3.11.76 \(\int (a+b x)^{10} (A+B x) (d+e x)^{12} \, dx\) [1076]
Optimal. Leaf size=464 \[ -\frac {(b d-a e)^{10} (B d-A e) (d+e x)^{13}}{13 e^{12}}+\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e) (d+e x)^{14}}{14 e^{12}}-\frac {b (b d-a e)^8 (11 b B d-9 A b e-2 a B e) (d+e x)^{15}}{3 e^{12}}+\frac {15 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e) (d+e x)^{16}}{16 e^{12}}-\frac {30 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e) (d+e x)^{17}}{17 e^{12}}+\frac {7 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) (d+e x)^{18}}{3 e^{12}}-\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) (d+e x)^{19}}{19 e^{12}}+\frac {3 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^{20}}{2 e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^{21}}{7 e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^{22}}{22 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^{23}}{23 e^{12}}+\frac {b^{10} B (d+e x)^{24}}{24 e^{12}} \]
[Out]
-1/13*(-a*e+b*d)^10*(-A*e+B*d)*(e*x+d)^13/e^12+1/14*(-a*e+b*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)*(e*x+d)^14/e^12-1/
3*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)*(e*x+d)^15/e^12+15/16*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d
)*(e*x+d)^16/e^12-30/17*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*b*d)*(e*x+d)^17/e^12+7/3*b^4*(-a*e+b*d)^5*(-6*
A*b*e-5*B*a*e+11*B*b*d)*(e*x+d)^18/e^12-42/19*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*(e*x+d)^19/e^12+3/2
*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*(e*x+d)^20/e^12-5/7*b^7*(-a*e+b*d)^2*(-3*A*b*e-8*B*a*e+11*B*b*d)
*(e*x+d)^21/e^12+5/22*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*(e*x+d)^22/e^12-1/23*b^9*(-A*b*e-10*B*a*e+11*
B*b*d)*(e*x+d)^23/e^12+1/24*b^10*B*(e*x+d)^24/e^12
________________________________________________________________________________________
Rubi [A]
time = 2.63, 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)^{23} (-10 a B e-A b e+11 b B d)}{23 e^{12}}+\frac {5 b^8 (d+e x)^{22} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{22 e^{12}}-\frac {5 b^7 (d+e x)^{21} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{7 e^{12}}+\frac {3 b^6 (d+e x)^{20} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12}}-\frac {42 b^5 (d+e x)^{19} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{19 e^{12}}+\frac {7 b^4 (d+e x)^{18} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{3 e^{12}}-\frac {30 b^3 (d+e x)^{17} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{17 e^{12}}+\frac {15 b^2 (d+e x)^{16} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{16 e^{12}}-\frac {b (d+e x)^{15} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12}}+\frac {(d+e x)^{14} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{14 e^{12}}-\frac {(d+e x)^{13} (b d-a e)^{10} (B d-A e)}{13 e^{12}}+\frac {b^{10} B (d+e x)^{24}}{24 e^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(a + b*x)^10*(A + B*x)*(d + e*x)^12,x]
[Out]
-1/13*((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^13)/e^12 + ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*(d + e*x)^
14)/(14*e^12) - (b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^15)/(3*e^12) + (15*b^2*(b*d - a*e)^7
*(11*b*B*d - 8*A*b*e - 3*a*B*e)*(d + e*x)^16)/(16*e^12) - (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)
*(d + e*x)^17)/(17*e^12) + (7*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^18)/(3*e^12) - (42*b^
5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^19)/(19*e^12) + (3*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*
b*e - 7*a*B*e)*(d + e*x)^20)/(2*e^12) - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^21)/(7*e
^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^22)/(22*e^12) - (b^9*(11*b*B*d - A*b*e - 10
*a*B*e)*(d + e*x)^23)/(23*e^12) + (b^10*B*(d + e*x)^24)/(24*e^12)
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)^{12} \, dx &=\int \left (\frac {(-b d+a e)^{10} (-B d+A e) (d+e x)^{12}}{e^{11}}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e) (d+e x)^{13}}{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)^{14}}{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)^{15}}{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)^{16}}{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)^{17}}{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)^{18}}{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)^{19}}{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)^{20}}{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)^{21}}{e^{11}}+\frac {b^9 (-11 b B d+A b e+10 a B e) (d+e x)^{22}}{e^{11}}+\frac {b^{10} B (d+e x)^{23}}{e^{11}}\right ) \, dx\\ &=-\frac {(b d-a e)^{10} (B d-A e) (d+e x)^{13}}{13 e^{12}}+\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e) (d+e x)^{14}}{14 e^{12}}-\frac {b (b d-a e)^8 (11 b B d-9 A b e-2 a B e) (d+e x)^{15}}{3 e^{12}}+\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}}{16 e^{12}}-\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}}{17 e^{12}}+\frac {7 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) (d+e x)^{18}}{3 e^{12}}-\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}}{19 e^{12}}+\frac {3 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^{20}}{2 e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^{21}}{7 e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^{22}}{22 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^{23}}{23 e^{12}}+\frac {b^{10} B (d+e x)^{24}}{24 e^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(3320\) vs. \(2(464)=928\).
