3.11.75 \(\int (a+b x)^{10} (A+B x) (d+e x)^{13} \, dx\) [1075]

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

[Out]

-1/14*(-a*e+b*d)^10*(-A*e+B*d)*(e*x+d)^14/e^12+1/15*(-a*e+b*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)*(e*x+d)^15/e^12-5/
16*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)*(e*x+d)^16/e^12+15/17*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*
d)*(e*x+d)^17/e^12-5/3*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*b*d)*(e*x+d)^18/e^12+42/19*b^4*(-a*e+b*d)^5*(-6
*A*b*e-5*B*a*e+11*B*b*d)*(e*x+d)^19/e^12-21/10*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*(e*x+d)^20/e^12+10
/7*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*(e*x+d)^21/e^12-15/22*b^7*(-a*e+b*d)^2*(-3*A*b*e-8*B*a*e+11*B*
b*d)*(e*x+d)^22/e^12+5/23*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*(e*x+d)^23/e^12-1/24*b^9*(-A*b*e-10*B*a*e
+11*B*b*d)*(e*x+d)^24/e^12+1/25*b^10*B*(e*x+d)^25/e^12

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Rubi [A]
time = 2.93, antiderivative size = 464, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} -\frac {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}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/14*((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^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)/(24*e^12) + (b^10*B*(d + e*x)^25)/(25*e^12)

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int (a+b x)^{10} (A+B x) (d+e x)^{13} \, dx &=\int \left (\frac {(-b d+a e)^{10} (-B d+A e) (d+e x)^{13}}{e^{11}}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e) (d+e x)^{14}}{e^{11}}+\frac {5 b (b d-a e)^8 (-11 b B d+9 A b e+2 a B e) (d+e x)^{15}}{e^{11}}-\frac {15 b^2 (b d-a e)^7 (-11 b B d+8 A b e+3 a B e) (d+e x)^{16}}{e^{11}}+\frac {30 b^3 (b d-a e)^6 (-11 b B d+7 A b e+4 a B e) (d+e x)^{17}}{e^{11}}-\frac {42 b^4 (b d-a e)^5 (-11 b B d+6 A b e+5 a B e) (d+e x)^{18}}{e^{11}}+\frac {42 b^5 (b d-a e)^4 (-11 b B d+5 A b e+6 a B e) (d+e x)^{19}}{e^{11}}-\frac {30 b^6 (b d-a e)^3 (-11 b B d+4 A b e+7 a B e) (d+e x)^{20}}{e^{11}}+\frac {15 b^7 (b d-a e)^2 (-11 b B d+3 A b e+8 a B e) (d+e x)^{21}}{e^{11}}-\frac {5 b^8 (b d-a e) (-11 b B d+2 A b e+9 a B e) (d+e x)^{22}}{e^{11}}+\frac {b^9 (-11 b B d+A b e+10 a B e) (d+e x)^{23}}{e^{11}}+\frac {b^{10} B (d+e x)^{24}}{e^{11}}\right ) \, dx\\ &=-\frac {(b d-a e)^{10} (B d-A e) (d+e x)^{14}}{14 e^{12}}+\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e) (d+e x)^{15}}{15 e^{12}}-\frac {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}}+\frac {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}}-\frac {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}}+\frac {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}}-\frac {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}}+\frac {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}}-\frac {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}}+\frac {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}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^{24}}{24 e^{12}}+\frac {b^{10} B (d+e x)^{25}}{25 e^{12}}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(3532\) vs. \(2(464)=928\).
time = 1.06, size = 3532, normalized size = 7.61 \begin {gather*} \text {Result too large to show} \end {gather*}

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 + 71
50*a^4*b*d*e^4 + 1287*a^5*e^5))*x^6)/6 + (a^4*d^7*(a*B*d*(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) + 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 + 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))*x^8)/8 + (a^2*d^5*(
a*B*d*(40*b^7*d^7 + 910*a*b^6*d^6*e + 6552*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 + 1
9305*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 + 42
9*a^8*e^8) + 5*A*(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))*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 + 360
36*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) + 30030*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^10*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) + 130*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*(13*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*(13*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 ...

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(3892\) vs. \(2(440)=880\).
time = 0.08, size = 3893, normalized size = 8.39

method	result	size
default	\(\text {Expression too large to display}\)	\(3893\)
norman	\(\text {Expression too large to display}\)	\(4237\)
gosper	\(\text {Expression too large to display}\)	\(5040\)
risch	\(\text {Expression too large to display}\)	\(5040\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)*(e*x+d)^13,x,method=_RETURNVERBOSE)

[Out]

1/25*b^10*B*e^13*x^25+a^10*A*d^13*x+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*(1716*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+1/24*((A*b^10+10*B*a*b^9)*e^13+13*b^10*B*d*e^12)*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
/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+1716*(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+120*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+1
0*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*(25
2*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+1/12*(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+1/14*(a^10*A*e^13+13*(10*A*a^9*b+B*a^10)*d*e^12+78*(45*A*a^8*b^2+1
0*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*(210*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+1716*(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+1
716*(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+1
0*B*a*b^9)*d^11*e^2+13*b^10*B*d^12*e)*x^13+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+1287*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*(120*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+715*(252*A*a^5*b^5+210*B*a^6*b^4)*d^4*e^9+1287*(210*A*a^4*b^6+25
2*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+1/2*(13*a^10*A*d^
12*e+(10*A*a^9*b+B*a^10)*d^13)*x^2+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*((21
0*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^...

