^6*d^7*b^2*a^8*B + 1716*x^
10*e^7*d^6*b*a^9*B + 1287/10*x^10*e^8*d^5*a^10*B + x^10*d^13*b^9*a*A + 117/2*x^1
0*e*d^12*b^8*a^2*A + 936*x^10*e^2*d^11*b^7*a^3*A + 6006*x^10*e^3*d^10*b^6*a^4*A
+ 18018*x^10*e^4*d^9*b^5*a^5*A + 27027*x^10*e^5*d^8*b^4*a^6*A + 20592*x^10*e^6*d
^7*b^3*a^7*A + 7722*x^10*e^7*d^6*b^2*a^8*A + 1287*x^10*e^8*d^5*b*a^9*A + 143/2*x
^10*e^9*d^4*a^10*A + 40/3*x^9*d^13*b^7*a^3*B + 910/3*x^9*e*d^12*b^6*a^4*B + 2184
*x^9*e^2*d^11*b^5*a^5*B + 20020/3*x^9*e^3*d^10*b^4*a^6*B + 28600/3*x^9*e^4*d^9*b
^3*a^7*B + 6435*x^9*e^5*d^8*b^2*a^8*B + 5720/3*x^9*e^6*d^7*b*a^9*B + 572/3*x^9*e
^7*d^6*a^10*B + 5*x^9*d^13*b^8*a^2*A + 520/3*x^9*e*d^12*b^7*a^3*A + 1820*x^9*e^2
*d^11*b^6*a^4*A + 8008*x^9*e^3*d^10*b^5*a^5*A + 50050/3*x^9*e^4*d^9*b^4*a^6*A +
17160*x^9*e^5*d^8*b^3*a^7*A + 8580*x^9*e^6*d^7*b^2*a^8*A + 5720/3*x^9*e^7*d^6*b*
a^9*A + 143*x^9*e^8*d^5*a^10*A + 105/4*x^8*d^13*b^6*a^4*B + 819/2*x^8*e*d^12*b^5
*a^5*B + 4095/2*x^8*e^2*d^11*b^4*a^6*B + 4290*x^8*e^3*d^10*b^3*a^7*B + 32175/8*x
^8*e^4*d^9*b^2*a^8*B + 6435/4*x^8*e^5*d^8*b*a^9*B + 429/2*x^8*e^6*d^7*a^10*B + 1
5*x^8*d^13*b^7*a^3*A + 1365/4*x^8*e*d^12*b^6*a^4*A + 2457*x^8*e^2*d^11*b^5*a^5*A
+ 15015/2*x^8*e^3*d^10*b^4*a^6*A + 10725*x^8*e^4*d^9*b^3*a^7*A + 57915/8*x^8*e^
5*d^8*b^2*a^8*A + 2145*x^8*e^6*d^7*b*a^9*A + 429/2*x^8*e^7*d^6*a^10*A + 36*x^7*d
^13*b^5*a^5*B + 390*x^7*e*d^12*b^4*a^6*B + 9360/7*x^7*e^2*d^11*b^3*a^7*B + 12870
/7*x^7*e^3*d^10*b^2*a^8*B + 7150/7*x^7*e^4*d^9*b*a^9*B + 1287/7*x^7*e^5*d^8*a^10
*B + 30*x^7*d^13*b^6*a^4*A + 468*x^7*e*d^12*b^5*a^5*A + 2340*x^7*e^2*d^11*b^4*a^
6*A + 34320/7*x^7*e^3*d^10*b^3*a^7*A + 32175/7*x^7*e^4*d^9*b^2*a^8*A + 12870/7*x
^7*e^5*d^8*b*a^9*A + 1716/7*x^7*e^6*d^7*a^10*A + 35*x^6*d^13*b^4*a^6*B + 260*x^6
*e*d^12*b^3*a^7*B + 585*x^6*e^2*d^11*b^2*a^8*B + 1430/3*x^6*e^3*d^10*b*a^9*B + 7
15/6*x^6*e^4*d^9*a^10*B + 42*x^6*d^13*b^5*a^5*A + 455*x^6*e*d^12*b^4*a^6*A + 156
0*x^6*e^2*d^11*b^3*a^7*A + 2145*x^6*e^3*d^10*b^2*a^8*A + 3575/3*x^6*e^4*d^9*b*a^