time = 1.04, size = 3320, normalized size = 7.16 \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)^12,x]
[Out]
a^10*A*d^12*x + (a^9*d^11*(a*B*d + 2*A*(5*b*d + 6*a*e))*x^2)/2 + (a^8*d^10*(2*a*B*d*(5*b*d + 6*a*e) + 3*A*(15*
b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2))*x^3)/3 + (a^7*d^9*(3*a*B*d*(15*b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2) + 20*A*(
6*b^3*d^3 + 27*a*b^2*d^2*e + 33*a^2*b*d*e^2 + 11*a^3*e^3))*x^4)/4 + a^6*d^8*(4*a*B*d*(6*b^3*d^3 + 27*a*b^2*d^2
*e + 33*a^2*b*d*e^2 + 11*a^3*e^3) + A*(42*b^4*d^4 + 288*a*b^3*d^3*e + 594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 +
99*a^4*e^4))*x^5 + (a^5*d^7*(5*a*B*d*(42*b^4*d^4 + 288*a*b^3*d^3*e + 594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 + 9
9*a^4*e^4) + 18*A*(14*b^5*d^5 + 140*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*d^2*e^3 + 275*a^4*b*d*e^4
+ 44*a^5*e^5))*x^6)/6 + (3*a^4*d^6*(6*a*B*d*(14*b^5*d^5 + 140*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*
d^2*e^3 + 275*a^4*b*d*e^4 + 44*a^5*e^5) + A*(70*b^6*d^6 + 1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3*b
^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308*a^6*e^6))*x^7)/7 + (3*a^3*d^5*(a*B*d*(70*b^6*d^6 +
1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3*b^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308
*a^6*e^6) + 8*A*(5*b^7*d^7 + 105*a*b^6*d^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^4*d^4*e^3 + 2475*a^4*b^3*d^3*e
^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*e^6 + 33*a^7*e^7))*x^8)/8 + (a^2*d^4*(8*a*B*d*(5*b^7*d^7 + 105*a*b^6*d
^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^4*d^4*e^3 + 2475*a^4*b^3*d^3*e^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*
e^6 + 33*a^7*e^7) + 15*A*(b^8*d^8 + 32*a*b^7*d^7*e + 308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^5*e^3 + 2310*a^4*b^4
*d^4*e^4 + 2112*a^5*b^3*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*a^7*b*d*e^7 + 11*a^8*e^8))*x^9)/3 + (a*d^3*(9*a*B*
d*(b^8*d^8 + 32*a*b^7*d^7*e + 308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^5*e^3 + 2310*a^4*b^4*d^4*e^4 + 2112*a^5*b^3
*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*a^7*b*d*e^7 + 11*a^8*e^8) + 2*A*(b^9*d^9 + 54*a*b^8*d^8*e + 792*a^2*b^7*d
^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*e^4 + 16632*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 3564*a
^7*b^2*d^2*e^7 + 495*a^8*b*d*e^8 + 22*a^9*e^9))*x^10)/2 + (d^2*(10*a*B*d*(b^9*d^9 + 54*a*b^8*d^8*e + 792*a^2*b