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 4005 vs. \(2 (471) = 942\).
time = 0.30, size = 4005, normalized size = 8.63 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/25*B*b^10*x^25*e^13 + A*a^10*d^13*x + 1/24*(13*B*b^10*d*e^12 + 10*B*a*b^9*e^13 + A*b^10*e^13)*x^24 + 1/23*(7
8*B*b^10*d^2*e^11 + 45*B*a^2*b^8*e^13 + 10*A*a*b^9*e^13 + 13*(10*B*a*b^9*e^12 + A*b^10*e^12)*d)*x^23 + 1/22*(2
86*B*b^10*d^3*e^10 + 120*B*a^3*b^7*e^13 + 45*A*a^2*b^8*e^13 + 78*(10*B*a*b^9*e^11 + A*b^10*e^11)*d^2 + 65*(9*B
*a^2*b^8*e^12 + 2*A*a*b^9*e^12)*d)*x^22 + 1/21*(715*B*b^10*d^4*e^9 + 210*B*a^4*b^6*e^13 + 120*A*a^3*b^7*e^13 +
286*(10*B*a*b^9*e^10 + A*b^10*e^10)*d^3 + 390*(9*B*a^2*b^8*e^11 + 2*A*a*b^9*e^11)*d^2 + 195*(8*B*a^3*b^7*e^12
+ 3*A*a^2*b^8*e^12)*d)*x^21 + 1/20*(1287*B*b^10*d^5*e^8 + 252*B*a^5*b^5*e^13 + 210*A*a^4*b^6*e^13 + 715*(10*B
*a*b^9*e^9 + A*b^10*e^9)*d^4 + 1430*(9*B*a^2*b^8*e^10 + 2*A*a*b^9*e^10)*d^3 + 1170*(8*B*a^3*b^7*e^11 + 3*A*a^2
*b^8*e^11)*d^2 + 390*(7*B*a^4*b^6*e^12 + 4*A*a^3*b^7*e^12)*d)*x^20 + 1/19*(1716*B*b^10*d^6*e^7 + 210*B*a^6*b^4
*e^13 + 252*A*a^5*b^5*e^13 + 1287*(10*B*a*b^9*e^8 + A*b^10*e^8)*d^5 + 3575*(9*B*a^2*b^8*e^9 + 2*A*a*b^9*e^9)*d
^4 + 4290*(8*B*a^3*b^7*e^10 + 3*A*a^2*b^8*e^10)*d^3 + 2340*(7*B*a^4*b^6*e^11 + 4*A*a^3*b^7*e^11)*d^2 + 546*(6*
B*a^5*b^5*e^12 + 5*A*a^4*b^6*e^12)*d)*x^19 + 1/6*(572*B*b^10*d^7*e^6 + 40*B*a^7*b^3*e^13 + 70*A*a^6*b^4*e^13 +
572*(10*B*a*b^9*e^7 + A*b^10*e^7)*d^6 + 2145*(9*B*a^2*b^8*e^8 + 2*A*a*b^9*e^8)*d^5 + 3575*(8*B*a^3*b^7*e^9 +
3*A*a^2*b^8*e^9)*d^4 + 2860*(7*B*a^4*b^6*e^10 + 4*A*a^3*b^7*e^10)*d^3 + 1092*(6*B*a^5*b^5*e^11 + 5*A*a^4*b^6*e
^11)*d^2 + 182*(5*B*a^6*b^4*e^12 + 6*A*a^5*b^5*e^12)*d)*x^18 + 3/17*(429*B*b^10*d^8*e^5 + 15*B*a^8*b^2*e^13 +
40*A*a^7*b^3*e^13 + 572*(10*B*a*b^9*e^6 + A*b^10*e^6)*d^7 + 2860*(9*B*a^2*b^8*e^7 + 2*A*a*b^9*e^7)*d^6 + 6435*
(8*B*a^3*b^7*e^8 + 3*A*a^2*b^8*e^8)*d^5 + 7150*(7*B*a^4*b^6*e^9 + 4*A*a^3*b^7*e^9)*d^4 + 4004*(6*B*a^5*b^5*e^1
0 + 5*A*a^4*b^6*e^10)*d^3 + 1092*(5*B*a^6*b^4*e^11 + 6*A*a^5*b^5*e^11)*d^2 + 130*(4*B*a^7*b^3*e^12 + 7*A*a^6*b
^4*e^12)*d)*x^17 + 1/16*(715*B*b^10*d^9*e^4 + 10*B*a^9*b*e^13 + 45*A*a^8*b^2*e^13 + 1287*(10*B*a*b^9*e^5 + A*b
^10*e^5)*d^8 + 8580*(9*B*a^2*b^8*e^6 + 2*A*a*b^9*e^6)*d^7 + 25740*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d^6 + 38
610*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d^5 + 30030*(6*B*a^5*b^5*e^9 + 5*A*a^4*b^6*e^9)*d^4 + 12012*(5*B*a^6*b
^4*e^10 + 6*A*a^5*b^5*e^10)*d^3 + 2340*(4*B*a^7*b^3*e^11 + 7*A*a^6*b^4*e^11)*d^2 + 195*(3*B*a^8*b^2*e^12 + 8*A
*a^7*b^3*e^12)*d)*x^16 + 1/15*(286*B*b^10*d^10*e^3 + B*a^10*e^13 + 10*A*a^9*b*e^13 + 715*(10*B*a*b^9*e^4 + A*b
^10*e^4)*d^9 + 6435*(9*B*a^2*b^8*e^5 + 2*A*a*b^9*e^5)*d^8 + 25740*(8*B*a^3*b^7*e^6 + 3*A*a^2*b^8*e^6)*d^7 + 51