9*A + 429/2*x^6*e^5*d^8*a^10*A + 24*x^5*d^13*b^3*a^7*B + 117*x^5*e*d^12*b^2*a^8*
B + 156*x^5*e^2*d^11*b*a^9*B + 286/5*x^5*e^3*d^10*a^10*B + 42*x^5*d^13*b^4*a^6*A
+ 312*x^5*e*d^12*b^3*a^7*A + 702*x^5*e^2*d^11*b^2*a^8*A + 572*x^5*e^3*d^10*b*a^
9*A + 143*x^5*e^4*d^9*a^10*A + 45/4*x^4*d^13*b^2*a^8*B + 65/2*x^4*e*d^12*b*a^9*B
+ 39/2*x^4*e^2*d^11*a^10*B + 30*x^4*d^13*b^3*a^7*A + 585/4*x^4*e*d^12*b^2*a^8*A
+ 195*x^4*e^2*d^11*b*a^9*A + 143/2*x^4*e^3*d^10*a^10*A + 10/3*x^3*d^13*b*a^9*B
+ 13/3*x^3*e*d^12*a^10*B + 15*x^3*d^13*b^2*a^8*A + 130/3*x^3*e*d^12*b*a^9*A + 26
*x^3*e^2*d^11*a^10*A + 1/2*x^2*d^13*a^10*B + 5*x^2*d^13*b*a^9*A + 13/2*x^2*e*d^1
2*a^10*A + x*d^13*a^10*A

_______________________________________________________________________________________

Sympy [A]  time = 1.99148, size = 5092, normalized size = 10.97 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**10*(B*x+A)*(e*x+d)**13,x)

[Out]

A*a**10*d**13*x + B*b**10*e**13*x**25/25 + x**24*(A*b**10*e**13/24 + 5*B*a*b**9*
e**13/12 + 13*B*b**10*d*e**12/24) + x**23*(10*A*a*b**9*e**13/23 + 13*A*b**10*d*e
**12/23 + 45*B*a**2*b**8*e**13/23 + 130*B*a*b**9*d*e**12/23 + 78*B*b**10*d**2*e*
*11/23) + x**22*(45*A*a**2*b**8*e**13/22 + 65*A*a*b**9*d*e**12/11 + 39*A*b**10*d
**2*e**11/11 + 60*B*a**3*b**7*e**13/11 + 585*B*a**2*b**8*d*e**12/22 + 390*B*a*b*
*9*d**2*e**11/11 + 13*B*b**10*d**3*e**10) + x**21*(40*A*a**3*b**7*e**13/7 + 195*
A*a**2*b**8*d*e**12/7 + 260*A*a*b**9*d**2*e**11/7 + 286*A*b**10*d**3*e**10/21 +
10*B*a**4*b**6*e**13 + 520*B*a**3*b**7*d*e**12/7 + 1170*B*a**2*b**8*d**2*e**11/7
+ 2860*B*a*b**9*d**3*e**10/21 + 715*B*b**10*d**4*e**9/21) + x**20*(21*A*a**4*b*
*6*e**13/2 + 78*A*a**3*b**7*d*e**12 + 351*A*a**2*b**8*d**2*e**11/2 + 143*A*a*b**
9*d**3*e**10 + 143*A*b**10*d**4*e**9/4 + 63*B*a**5*b**5*e**13/5 + 273*B*a**4*b**
6*d*e**12/2 + 468*B*a**3*b**7*d**2*e**11 + 1287*B*a**2*b**8*d**3*e**10/2 + 715*B
*a*b**9*d**4*e**9/2 + 1287*B*b**10*d**5*e**8/20) + x**19*(252*A*a**5*b**5*e**13/
19 + 2730*A*a**4*b**6*d*e**12/19 + 9360*A*a**3*b**7*d**2*e**11/19 + 12870*A*a**2