^7*d^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*e^4 + 16632*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 35
64*a^7*b^2*d^2*e^7 + 495*a^8*b*d*e^8 + 22*a^9*e^9) + A*(b^10*d^10 + 120*a*b^9*d^9*e + 2970*a^2*b^8*d^8*e^2 + 2
6400*a^3*b^7*d^7*e^3 + 103950*a^4*b^6*d^6*e^4 + 199584*a^5*b^5*d^5*e^5 + 194040*a^6*b^4*d^4*e^6 + 95040*a^7*b^
3*d^3*e^7 + 22275*a^8*b^2*d^2*e^8 + 2200*a^9*b*d*e^9 + 66*a^10*e^10))*x^11)/11 + (d*(6*a^10*e^10*(11*B*d + 2*A
*e) + 220*a^9*b*d*e^9*(10*B*d + 3*A*e) + 2475*a^8*b^2*d^2*e^8*(9*B*d + 4*A*e) + 11880*a^7*b^3*d^3*e^7*(8*B*d +
5*A*e) + 27720*a^6*b^4*d^4*e^6*(7*B*d + 6*A*e) + 33264*a^5*b^5*d^5*e^5*(6*B*d + 7*A*e) + 20790*a^4*b^6*d^6*e^
4*(5*B*d + 8*A*e) + 6600*a^3*b^7*d^7*e^3*(4*B*d + 9*A*e) + 990*a^2*b^8*d^8*e^2*(3*B*d + 10*A*e) + 60*a*b^9*d^9
*e*(2*B*d + 11*A*e) + b^10*d^10*(B*d + 12*A*e))*x^12)/12 + (e*(a^10*e^10*(12*B*d + A*e) + 60*a^9*b*d*e^9*(11*B
*d + 2*A*e) + 990*a^8*b^2*d^2*e^8*(10*B*d + 3*A*e) + 6600*a^7*b^3*d^3*e^7*(9*B*d + 4*A*e) + 20790*a^6*b^4*d^4*
e^6*(8*B*d + 5*A*e) + 33264*a^5*b^5*d^5*e^5*(7*B*d + 6*A*e) + 27720*a^4*b^6*d^6*e^4*(6*B*d + 7*A*e) + 11880*a^
3*b^7*d^7*e^3*(5*B*d + 8*A*e) + 2475*a^2*b^8*d^8*e^2*(4*B*d + 9*A*e) + 220*a*b^9*d^9*e*(3*B*d + 10*A*e) + 6*b^
10*d^10*(2*B*d + 11*A*e))*x^13)/13 + (e^2*(a^10*B*e^10 + 10*a^9*b*e^9*(12*B*d + A*e) + 270*a^8*b^2*d*e^8*(11*B
*d + 2*A*e) + 2640*a^7*b^3*d^2*e^7*(10*B*d + 3*A*e) + 11550*a^6*b^4*d^3*e^6*(9*B*d + 4*A*e) + 24948*a^5*b^5*d^
4*e^5*(8*B*d + 5*A*e) + 27720*a^4*b^6*d^5*e^4*(7*B*d + 6*A*e) + 15840*a^3*b^7*d^6*e^3*(6*B*d + 7*A*e) + 4455*a
^2*b^8*d^7*e^2*(5*B*d + 8*A*e) + 550*a*b^9*d^8*e*(4*B*d + 9*A*e) + 22*b^10*d^9*(3*B*d + 10*A*e))*x^14)/14 + (b
*e^3*(2*a^9*B*e^9 + 9*a^8*b*e^8*(12*B*d + A*e) + 144*a^7*b^2*d*e^7*(11*B*d + 2*A*e) + 924*a^6*b^3*d^2*e^6*(10*
B*d + 3*A*e) + 2772*a^5*b^4*d^3*e^5*(9*B*d + 4*A*e) + 4158*a^4*b^5*d^4*e^4*(8*B*d + 5*A*e) + 3168*a^3*b^6*d^5*
e^3*(7*B*d + 6*A*e) + 1188*a^2*b^7*d^6*e^2*(6*B*d + 7*A*e) + 198*a*b^8*d^7*e*(5*B*d + 8*A*e) + 11*b^9*d^8*(4*B
*d + 9*A*e))*x^15)/3 + (3*b^2*e^4*(15*a^8*B*e^8 + 40*a^7*b*e^7*(12*B*d + A*e) + 420*a^6*b^2*d*e^6*(11*B*d + 2*
A*e) + 1848*a^5*b^3*d^2*e^5*(10*B*d + 3*A*e) + 3850*a^4*b^4*d^3*e^4*(9*B*d + 4*A*e) + 3960*a^3*b^5*d^4*e^3*(8*
B*d + 5*A*e) + 1980*a^2*b^6*d^5*e^2*(7*B*d + 6*A*e) + 440*a*b^7*d^6*e*(6*B*d + 7*A*e) + 33*b^8*d^7*(5*B*d + 8*
A*e))*x^16)/16 + (3*b^3*e^5*(40*a^7*B*e^7 + 70*a^6*b*e^6*(12*B*d + A*e) + 504*a^5*b^2*d*e^5*(11*B*d + 2*A*e) +