480*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d^6 + 54054*(6*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^5 + 30030*(5*B*a^6*b
^4*e^9 + 6*A*a^5*b^5*e^9)*d^4 + 8580*(4*B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10)*d^3 + 1170*(3*B*a^8*b^2*e^11 + 8*A*
a^7*b^3*e^11)*d^2 + 65*(2*B*a^9*b*e^12 + 9*A*a^8*b^2*e^12)*d)*x^15 + 1/14*(78*B*b^10*d^11*e^2 + A*a^10*e^13 +
286*(10*B*a*b^9*e^3 + A*b^10*e^3)*d^10 + 3575*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d^9 + 19305*(8*B*a^3*b^7*e^5 +
3*A*a^2*b^8*e^5)*d^8 + 51480*(7*B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^7 + 72072*(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e
^7)*d^6 + 54054*(5*B*a^6*b^4*e^8 + 6*A*a^5*b^5*e^8)*d^5 + 21450*(4*B*a^7*b^3*e^9 + 7*A*a^6*b^4*e^9)*d^4 + 4290
*(3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10)*d^3 + 390*(2*B*a^9*b*e^11 + 9*A*a^8*b^2*e^11)*d^2 + 13*(B*a^10*e^12 + 1
0*A*a^9*b*e^12)*d)*x^14 + (B*b^10*d^12*e + A*a^10*d*e^12 + 6*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^11 + 110*(9*B*a^2
*b^8*e^3 + 2*A*a*b^9*e^3)*d^10 + 825*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d^9 + 2970*(7*B*a^4*b^6*e^5 + 4*A*a^3
*b^7*e^5)*d^8 + 5544*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^7 + 5544*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d^6 +
2970*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^5 + 825*(3*B*a^8*b^2*e^9 + 8*A*a^7*b^3*e^9)*d^4 + 110*(2*B*a^9*b*e^
10 + 9*A*a^8*b^2*e^10)*d^3 + 6*(B*a^10*e^11 + 10*A*a^9*b*e^11)*d^2)*x^13 + 1/12*(B*b^10*d^13 + 78*A*a^10*d^2*e
^11 + 13*(10*B*a*b^9*e + A*b^10*e)*d^12 + 390*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^11 + 4290*(8*B*a^3*b^7*e^3 +
3*A*a^2*b^8*e^3)*d^10 + 21450*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^9 + 54054*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*
e^5)*d^8 + 72072*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^7 + 51480*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^6 + 193
05*(3*B*a^8*b^2*e^8 + 8*A*a^7*b^3*e^8)*d^5 + 3575*(2*B*a^9*b*e^9 + 9*A*a^8*b^2*e^9)*d^4 + 286*(B*a^10*e^10 + 1
0*A*a^9*b*e^10)*d^3)*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*e + 2*A*a
*b^9*e)*d^12 + 1170*(8*B*a^3*b^7*e^2 + 3*A*a^2*b^8*e^2)*d^11 + 8580*(7*B*a^4*b^6*e^3 + 4*A*a^3*b^7*e^3)*d^10 +
30030*(6*B*a^5*b^5*e^4 + 5*A*a^4*b^6*e^4)*d^9 + 54054*(5*B*a^6*b^4*e^5 + 6*A*a^5*b^5*e^5)*d^8 + 51480*(4*B*a^
7*b^3*e^6 + 7*A*a^6*b^4*e^6)*d^7 + 25740*(3*B*a^8*b^2*e^7 + 8*A*a^7*b^3*e^7)*d^6 + 6435*(2*B*a^9*b*e^8 + 9*A*a
^8*b^2*e^8)*d^5 + 715*(B*a^10*e^9 + 10*A*a^9*b*e^9)*d^4)*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*e + 3*A*a^2*b^8*e)*d^12 + 2340*(7*B*a^4*b^6*e^2 + 4*A*a^3*b^7*e^2)*d^11 + 120
12*(6*B*a^5*b^5*e^3 + 5*A*a^4*b^6*e^3)*d^10 + 3...