*b**8*d**3*e**10/19 + 7150*A*a*b**9*d**4*e**9/19 + 1287*A*b**10*d**5*e**8/19 + 2
10*B*a**6*b**4*e**13/19 + 3276*B*a**5*b**5*d*e**12/19 + 16380*B*a**4*b**6*d**2*e
**11/19 + 34320*B*a**3*b**7*d**3*e**10/19 + 32175*B*a**2*b**8*d**4*e**9/19 + 128
70*B*a*b**9*d**5*e**8/19 + 1716*B*b**10*d**6*e**7/19) + x**18*(35*A*a**6*b**4*e*
*13/3 + 182*A*a**5*b**5*d*e**12 + 910*A*a**4*b**6*d**2*e**11 + 5720*A*a**3*b**7*
d**3*e**10/3 + 3575*A*a**2*b**8*d**4*e**9/2 + 715*A*a*b**9*d**5*e**8 + 286*A*b**
10*d**6*e**7/3 + 20*B*a**7*b**3*e**13/3 + 455*B*a**6*b**4*d*e**12/3 + 1092*B*a**
5*b**5*d**2*e**11 + 10010*B*a**4*b**6*d**3*e**10/3 + 14300*B*a**3*b**7*d**4*e**9
/3 + 6435*B*a**2*b**8*d**5*e**8/2 + 2860*B*a*b**9*d**6*e**7/3 + 286*B*b**10*d**7
*e**6/3) + x**17*(120*A*a**7*b**3*e**13/17 + 2730*A*a**6*b**4*d*e**12/17 + 19656
*A*a**5*b**5*d**2*e**11/17 + 60060*A*a**4*b**6*d**3*e**10/17 + 85800*A*a**3*b**7
*d**4*e**9/17 + 57915*A*a**2*b**8*d**5*e**8/17 + 17160*A*a*b**9*d**6*e**7/17 + 1
716*A*b**10*d**7*e**6/17 + 45*B*a**8*b**2*e**13/17 + 1560*B*a**7*b**3*d*e**12/17
+ 16380*B*a**6*b**4*d**2*e**11/17 + 72072*B*a**5*b**5*d**3*e**10/17 + 150150*B*
a**4*b**6*d**4*e**9/17 + 154440*B*a**3*b**7*d**5*e**8/17 + 77220*B*a**2*b**8*d**
6*e**7/17 + 17160*B*a*b**9*d**7*e**6/17 + 1287*B*b**10*d**8*e**5/17) + x**16*(45
*A*a**8*b**2*e**13/16 + 195*A*a**7*b**3*d*e**12/2 + 4095*A*a**6*b**4*d**2*e**11/
4 + 9009*A*a**5*b**5*d**3*e**10/2 + 75075*A*a**4*b**6*d**4*e**9/8 + 19305*A*a**3
*b**7*d**5*e**8/2 + 19305*A*a**2*b**8*d**6*e**7/4 + 2145*A*a*b**9*d**7*e**6/2 +
1287*A*b**10*d**8*e**5/16 + 5*B*a**9*b*e**13/8 + 585*B*a**8*b**2*d*e**12/16 + 58
5*B*a**7*b**3*d**2*e**11 + 15015*B*a**6*b**4*d**3*e**10/4 + 45045*B*a**5*b**5*d*
*4*e**9/4 + 135135*B*a**4*b**6*d**5*e**8/8 + 12870*B*a**3*b**7*d**6*e**7 + 19305
*B*a**2*b**8*d**7*e**6/4 + 6435*B*a*b**9*d**8*e**5/8 + 715*B*b**10*d**9*e**4/16)
+ x**15*(2*A*a**9*b*e**13/3 + 39*A*a**8*b**2*d*e**12 + 624*A*a**7*b**3*d**2*e**