1540*a^4*b^3*d^2*e^4*(10*B*d + 3*A*e) + 2200*a^3*b^4*d^3*e^3*(9*B*d + 4*A*e) + 1485*a^2*b^5*d^4*e^2*(8*B*d +
5*A*e) + 440*a*b^6*d^5*e*(7*B*d + 6*A*e) + 44*b^7*d^6*(6*B*d + 7*A*e))*x^17)/17 + (b^4*e^6*(70*a^6*B*e^6 + 84*
a^5*b*e^5*(12*B*d + A*e) + 420*a^4*b^2*d*e^4*(11*B*d + 2*A*e) + 880*a^3*b^3*d^2*e^3*(10*B*d + 3*A*e) + 825*a^2
*b^4*d^3*e^2*(9*B*d + 4*A*e) + 330*a*b^5*d^4*e*(8*B*d + 5*A*e) + 44*b^6*d^5*(7*B*d + 6*A*e))*x^18)/6 + (b^5*e^
7*(252*a^5*B*e^5 + 210*a^4*b*e^4*(12*B*d + A*e)...
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(3608\) vs.
\(2(440)=880\).
time = 0.09, size = 3609, normalized size = 7.78
| | |
method |
result |
size |
| | |
default |
\(\text {Expression too large to display}\) |
\(3609\) |
norman |
\(\text {Expression too large to display}\) |
\(3922\) |
gosper |
\(\text {Expression too large to display}\) |
\(4664\) |
risch |
\(\text {Expression too large to display}\) |
\(4664\) |
| | |
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(B*x+A)*(e*x+d)^12,x,method=_RETURNVERBOSE)
[Out]
1/24*b^10*B*e^12*x^24+1/23*((A*b^10+10*B*a*b^9)*e^12+12*b^10*B*d*e^11)*x^23+1/22*((10*A*a*b^9+45*B*a^2*b^8)*e^
12+12*(A*b^10+10*B*a*b^9)*d*e^11+66*b^10*B*d^2*e^10)*x^22+1/21*((45*A*a^2*b^8+120*B*a^3*b^7)*e^12+12*(10*A*a*b
^9+45*B*a^2*b^8)*d*e^11+66*(A*b^10+10*B*a*b^9)*d^2*e^10+220*b^10*B*d^3*e^9)*x^21+1/20*((120*A*a^3*b^7+210*B*a^
4*b^6)*e^12+12*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^11+66*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^10+220*(A*b^10+10*B*a*b^
9)*d^3*e^9+495*b^10*B*d^4*e^8)*x^20+1/19*((210*A*a^4*b^6+252*B*a^5*b^5)*e^12+12*(120*A*a^3*b^7+210*B*a^4*b^6)*
d*e^11+66*(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^10+220*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^9+495*(A*b^10+10*B*a*b^9)*
d^4*e^8+792*b^10*B*d^5*e^7)*x^19+1/18*((252*A*a^5*b^5+210*B*a^6*b^4)*e^12+12*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e
^11+66*(120*A*a^3*b^7+210*B*a^4*b^6)*d^2*e^10+220*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^9+495*(10*A*a*b^9+45*B*a^
2*b^8)*d^4*e^8+792*(A*b^10+10*B*a*b^9)*d^5*e^7+924*b^10*B*d^6*e^6)*x^18+1/17*((210*A*a^6*b^4+120*B*a^7*b^3)*e^
12+12*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^11+66*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^10+220*(120*A*a^3*b^7+210*B*
a^4*b^6)*d^3*e^9+495*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*e^8+792*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e^7+924*(A*b^10+10