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 3895 vs. \(2 (471) = 942\).
time = 0.90, size = 3895, normalized size = 8.39 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)*(e*x+d)^13,x, algorithm="fricas")

[Out]

1/12*B*b^10*d^13*x^12 + A*a^10*d^13*x + 1/11*(10*B*a*b^9 + A*b^10)*d^13*x^11 + 1/2*(9*B*a^2*b^8 + 2*A*a*b^9)*d
^13*x^10 + 5/3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^13*x^9 + 15/4*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^13*x^8 + 6*(6*B*a^5*b
^5 + 5*A*a^4*b^6)*d^13*x^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^13*x^6 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^13*x^5 +
15/4*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^13*x^4 + 5/3*(2*B*a^9*b + 9*A*a^8*b^2)*d^13*x^3 + 1/2*(B*a^10 + 10*A*a^9*b
)*d^13*x^2 + 1/686439600*(27457584*B*b^10*x^25 + 49031400*A*a^10*x^14 + 28601650*(10*B*a*b^9 + A*b^10)*x^24 +
149226000*(9*B*a^2*b^8 + 2*A*a*b^9)*x^23 + 468027000*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^22 + 980628000*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*x^21 + 1441523160*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^20 + 1517392800*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^
19 + 1144066000*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^18 + 605682000*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^17 + 214512375*(2*B
*a^9*b + 9*A*a^8*b^2)*x^16 + 45762640*(B*a^10 + 10*A*a^9*b)*x^15)*e^13 + 1/27457584*(14872858*B*b^10*d*x^24 +
27457584*A*a^10*d*x^13 + 15519504*(10*B*a*b^9 + A*b^10)*d*x^23 + 81124680*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^22 + 2
54963280*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^21 + 535422888*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*x^20 + 789044256*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*d*x^19 + 832880048*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^18 + 629909280*(4*B*a^7*b^3 + 7*A*a^6*
b^4)*d*x^17 + 334639305*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^16 + 118982864*(2*B*a^9*b + 9*A*a^8*b^2)*d*x^15 + 2549
6328*(B*a^10 + 10*A*a^9*b)*d*x^14)*e^12 + 1/2288132*(7759752*B*b^10*d^2*x^23 + 14872858*A*a^10*d^2*x^12 + 8112
468*(10*B*a*b^9 + A*b^10)*d^2*x^22 + 42493880*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^21 + 133855722*(8*B*a^3*b^7 + 3*
A*a^2*b^8)*d^2*x^20 + 281801520*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^19 + 416440024*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d
^2*x^18 + 440936496*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^17 + 334639305*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x^16 + 17
8474296*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x^15 + 63740820*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*x^14 + 13728792*(B*a^10
+ 10*A*a^9*b)*d^2*x^13)*e^11 + 1/27132*(352716*B*b^10*d^3*x^22 + 705432*A*a^10*d^3*x^11 + 369512*(10*B*a*b^9 +
A*b^10)*d^3*x^21 + 1939938*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^20 + 6126120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x^19
+ 12932920*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*x^18 + 19171152*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^17 + 20369349*(5*
B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^16 + 15519504*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x^15 + 8314020*(3*B*a^8*b^2 + 8*A
*a^7*b^3)*d^3*x^14 + 2984520*(2*B*a^9*b + 9*A*a^8*b^2)*d^3*x^13 + 646646*(B*a^10 + 10*A*a^9*b)*d^3*x^12)*e^10
+ 1/54264*(1847560*B*b^10*d^4*x^21 + 3879876*A*a^10*d^4*x^10 + 1939938*(10*B*a*b^9 + A*b^10)*d^4*x^20 + 102102
00*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^19 + 32332300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^18 + 68468400*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^4*x^17 + 101846745*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^16 + 108636528*(5*B*a^6*b^4 + 6*A*a^5*b^
5)*d^4*x^15 + 83140200*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*x^14 + 44767800*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*x^13 +
16166150*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*x^12 + 3527160*(B*a^10 + 10*A*a^9*b)*d^4*x^11)*e^9 + 1/12920*(831402*B*
b^10*d^5*x^20 + 1847560*A*a^10*d^5*x^9 + 875160*(10*B*a*b^9 + A*b^10)*d^5*x^19 + 4618900*(9*B*a^2*b^8 + 2*A*a*
b^9)*d^5*x^18 + 14671800*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^17 + 31177575*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^16
+ 46558512*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x^15 + 49884120*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*x^14 + 38372400*(4*
B*a^7*b^3 + 7*A*a^6*b^4)*d^5*x^13 + 20785050*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*x^12 + 7558200*(2*B*a^9*b + 9*A*a
^8*b^2)*d^5*x^11 + 1662804*(B*a^10 + 10*A*a^9*b)*d^5*x^10)*e^8 + 1/3876*(350064*B*b^10*d^6*x^19 + 831402*A*a^1
0*d^6*x^8 + 369512*(10*B*a*b^9 + A*b^10)*d^6*x^18 + 1956240*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^17 + 6235515*(8*B*
a^3*b^7 + 3*A*a^2*b^8)*d^6*x^16 + 13302432*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x^15 + 19953648*(6*B*a^5*b^5 + 5*A*
a^4*b^6)*d^6*x^14 + 21488544*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*x^13 + 16628040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*x
^12 + 9069840*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*x^11 + 3325608*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*x^10 + 739024*(B*a^
10 + 10*A*a^9*b)*d^6*x^9)*e^7 + 1/1428*(136136*B*b^10*d^7*x^18 + 350064*A*a^10*d^7*x^7 + 144144*(10*B*a*b^9 +
A*b^10)*d^7*x^17 + 765765*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^16 + 2450448*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x^15 +
5250960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*x^14 + 7916832*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*x^13 + 8576568*(5*B*a^6
*b^4 + 6*A*a^5*b^5)*d^7*x^12 + 6683040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^7*x^11 + 3675672*(3*B*a^8*b^2 + 8*A*a^7*b
^3)*d^7*x^10 + 1361360*(2*B*a^9*b + 9*A*a^8*b^2)*d^7*x^9 + 306306*(B*a^10 + 10*A*a^9*b)*d^7*x^8)*e^6 + 3/1904*
(48048*B*b^10*d^8*x^17 + 136136*A*a^10*d^8*x^6 + 51051*(10*B*a*b^9 + A*b^10)*d^8*x^16 + 272272*(9*B*a^2*b^8 +
2*A*a*b^9)*d^8*x^15 + 875160*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*x^14 + 1884960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*x^
13 + 2858856*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^8*x^12 + 3118752*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*x^11 + 2450448*(4*
B*a^7*b^3 + 7*A*a^6*b^4)*d^8*x^10 + 1361360*(3*...

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 5092 vs. \(2 (479) = 958\).
time = 0.61, size = 5092, normalized size = 10.97 \begin {gather*} \text {Too large to display} \end {gather*}

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 + 210*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**10/1
9 + 32175*B*a**2*b**8*d**4*e**9/19 + 12870*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 + 1716*A*b**1
0*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 + 720
72*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**13/1
6 + 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 + 585*B*a**7*b**3*d**2*e**11 + 150
15*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**12/7 + 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**1
0/7 + 42900*B*a**7*b**3*d**4*e**9/7 + 19305*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 + 66
00*A*a**7*b**3*d**4*e**9 + 20790*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**10 + 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 + 10725*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 +...