11 + 4004*A*a**6*b**4*d**3*e**10 + 12012*A*a**5*b**5*d**4*e**9 + 18018*A*a**4*b*
*6*d**5*e**8 + 13728*A*a**3*b**7*d**6*e**7 + 5148*A*a**2*b**8*d**7*e**6 + 858*A*
a*b**9*d**8*e**5 + 143*A*b**10*d**9*e**4/3 + B*a**10*e**13/15 + 26*B*a**9*b*d*e*
*12/3 + 234*B*a**8*b**2*d**2*e**11 + 2288*B*a**7*b**3*d**3*e**10 + 10010*B*a**6*
b**4*d**4*e**9 + 108108*B*a**5*b**5*d**5*e**8/5 + 24024*B*a**4*b**6*d**6*e**7 +
13728*B*a**3*b**7*d**7*e**6 + 3861*B*a**2*b**8*d**8*e**5 + 1430*B*a*b**9*d**9*e*
*4/3 + 286*B*b**10*d**10*e**3/15) + x**14*(A*a**10*e**13/14 + 65*A*a**9*b*d*e**1
2/7 + 1755*A*a**8*b**2*d**2*e**11/7 + 17160*A*a**7*b**3*d**3*e**10/7 + 10725*A*a
**6*b**4*d**4*e**9 + 23166*A*a**5*b**5*d**5*e**8 + 25740*A*a**4*b**6*d**6*e**7 +
102960*A*a**3*b**7*d**7*e**6/7 + 57915*A*a**2*b**8*d**8*e**5/14 + 3575*A*a*b**9
*d**9*e**4/7 + 143*A*b**10*d**10*e**3/7 + 13*B*a**10*d*e**12/14 + 390*B*a**9*b*d
**2*e**11/7 + 6435*B*a**8*b**2*d**3*e**10/7 + 42900*B*a**7*b**3*d**4*e**9/7 + 19
305*B*a**6*b**4*d**5*e**8 + 30888*B*a**5*b**5*d**6*e**7 + 25740*B*a**4*b**6*d**7
*e**6 + 77220*B*a**3*b**7*d**8*e**5/7 + 32175*B*a**2*b**8*d**9*e**4/14 + 1430*B*
a*b**9*d**10*e**3/7 + 39*B*b**10*d**11*e**2/7) + x**13*(A*a**10*d*e**12 + 60*A*a
**9*b*d**2*e**11 + 990*A*a**8*b**2*d**3*e**10 + 6600*A*a**7*b**3*d**4*e**9 + 207
90*A*a**6*b**4*d**5*e**8 + 33264*A*a**5*b**5*d**6*e**7 + 27720*A*a**4*b**6*d**7*
e**6 + 11880*A*a**3*b**7*d**8*e**5 + 2475*A*a**2*b**8*d**9*e**4 + 220*A*a*b**9*d
**10*e**3 + 6*A*b**10*d**11*e**2 + 6*B*a**10*d**2*e**11 + 220*B*a**9*b*d**3*e**1
0 + 2475*B*a**8*b**2*d**4*e**9 + 11880*B*a**7*b**3*d**5*e**8 + 27720*B*a**6*b**4
*d**6*e**7 + 33264*B*a**5*b**5*d**7*e**6 + 20790*B*a**4*b**6*d**8*e**5 + 6600*B*
a**3*b**7*d**9*e**4 + 990*B*a**2*b**8*d**10*e**3 + 60*B*a*b**9*d**11*e**2 + B*b*
*10*d**12*e) + x**12*(13*A*a**10*d**2*e**11/2 + 715*A*a**9*b*d**3*e**10/3 + 1072
5*A*a**8*b**2*d**4*e**9/4 + 12870*A*a**7*b**3*d**5*e**8 + 30030*A*a**6*b**4*d**6
*e**7 + 36036*A*a**5*b**5*d**7*e**6 + 45045*A*a**4*b**6*d**8*e**5/2 + 7150*A*a**