*B*a*b^9)*d^6*e^6+792*b^10*B*d^7*e^5)*x^17+1/16*((120*A*a^7*b^3+45*B*a^8*b^2)*e^12+12*(210*A*a^6*b^4+120*B*a^7
*b^3)*d*e^11+66*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^10+220*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^9+495*(120*A*a^
3*b^7+210*B*a^4*b^6)*d^4*e^8+792*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e^7+924*(10*A*a*b^9+45*B*a^2*b^8)*d^6*e^6+79
2*(A*b^10+10*B*a*b^9)*d^7*e^5+495*b^10*B*d^8*e^4)*x^16+1/15*((45*A*a^8*b^2+10*B*a^9*b)*e^12+12*(120*A*a^7*b^3+
45*B*a^8*b^2)*d*e^11+66*(210*A*a^6*b^4+120*B*a^7*b^3)*d^2*e^10+220*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^9+495*(
210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^8+792*(120*A*a^3*b^7+210*B*a^4*b^6)*d^5*e^7+924*(45*A*a^2*b^8+120*B*a^3*b^7
)*d^6*e^6+792*(10*A*a*b^9+45*B*a^2*b^8)*d^7*e^5+495*(A*b^10+10*B*a*b^9)*d^8*e^4+220*b^10*B*d^9*e^3)*x^15+1/14*
((10*A*a^9*b+B*a^10)*e^12+12*(45*A*a^8*b^2+10*B*a^9*b)*d*e^11+66*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^10+220*(21
0*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^9+495*(252*A*a^5*b^5+210*B*a^6*b^4)*d^4*e^8+792*(210*A*a^4*b^6+252*B*a^5*b^5)
*d^5*e^7+924*(120*A*a^3*b^7+210*B*a^4*b^6)*d^6*e^6+792*(45*A*a^2*b^8+120*B*a^3*b^7)*d^7*e^5+495*(10*A*a*b^9+45
*B*a^2*b^8)*d^8*e^4+220*(A*b^10+10*B*a*b^9)*d^9*e^3+66*b^10*B*d^10*e^2)*x^14+1/13*(a^10*A*e^12+12*(10*A*a^9*b+
B*a^10)*d*e^11+66*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^10+220*(120*A*a^7*b^3+45*B*a^8*b^2)*d^3*e^9+495*(210*A*a^6*b
^4+120*B*a^7*b^3)*d^4*e^8+792*(252*A*a^5*b^5+210*B*a^6*b^4)*d^5*e^7+924*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^6+
792*(120*A*a^3*b^7+210*B*a^4*b^6)*d^7*e^5+495*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e^4+220*(10*A*a*b^9+45*B*a^2*b^
8)*d^9*e^3+66*(A*b^10+10*B*a*b^9)*d^10*e^2+12*b^10*B*d^11*e)*x^13+1/12*(12*a^10*A*d*e^11+66*(10*A*a^9*b+B*a^10
)*d^2*e^10+220*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e^9+495*(120*A*a^7*b^3+45*B*a^8*b^2)*d^4*e^8+792*(210*A*a^6*b^4+1
20*B*a^7*b^3)*d^5*e^7+924*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^6+792*(210*A*a^4*b^6+252*B*a^5*b^5)*d^7*e^5+495*
(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e^4+220*(45*A*a^2*b^8+120*B*a^3*b^7)*d^9*e^3+66*(10*A*a*b^9+45*B*a^2*b^8)*d^
10*e^2+12*(A*b^10+10*B*a*b^9)*d^11*e+b^10*B*d^12)*x^12+1/11*(66*a^10*A*d^2*e^10+220*(10*A*a^9*b+B*a^10)*d^3*e^
9+495*(45*A*a^8*b^2+10*B*a^9*b)*d^4*e^8+792*(120*A*a^7*b^3+45*B*a^8*b^2)*d^5*e^7+924*(210*A*a^6*b^4+120*B*a^7*