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 4797 vs. \(2 (471) = 942\).
time = 1.36, size = 4797, normalized size = 10.34 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)*(e*x+d)^13,x, algorithm="giac")

[Out]

1/25*B*b^10*x^25*e^13 + 13/24*B*b^10*d*x^24*e^12 + 78/23*B*b^10*d^2*x^23*e^11 + 13*B*b^10*d^3*x^22*e^10 + 715/
21*B*b^10*d^4*x^21*e^9 + 1287/20*B*b^10*d^5*x^20*e^8 + 1716/19*B*b^10*d^6*x^19*e^7 + 286/3*B*b^10*d^7*x^18*e^6
+ 1287/17*B*b^10*d^8*x^17*e^5 + 715/16*B*b^10*d^9*x^16*e^4 + 286/15*B*b^10*d^10*x^15*e^3 + 39/7*B*b^10*d^11*x
^14*e^2 + B*b^10*d^12*x^13*e + 1/12*B*b^10*d^13*x^12 + 5/12*B*a*b^9*x^24*e^13 + 1/24*A*b^10*x^24*e^13 + 130/23
*B*a*b^9*d*x^23*e^12 + 13/23*A*b^10*d*x^23*e^12 + 390/11*B*a*b^9*d^2*x^22*e^11 + 39/11*A*b^10*d^2*x^22*e^11 +
2860/21*B*a*b^9*d^3*x^21*e^10 + 286/21*A*b^10*d^3*x^21*e^10 + 715/2*B*a*b^9*d^4*x^20*e^9 + 143/4*A*b^10*d^4*x^
20*e^9 + 12870/19*B*a*b^9*d^5*x^19*e^8 + 1287/19*A*b^10*d^5*x^19*e^8 + 2860/3*B*a*b^9*d^6*x^18*e^7 + 286/3*A*b
^10*d^6*x^18*e^7 + 17160/17*B*a*b^9*d^7*x^17*e^6 + 1716/17*A*b^10*d^7*x^17*e^6 + 6435/8*B*a*b^9*d^8*x^16*e^5 +
1287/16*A*b^10*d^8*x^16*e^5 + 1430/3*B*a*b^9*d^9*x^15*e^4 + 143/3*A*b^10*d^9*x^15*e^4 + 1430/7*B*a*b^9*d^10*x
^14*e^3 + 143/7*A*b^10*d^10*x^14*e^3 + 60*B*a*b^9*d^11*x^13*e^2 + 6*A*b^10*d^11*x^13*e^2 + 65/6*B*a*b^9*d^12*x
^12*e + 13/12*A*b^10*d^12*x^12*e + 10/11*B*a*b^9*d^13*x^11 + 1/11*A*b^10*d^13*x^11 + 45/23*B*a^2*b^8*x^23*e^13
+ 10/23*A*a*b^9*x^23*e^13 + 585/22*B*a^2*b^8*d*x^22*e^12 + 65/11*A*a*b^9*d*x^22*e^12 + 1170/7*B*a^2*b^8*d^2*x
^21*e^11 + 260/7*A*a*b^9*d^2*x^21*e^11 + 1287/2*B*a^2*b^8*d^3*x^20*e^10 + 143*A*a*b^9*d^3*x^20*e^10 + 32175/19
*B*a^2*b^8*d^4*x^19*e^9 + 7150/19*A*a*b^9*d^4*x^19*e^9 + 6435/2*B*a^2*b^8*d^5*x^18*e^8 + 715*A*a*b^9*d^5*x^18*
e^8 + 77220/17*B*a^2*b^8*d^6*x^17*e^7 + 17160/17*A*a*b^9*d^6*x^17*e^7 + 19305/4*B*a^2*b^8*d^7*x^16*e^6 + 2145/
2*A*a*b^9*d^7*x^16*e^6 + 3861*B*a^2*b^8*d^8*x^15*e^5 + 858*A*a*b^9*d^8*x^15*e^5 + 32175/14*B*a^2*b^8*d^9*x^14*
e^4 + 3575/7*A*a*b^9*d^9*x^14*e^4 + 990*B*a^2*b^8*d^10*x^13*e^3 + 220*A*a*b^9*d^10*x^13*e^3 + 585/2*B*a^2*b^8*
d^11*x^12*e^2 + 65*A*a*b^9*d^11*x^12*e^2 + 585/11*B*a^2*b^8*d^12*x^11*e + 130/11*A*a*b^9*d^12*x^11*e + 9/2*B*a
^2*b^8*d^13*x^10 + A*a*b^9*d^13*x^10 + 60/11*B*a^3*b^7*x^22*e^13 + 45/22*A*a^2*b^8*x^22*e^13 + 520/7*B*a^3*b^7
*d*x^21*e^12 + 195/7*A*a^2*b^8*d*x^21*e^12 + 468*B*a^3*b^7*d^2*x^20*e^11 + 351/2*A*a^2*b^8*d^2*x^20*e^11 + 343
20/19*B*a^3*b^7*d^3*x^19*e^10 + 12870/19*A*a^2*b^8*d^3*x^19*e^10 + 14300/3*B*a^3*b^7*d^4*x^18*e^9 + 3575/2*A*a
^2*b^8*d^4*x^18*e^9 + 154440/17*B*a^3*b^7*d^5*x^17*e^8 + 57915/17*A*a^2*b^8*d^5*x^17*e^8 + 12870*B*a^3*b^7*d^6