3*b**7*d**9*e**4 + 2145*A*a**2*b**8*d**10*e**3/2 + 65*A*a*b**9*d**11*e**2 + 13*A
*b**10*d**12*e/12 + 143*B*a**10*d**3*e**10/6 + 3575*B*a**9*b*d**4*e**9/6 + 19305
*B*a**8*b**2*d**5*e**8/4 + 17160*B*a**7*b**3*d**6*e**7 + 30030*B*a**6*b**4*d**7*
e**6 + 27027*B*a**5*b**5*d**8*e**5 + 25025*B*a**4*b**6*d**9*e**4/2 + 2860*B*a**3
*b**7*d**10*e**3 + 585*B*a**2*b**8*d**11*e**2/2 + 65*B*a*b**9*d**12*e/6 + B*b**1
0*d**13/12) + x**11*(26*A*a**10*d**3*e**10 + 650*A*a**9*b*d**4*e**9 + 5265*A*a**
8*b**2*d**5*e**8 + 18720*A*a**7*b**3*d**6*e**7 + 32760*A*a**6*b**4*d**7*e**6 + 2
9484*A*a**5*b**5*d**8*e**5 + 13650*A*a**4*b**6*d**9*e**4 + 3120*A*a**3*b**7*d**1
0*e**3 + 3510*A*a**2*b**8*d**11*e**2/11 + 130*A*a*b**9*d**12*e/11 + A*b**10*d**1
3/11 + 65*B*a**10*d**4*e**9 + 1170*B*a**9*b*d**5*e**8 + 7020*B*a**8*b**2*d**6*e*
*7 + 18720*B*a**7*b**3*d**7*e**6 + 24570*B*a**6*b**4*d**8*e**5 + 16380*B*a**5*b*
*5*d**9*e**4 + 5460*B*a**4*b**6*d**10*e**3 + 9360*B*a**3*b**7*d**11*e**2/11 + 58
5*B*a**2*b**8*d**12*e/11 + 10*B*a*b**9*d**13/11) + x**10*(143*A*a**10*d**4*e**9/
2 + 1287*A*a**9*b*d**5*e**8 + 7722*A*a**8*b**2*d**6*e**7 + 20592*A*a**7*b**3*d**
7*e**6 + 27027*A*a**6*b**4*d**8*e**5 + 18018*A*a**5*b**5*d**9*e**4 + 6006*A*a**4
*b**6*d**10*e**3 + 936*A*a**3*b**7*d**11*e**2 + 117*A*a**2*b**8*d**12*e/2 + A*a*
b**9*d**13 + 1287*B*a**10*d**5*e**8/10 + 1716*B*a**9*b*d**6*e**7 + 7722*B*a**8*b
**2*d**7*e**6 + 15444*B*a**7*b**3*d**8*e**5 + 15015*B*a**6*b**4*d**9*e**4 + 3603
6*B*a**5*b**5*d**10*e**3/5 + 1638*B*a**4*b**6*d**11*e**2 + 156*B*a**3*b**7*d**12
*e + 9*B*a**2*b**8*d**13/2) + x**9*(143*A*a**10*d**5*e**8 + 5720*A*a**9*b*d**6*e
**7/3 + 8580*A*a**8*b**2*d**7*e**6 + 17160*A*a**7*b**3*d**8*e**5 + 50050*A*a**6*
b**4*d**9*e**4/3 + 8008*A*a**5*b**5*d**10*e**3 + 1820*A*a**4*b**6*d**11*e**2 + 5
20*A*a**3*b**7*d**12*e/3 + 5*A*a**2*b**8*d**13 + 572*B*a**10*d**6*e**7/3 + 5720*
B*a**9*b*d**7*e**6/3 + 6435*B*a**8*b**2*d**8*e**5 + 28600*B*a**7*b**3*d**9*e**4/