b^3)*d^6*e^6+792*(252*A*a^5*b^5+210*B*a^6*b^4)*d^7*e^5+495*(210*A*a^4*b^6+252*B*a^5*b^5)*d^8*e^4+220*(120*A*a^
3*b^7+210*B*a^4*b^6)*d^9*e^3+66*(45*A*a^2*b^8+120*B*a^3*b^7)*d^10*e^2+12*(10*A*a*b^9+45*B*a^2*b^8)*d^11*e+(A*b
^10+10*B*a*b^9)*d^12)*x^11+1/10*(220*a^10*A*d^3*e^9+495*(10*A*a^9*b+B*a^10)*d^4*e^8+792*(45*A*a^8*b^2+10*B*a^9
*b)*d^5*e^7+924*(120*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^6+792*(210*A*a^6*b^4+120*B*a^7*b^3)*d^7*e^5+495*(252*A*a^5*
b^5+210*B*a^6*b^4)*d^8*e^4+220*(210*A*a^4*b^6+252*B*a^5*b^5)*d^9*e^3+66*(120*A*a^3*b^7+210*B*a^4*b^6)*d^10*e^2
+12*(45*A*a^2*b^8+120*B*a^3*b^7)*d^11*e+(10*A*a*b^9+45*B*a^2*b^8)*d^12)*x^10+1/9*(495*a^10*A*d^4*e^8+792*(10*A
*a^9*b+B*a^10)*d^5*e^7+924*(45*A*a^8*b^2+10*B*a^9*b)*d^6*e^6+792*(120*A*a^7*b^3+45*B*a^8*b^2)*d^7*e^5+495*(210
*A*a^6*b^4+120*B*a^7*b^3)*d^8*e^4+220*(252*A*a^5*b^5+210*B*a^6*b^4)*d^9*e^3+66*(210*A*a^4*b^6+252*B*a^5*b^5)*d
^10*e^2+12*(120*A*a^3*b^7+210*B*a^4*b^6)*d^11*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^12)*x^9+1/8*(792*a^10*A*d^5*e^7
+924*(10*A*a^9*b+B*a^10)*d^6*e^6+792*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^5+495*(120*A*a^7*b^3+45*B*a^8*b^2)*d^8*e^
4+220*(210*A*a^6*b^4+120*B*a^7*b^3)*d^9*e^3+66*(252*A*a^5*b^5+210*B*a^6*b^4)*d^10*e^2+12*(210*A*a^4*b^6+252*B*
a^5*b^5)*d^11*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^12)*x^8+1/7*(924*a^10*A*d^6*e^6+792*(10*A*a^9*b+B*a^10)*d^7*e^
5+495*(45*A*a^8*b^2+10*B*a^9*b)*d^8*e^4+220*(120*A*a^7*b^3+45*B*a^8*b^2)*d^9*e^3+66*(210*A*a^6*b^4+120*B*a^7*b
^3)*d^10*e^2+12*(252*A*a^5*b^5+210*B*a^6*b^4)*d^11*e+(210*A*a^4*b^6+252*B*a^5*b^5)*d^12)*x^7+1/6*(792*a^10*A*d
^7*e^5+495*(10*A*a^9*b+B*a^10)*d^8*e^4+220*(45*...
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 3714 vs.
\(2 (471) = 942\).
time = 0.34, size = 3714, normalized size = 8.00 \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)^12,x, algorithm="maxima")
[Out]
1/24*B*b^10*x^24*e^12 + A*a^10*d^12*x + 1/23*(12*B*b^10*d*e^11 + 10*B*a*b^9*e^12 + A*b^10*e^12)*x^23 + 1/22*(6
6*B*b^10*d^2*e^10 + 45*B*a^2*b^8*e^12 + 10*A*a*b^9*e^12 + 12*(10*B*a*b^9*e^11 + A*b^10*e^11)*d)*x^22 + 1/21*(2
20*B*b^10*d^3*e^9 + 120*B*a^3*b^7*e^12 + 45*A*a^2*b^8*e^12 + 66*(10*B*a*b^9*e^10 + A*b^10*e^10)*d^2 + 60*(9*B*
a^2*b^8*e^11 + 2*A*a*b^9*e^11)*d)*x^21 + 1/4*(99*B*b^10*d^4*e^8 + 42*B*a^4*b^6*e^12 + 24*A*a^3*b^7*e^12 + 44*(
10*B*a*b^9*e^9 + A*b^10*e^9)*d^3 + 66*(9*B*a^2*b^8*e^10 + 2*A*a*b^9*e^10)*d^2 + 36*(8*B*a^3*b^7*e^11 + 3*A*a^2