*x^16*e^7 + 19305/4*A*a^2*b^8*d^6*x^16*e^7 + 13728*B*a^3*b^7*d^7*x^15*e^6 + 5148*A*a^2*b^8*d^7*x^15*e^6 + 7722
0/7*B*a^3*b^7*d^8*x^14*e^5 + 57915/14*A*a^2*b^8*d^8*x^14*e^5 + 6600*B*a^3*b^7*d^9*x^13*e^4 + 2475*A*a^2*b^8*d^
9*x^13*e^4 + 2860*B*a^3*b^7*d^10*x^12*e^3 + 2145/2*A*a^2*b^8*d^10*x^12*e^3 + 9360/11*B*a^3*b^7*d^11*x^11*e^2 +
3510/11*A*a^2*b^8*d^11*x^11*e^2 + 156*B*a^3*b^7*d^12*x^10*e + 117/2*A*a^2*b^8*d^12*x^10*e + 40/3*B*a^3*b^7*d^
13*x^9 + 5*A*a^2*b^8*d^13*x^9 + 10*B*a^4*b^6*x^21*e^13 + 40/7*A*a^3*b^7*x^21*e^13 + 273/2*B*a^4*b^6*d*x^20*e^1
2 + 78*A*a^3*b^7*d*x^20*e^12 + 16380/19*B*a^4*b^6*d^2*x^19*e^11 + 9360/19*A*a^3*b^7*d^2*x^19*e^11 + 10010/3*B*
a^4*b^6*d^3*x^18*e^10 + 5720/3*A*a^3*b^7*d^3*x^18*e^10 + 150150/17*B*a^4*b^6*d^4*x^17*e^9 + 85800/17*A*a^3*b^7
*d^4*x^17*e^9 + 135135/8*B*a^4*b^6*d^5*x^16*e^8 + 19305/2*A*a^3*b^7*d^5*x^16*e^8 + 24024*B*a^4*b^6*d^6*x^15*e^
7 + 13728*A*a^3*b^7*d^6*x^15*e^7 + 25740*B*a^4*b^6*d^7*x^14*e^6 + 102960/7*A*a^3*b^7*d^7*x^14*e^6 + 20790*B*a^
4*b^6*d^8*x^13*e^5 + 11880*A*a^3*b^7*d^8*x^13*e^5 + 25025/2*B*a^4*b^6*d^9*x^12*e^4 + 7150*A*a^3*b^7*d^9*x^12*e
^4 + 5460*B*a^4*b^6*d^10*x^11*e^3 + 3120*A*a^3*b^7*d^10*x^11*e^3 + 1638*B*a^4*b^6*d^11*x^10*e^2 + 936*A*a^3*b^
7*d^11*x^10*e^2 + 910/3*B*a^4*b^6*d^12*x^9*e + 520/3*A*a^3*b^7*d^12*x^9*e + 105/4*B*a^4*b^6*d^13*x^8 + 15*A*a^
3*b^7*d^13*x^8 + 63/5*B*a^5*b^5*x^20*e^13 + 21/2*A*a^4*b^6*x^20*e^13 + 3276/19*B*a^5*b^5*d*x^19*e^12 + 2730/19
*A*a^4*b^6*d*x^19*e^12 + 1092*B*a^5*b^5*d^2*x^18*e^11 + 910*A*a^4*b^6*d^2*x^18*e^11 + 72072/17*B*a^5*b^5*d^3*x
^17*e^10 + 60060/17*A*a^4*b^6*d^3*x^17*e^10 + 45045/4*B*a^5*b^5*d^4*x^16*e^9 + 75075/8*A*a^4*b^6*d^4*x^16*e^9
+ 108108/5*B*a^5*b^5*d^5*x^15*e^8 + 18018*A*a^4*b^6*d^5*x^15*e^8 + 30888*B*a^5*b^5*d^6*x^14*e^7 + 25740*A*a^4*
b^6*d^6*x^14*e^7 + 33264*B*a^5*b^5*d^7*x^13*e^6 + 27720*A*a^4*b^6*d^7*x^13*e^6 + 27027*B*a^5*b^5*d^8*x^12*e^5
+ 45045/2*A*a^4*b^6*d^8*x^12*e^5 + 16380*B*a^5*b^5*d^9*x^11*e^4 + 13650*A*a^4*b^6*d^9*x^11*e^4 + 36036/5*B*a^5
*b^5*d^10*x^10*e^3 + 6006*A*a^4*b^6*d^10*x^10*e^3 + 2184*B*a^5*b^5*d^11*x^9*e^2 + 1820*A*a^4*b^6*d^11*x^9*e^2
+ 819/2*B*a^5*b^5*d^12*x^8*e + 1365/4*A*a^4*b^6*d^12*x^8*e + 36*B*a^5*b^5*d^13*x^7 + 30*A*a^4*b^6*d^13*x^7 + 2
10/19*B*a^6*b^4*x^19*e^13 + 252/19*A*a^5*b^5*x^19*e^13 + 455/3*B*a^6*b^4*d*x^18*e^12 + 182*A*a^5*b^5*d*x^18*e^
12 + 16380/17*B*a^6*b^4*d^2*x^17*e^11 + 19656/17*A*a^5*b^5*d^2*x^17*e^11 + 15015/4*B*a^6*b^4*d^3*x^16*e^10 + 9
009/2*A*a^5*b^5*d^3*x^16*e^10 + 10010*B*a^6*b^4*d^4*x^15*e^9 + 12012*A*a^5*b^5*d^4*x^15*e^9 + 19305*B*a^6*b^4*
d^5*x^14*e^8 + 23166*A*a^5*b^5*d^5*x^14*e^8 + 2...