3 + 20020*B*a**6*b**4*d**10*e**3/3 + 2184*B*a**5*b**5*d**11*e**2 + 910*B*a**4*b*
*6*d**12*e/3 + 40*B*a**3*b**7*d**13/3) + x**8*(429*A*a**10*d**6*e**7/2 + 2145*A*
a**9*b*d**7*e**6 + 57915*A*a**8*b**2*d**8*e**5/8 + 10725*A*a**7*b**3*d**9*e**4 +
15015*A*a**6*b**4*d**10*e**3/2 + 2457*A*a**5*b**5*d**11*e**2 + 1365*A*a**4*b**6
*d**12*e/4 + 15*A*a**3*b**7*d**13 + 429*B*a**10*d**7*e**6/2 + 6435*B*a**9*b*d**8
*e**5/4 + 32175*B*a**8*b**2*d**9*e**4/8 + 4290*B*a**7*b**3*d**10*e**3 + 4095*B*a
**6*b**4*d**11*e**2/2 + 819*B*a**5*b**5*d**12*e/2 + 105*B*a**4*b**6*d**13/4) + x
**7*(1716*A*a**10*d**7*e**6/7 + 12870*A*a**9*b*d**8*e**5/7 + 32175*A*a**8*b**2*d
**9*e**4/7 + 34320*A*a**7*b**3*d**10*e**3/7 + 2340*A*a**6*b**4*d**11*e**2 + 468*
A*a**5*b**5*d**12*e + 30*A*a**4*b**6*d**13 + 1287*B*a**10*d**8*e**5/7 + 7150*B*a
**9*b*d**9*e**4/7 + 12870*B*a**8*b**2*d**10*e**3/7 + 9360*B*a**7*b**3*d**11*e**2
/7 + 390*B*a**6*b**4*d**12*e + 36*B*a**5*b**5*d**13) + x**6*(429*A*a**10*d**8*e*
*5/2 + 3575*A*a**9*b*d**9*e**4/3 + 2145*A*a**8*b**2*d**10*e**3 + 1560*A*a**7*b**
3*d**11*e**2 + 455*A*a**6*b**4*d**12*e + 42*A*a**5*b**5*d**13 + 715*B*a**10*d**9
*e**4/6 + 1430*B*a**9*b*d**10*e**3/3 + 585*B*a**8*b**2*d**11*e**2 + 260*B*a**7*b
**3*d**12*e + 35*B*a**6*b**4*d**13) + x**5*(143*A*a**10*d**9*e**4 + 572*A*a**9*b
*d**10*e**3 + 702*A*a**8*b**2*d**11*e**2 + 312*A*a**7*b**3*d**12*e + 42*A*a**6*b
**4*d**13 + 286*B*a**10*d**10*e**3/5 + 156*B*a**9*b*d**11*e**2 + 117*B*a**8*b**2
*d**12*e + 24*B*a**7*b**3*d**13) + x**4*(143*A*a**10*d**10*e**3/2 + 195*A*a**9*b
*d**11*e**2 + 585*A*a**8*b**2*d**12*e/4 + 30*A*a**7*b**3*d**13 + 39*B*a**10*d**1
1*e**2/2 + 65*B*a**9*b*d**12*e/2 + 45*B*a**8*b**2*d**13/4) + x**3*(26*A*a**10*d*
*11*e**2 + 130*A*a**9*b*d**12*e/3 + 15*A*a**8*b**2*d**13 + 13*B*a**10*d**12*e/3
+ 10*B*a**9*b*d**13/3) + x**2*(13*A*a**10*d**12*e/2 + 5*A*a**9*b*d**13 + B*a**10
*d**13/2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.223165, 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)^13,x, algorithm="giac")

[Out]

Done