*b^8*e^11)*d)*x^20 + 1/19*(792*B*b^10*d^5*e^7 + 252*B*a^5*b^5*e^12 + 210*A*a^4*b^6*e^12 + 495*(10*B*a*b^9*e^8
+ A*b^10*e^8)*d^4 + 1100*(9*B*a^2*b^8*e^9 + 2*A*a*b^9*e^9)*d^3 + 990*(8*B*a^3*b^7*e^10 + 3*A*a^2*b^8*e^10)*d^2
+ 360*(7*B*a^4*b^6*e^11 + 4*A*a^3*b^7*e^11)*d)*x^19 + 1/6*(308*B*b^10*d^6*e^6 + 70*B*a^6*b^4*e^12 + 84*A*a^5*
b^5*e^12 + 264*(10*B*a*b^9*e^7 + A*b^10*e^7)*d^5 + 825*(9*B*a^2*b^8*e^8 + 2*A*a*b^9*e^8)*d^4 + 1100*(8*B*a^3*b
^7*e^9 + 3*A*a^2*b^8*e^9)*d^3 + 660*(7*B*a^4*b^6*e^10 + 4*A*a^3*b^7*e^10)*d^2 + 168*(6*B*a^5*b^5*e^11 + 5*A*a^
4*b^6*e^11)*d)*x^18 + 3/17*(264*B*b^10*d^7*e^5 + 40*B*a^7*b^3*e^12 + 70*A*a^6*b^4*e^12 + 308*(10*B*a*b^9*e^6 +
A*b^10*e^6)*d^6 + 1320*(9*B*a^2*b^8*e^7 + 2*A*a*b^9*e^7)*d^5 + 2475*(8*B*a^3*b^7*e^8 + 3*A*a^2*b^8*e^8)*d^4 +
2200*(7*B*a^4*b^6*e^9 + 4*A*a^3*b^7*e^9)*d^3 + 924*(6*B*a^5*b^5*e^10 + 5*A*a^4*b^6*e^10)*d^2 + 168*(5*B*a^6*b
^4*e^11 + 6*A*a^5*b^5*e^11)*d)*x^17 + 3/16*(165*B*b^10*d^8*e^4 + 15*B*a^8*b^2*e^12 + 40*A*a^7*b^3*e^12 + 264*(
10*B*a*b^9*e^5 + A*b^10*e^5)*d^7 + 1540*(9*B*a^2*b^8*e^6 + 2*A*a*b^9*e^6)*d^6 + 3960*(8*B*a^3*b^7*e^7 + 3*A*a^
2*b^8*e^7)*d^5 + 4950*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d^4 + 3080*(6*B*a^5*b^5*e^9 + 5*A*a^4*b^6*e^9)*d^3 +
924*(5*B*a^6*b^4*e^10 + 6*A*a^5*b^5*e^10)*d^2 + 120*(4*B*a^7*b^3*e^11 + 7*A*a^6*b^4*e^11)*d)*x^16 + 1/3*(44*B
*b^10*d^9*e^3 + 2*B*a^9*b*e^12 + 9*A*a^8*b^2*e^12 + 99*(10*B*a*b^9*e^4 + A*b^10*e^4)*d^8 + 792*(9*B*a^2*b^8*e^
5 + 2*A*a*b^9*e^5)*d^7 + 2772*(8*B*a^3*b^7*e^6 + 3*A*a^2*b^8*e^6)*d^6 + 4752*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^
7)*d^5 + 4158*(6*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^4 + 1848*(5*B*a^6*b^4*e^9 + 6*A*a^5*b^5*e^9)*d^3 + 396*(4*
B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10)*d^2 + 36*(3*B*a^8*b^2*e^11 + 8*A*a^7*b^3*e^11)*d)*x^15 + 1/14*(66*B*b^10*d^
10*e^2 + B*a^10*e^12 + 10*A*a^9*b*e^12 + 220*(10*B*a*b^9*e^3 + A*b^10*e^3)*d^9 + 2475*(9*B*a^2*b^8*e^4 + 2*A*a
*b^9*e^4)*d^8 + 11880*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^7 + 27720*(7*B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^6
+ 33264*(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d^5 + 20790*(5*B*a^6*b^4*e^8 + 6*A*a^5*b^5*e^8)*d^4 + 6600*(4*B*a^
7*b^3*e^9 + 7*A*a^6*b^4*e^9)*d^3 + 990*(3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10)*d^2 + 60*(2*B*a^9*b*e^11 + 9*A*a^
8*b^2*e^11)*d)*x^14 + 1/13*(12*B*b^10*d^11*e + A*a^10*e^12 + 66*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^10 + 1100*(9*B