________________________________________________________________________________________

Mupad [B]
time = 1.65, size = 2500, normalized size = 5.39 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^13*(A*a^10*d*e^12 + B*b^10*d^12*e + 6*A*b^10*d^11*e^2 + 6*B*a^10*d^2*e^11 + 220*A*a*b^9*d^10*e^3 + 60*A*a^9*
b*d^2*e^11 + 60*B*a*b^9*d^11*e^2 + 220*B*a^9*b*d^3*e^10 + 2475*A*a^2*b^8*d^9*e^4 + 11880*A*a^3*b^7*d^8*e^5 + 2
7720*A*a^4*b^6*d^7*e^6 + 33264*A*a^5*b^5*d^6*e^7 + 20790*A*a^6*b^4*d^5*e^8 + 6600*A*a^7*b^3*d^4*e^9 + 990*A*a^
8*b^2*d^3*e^10 + 990*B*a^2*b^8*d^10*e^3 + 6600*B*a^3*b^7*d^9*e^4 + 20790*B*a^4*b^6*d^8*e^5 + 33264*B*a^5*b^5*d
^7*e^6 + 27720*B*a^6*b^4*d^6*e^7 + 11880*B*a^7*b^3*d^5*e^8 + 2475*B*a^8*b^2*d^4*e^9) + x^5*(42*A*a^6*b^4*d^13
+ 24*B*a^7*b^3*d^13 + 143*A*a^10*d^9*e^4 + (286*B*a^10*d^10*e^3)/5 + 312*A*a^7*b^3*d^12*e + 572*A*a^9*b*d^10*e
^3 + 117*B*a^8*b^2*d^12*e + 156*B*a^9*b*d^11*e^2 + 702*A*a^8*b^2*d^11*e^2) + x^8*(15*A*a^3*b^7*d^13 + (105*B*a
^4*b^6*d^13)/4 + (429*A*a^10*d^6*e^7)/2 + (429*B*a^10*d^7*e^6)/2 + (1365*A*a^4*b^6*d^12*e)/4 + 2145*A*a^9*b*d^
7*e^6 + (819*B*a^5*b^5*d^12*e)/2 + (6435*B*a^9*b*d^8*e^5)/4 + 2457*A*a^5*b^5*d^11*e^2 + (15015*A*a^6*b^4*d^10*
e^3)/2 + 10725*A*a^7*b^3*d^9*e^4 + (57915*A*a^8*b^2*d^8*e^5)/8 + (4095*B*a^6*b^4*d^11*e^2)/2 + 4290*B*a^7*b^3*
d^10*e^3 + (32175*B*a^8*b^2*d^9*e^4)/8) + x^21*((40*A*a^3*b^7*e^13)/7 + 10*B*a^4*b^6*e^13 + (286*A*b^10*d^3*e^
10)/21 + (715*B*b^10*d^4*e^9)/21 + (260*A*a*b^9*d^2*e^11)/7 + (195*A*a^2*b^8*d*e^12)/7 + (2860*B*a*b^9*d^3*e^1
0)/21 + (520*B*a^3*b^7*d*e^12)/7 + (1170*B*a^2*b^8*d^2*e^11)/7) + x^18*((35*A*a^6*b^4*e^13)/3 + (20*B*a^7*b^3*
e^13)/3 + (286*A*b^10*d^6*e^7)/3 + (286*B*b^10*d^7*e^6)/3 + 715*A*a*b^9*d^5*e^8 + 182*A*a^5*b^5*d*e^12 + (2860
*B*a*b^9*d^6*e^7)/3 + (455*B*a^6*b^4*d*e^12)/3 + (3575*A*a^2*b^8*d^4*e^9)/2 + (5720*A*a^3*b^7*d^3*e^10)/3 + 91
0*A*a^4*b^6*d^2*e^11 + (6435*B*a^2*b^8*d^5*e^8)/2 + (14300*B*a^3*b^7*d^4*e^9)/3 + (10010*B*a^4*b^6*d^3*e^10)/3
+ 1092*B*a^5*b^5*d^2*e^11) + x^12*((B*b^10*d^13)/12 + (13*A*b^10*d^12*e)/12 + (13*A*a^10*d^2*e^11)/2 + (143*B
*a^10*d^3*e^10)/6 + 65*A*a*b^9*d^11*e^2 + (715*A*a^9*b*d^3*e^10)/3 + (3575*B*a^9*b*d^4*e^9)/6 + (2145*A*a^2*b^
8*d^10*e^3)/2 + 7150*A*a^3*b^7*d^9*e^4 + (45045*A*a^4*b^6*d^8*e^5)/2 + 36036*A*a^5*b^5*d^7*e^6 + 30030*A*a^6*b
^4*d^6*e^7 + 12870*A*a^7*b^3*d^5*e^8 + (10725*A*a^8*b^2*d^4*e^9)/4 + (585*B*a^2*b^8*d^11*e^2)/2 + 2860*B*a^3*b
^7*d^10*e^3 + (25025*B*a^4*b^6*d^9*e^4)/2 + 27027*B*a^5*b^5*d^8*e^5 + 30030*B*a^6*b^4*d^7*e^6 + 17160*B*a^7*b^
3*d^6*e^7 + (19305*B*a^8*b^2*d^5*e^8)/4 + (65*B*a*b^9*d^12*e)/6) + x^14*((A*a^10*e^13)/14 + (13*B*a^10*d*e^12)
/14 + (143*A*b^10*d^10*e^3)/7 + (39*B*b^10*d^11*e^2)/7 + (3575*A*a*b^9*d^9*e^4)/7 + (1430*B*a*b^9*d^10*e^3)/7
+ (390*B*a^9*b*d^2*e^11)/7 + (57915*A*a^2*b^8*d^8*e^5)/14 + (102960*A*a^3*b^7*d^7*e^6)/7 + 25740*A*a^4*b^6*d^6
*e^7 + 23166*A*a^5*b^5*d^5*e^8 + 10725*A*a^6*b^4*d^4*e^9 + (17160*A*a^7*b^3*d^3*e^10)/7 + (1755*A*a^8*b^2*d^2*
e^11)/7 + (32175*B*a^2*b^8*d^9*e^4)/14 + (77220*B*a^3*b^7*d^8*e^5)/7 + 25740*B*a^4*b^6*d^7*e^6 + 30888*B*a^5*b
^5*d^6*e^7 + 19305*B*a^6*b^4*d^5*e^8 + (42900*B*a^7*b^3*d^4*e^9)/7 + (6435*B*a^8*b^2*d^3*e^10)/7 + (65*A*a^9*b
*d*e^12)/7) + x^10*(A*a*b^9*d^13 + (9*B*a^2*b^8*d^13)/2 + (143*A*a^10*d^4*e^9)/2 + (1287*B*a^10*d^5*e^8)/10 +
(117*A*a^2*b^8*d^12*e)/2 + 1287*A*a^9*b*d^5*e^8 + 156*B*a^3*b^7*d^12*e + 1716*B*a^9*b*d^6*e^7 + 936*A*a^3*b^7*
d^11*e^2 + 6006*A*a^4*b^6*d^10*e^3 + 18018*A*a^5*b^5*d^9*e^4 + 27027*A*a^6*b^4*d^8*e^5 + 20592*A*a^7*b^3*d^7*e
^6 + 7722*A*a^8*b^2*d^6*e^7 + 1638*B*a^4*b^6*d^11*e^2 + (36036*B*a^5*b^5*d^10*e^3)/5 + 15015*B*a^6*b^4*d^9*e^4
+ 15444*B*a^7*b^3*d^8*e^5 + 7722*B*a^8*b^2*d^7*e^6) + x^16*((5*B*a^9*b*e^13)/8 + (45*A*a^8*b^2*e^13)/16 + (12
87*A*b^10*d^8*e^5)/16 + (715*B*b^10*d^9*e^4)/16 + (2145*A*a*b^9*d^7*e^6)/2 + (195*A*a^7*b^3*d*e^12)/2 + (6435*
B*a*b^9*d^8*e^5)/8 + (585*B*a^8*b^2*d*e^12)/16 + (19305*A*a^2*b^8*d^6*e^7)/4 + (19305*A*a^3*b^7*d^5*e^8)/2 + (
75075*A*a^4*b^6*d^4*e^9)/8 + (9009*A*a^5*b^5*d^3*e^10)/2 + (4095*A*a^6*b^4*d^2*e^11)/4 + (19305*B*a^2*b^8*d^7*
e^6)/4 + 12870*B*a^3*b^7*d^6*e^7 + (135135*B*a^4*b^6*d^5*e^8)/8 + (45045*B*a^5*b^5*d^4*e^9)/4 + (15015*B*a^6*b
^4*d^3*e^10)/4 + 585*B*a^7*b^3*d^2*e^11) + x^6*(42*A*a^5*b^5*d^13 + 35*B*a^6*b^4*d^13 + (429*A*a^10*d^8*e^5)/2
+ (715*B*a^10*d^9*e^4)/6 + 455*A*a^6*b^4*d^12*e + (3575*A*a^9*b*d^9*e^4)/3 + 260*B*a^7*b^3*d^12*e + (1430*B*a
^9*b*d^10*e^3)/3 + 1560*A*a^7*b^3*d^11*e^2 + 2145*A*a^8*b^2*d^10*e^3 + 585*B*a^8*b^2*d^11*e^2) + x^9*(5*A*a^2*
b^8*d^13 + (40*B*a^3*b^7*d^13)/3 + 143*A*a^10*d^5*e^8 + (572*B*a^10*d^6*e^7)/3 + (520*A*a^3*b^7*d^12*e)/3 + (5
720*A*a^9*b*d^6*e^7)/3 + (910*B*a^4*b^6*d^12*e)/3 + (5720*B*a^9*b*d^7*e^6)/3 + 1820*A*a^4*b^6*d^11*e^2 + 8008*
A*a^5*b^5*d^10*e^3 + (50050*A*a^6*b^4*d^9*e^4)/3 + 17160*A*a^7*b^3*d^8*e^5 + 8580*A*a^8*b^2*d^7*e^6 + 2184*B*a
^5*b^5*d^11*e^2 + (20020*B*a^6*b^4*d^10*e^3)/3 + (28600*B*a^7*b^3*d^9*e^4)/3 + 6435*B*a^8*b^2*d^8*e^5) + x^20*
((21*A*a^4*b^6*e^13)/2 + (63*B*a^5*b^5*e^13)/5 + (143*A*b^10*d^4*e^9)/4 + (1287*B*b^10*d^5*e^8)/20 + 143*A*a*b
^9*d^3*e^10 + 78*A*a^3*b^7*d*e^12 + (715*B*a*b^9*d^4*e^9)/2 + (273*B*a^4*b^6*d*e^12)/2 + (351*A*a^2*b^8*d^2*e^
11)/2 + (1287*B*a^2*b^8*d^3*e^10)/2 + 468*B*a^3...

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