*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^9 + 7425*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d^8 + 23760*(7*B*a^4*b^6*e^5 + 4*
A*a^3*b^7*e^5)*d^7 + 38808*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^6 + 33264*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)
*d^5 + 14850*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^4 + 3300*(3*B*a^8*b^2*e^9 + 8*A*a^7*b^3*e^9)*d^3 + 330*(2*B
*a^9*b*e^10 + 9*A*a^8*b^2*e^10)*d^2 + 12*(B*a^10*e^11 + 10*A*a^9*b*e^11)*d)*x^13 + 1/12*(B*b^10*d^12 + 12*A*a^
10*d*e^11 + 12*(10*B*a*b^9*e + A*b^10*e)*d^11 + 330*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^10 + 3300*(8*B*a^3*b^7
*e^3 + 3*A*a^2*b^8*e^3)*d^9 + 14850*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^8 + 33264*(6*B*a^5*b^5*e^5 + 5*A*a^4
*b^6*e^5)*d^7 + 38808*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^6 + 23760*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^5
+ 7425*(3*B*a^8*b^2*e^8 + 8*A*a^7*b^3*e^8)*d^4 + 1100*(2*B*a^9*b*e^9 + 9*A*a^8*b^2*e^9)*d^3 + 66*(B*a^10*e^10
+ 10*A*a^9*b*e^10)*d^2)*x^12 + 1/11*(66*A*a^10*d^2*e^10 + (10*B*a*b^9 + A*b^10)*d^12 + 60*(9*B*a^2*b^8*e + 2*A
*a*b^9*e)*d^11 + 990*(8*B*a^3*b^7*e^2 + 3*A*a^2*b^8*e^2)*d^10 + 6600*(7*B*a^4*b^6*e^3 + 4*A*a^3*b^7*e^3)*d^9 +
20790*(6*B*a^5*b^5*e^4 + 5*A*a^4*b^6*e^4)*d^8 + 33264*(5*B*a^6*b^4*e^5 + 6*A*a^5*b^5*e^5)*d^7 + 27720*(4*B*a^
7*b^3*e^6 + 7*A*a^6*b^4*e^6)*d^6 + 11880*(3*B*a^8*b^2*e^7 + 8*A*a^7*b^3*e^7)*d^5 + 2475*(2*B*a^9*b*e^8 + 9*A*a
^8*b^2*e^8)*d^4 + 220*(B*a^10*e^9 + 10*A*a^9*b*e^9)*d^3)*x^11 + 1/2*(44*A*a^10*d^3*e^9 + (9*B*a^2*b^8 + 2*A*a*
b^9)*d^12 + 36*(8*B*a^3*b^7*e + 3*A*a^2*b^8*e)*d^11 + 396*(7*B*a^4*b^6*e^2 + 4*A*a^3*b^7*e^2)*d^10 + 1848*(6*B
*a^5*b^5*e^3 + 5*A*a^4*b^6*e^3)*d^9 + 4158*(5*B*a^6*b^4*e^4 + 6*A*a^5*b^5*e^4)*d^8 + 4752*(4*B*a^7*b^3*e^5 + 7
*A*a^6*b^4*e^5)*d^7 + 2772*(3*B*a^8*b^2*e^6 + 8*A*a^7*b^3*e^6)*d^6 + 792*(2*B*a^9*b*e^7 + 9*A*a^8*b^2*e^7)*d^5
+ 99*(B*a^10*e^8 + 10*A*a^9*b*e^8)*d^4)*x^10 + 1/3*(165*A*a^10*d^4*e^8 + 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^12 +
120*(7*B*a^4*b^6*e + 4*A*a^3*b^7*e)*d^11 + 924*(6*B*a^5*b^5*e^2 + 5*A*a^4*b^6*e^2)*d^10 + 3080*(5*B*a^6*b^4*e
^3 + 6*A*a^5*b^5*e^3)*d^9 + 4950*(4*B*a^7*b^3*e^4 + 7*A*a^6*b^4*e^4)*d^8 + 3960*(3*B*a^8*b^2*e^5 + 8*A*a^7*b^3
*e^5)*d^7 + 1540*(2*B*a^9*b*e^6 + 9*A*a^8*b^2*e...
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 3612 vs.
\(2 (471) = 942\).
time = 1.20, size = 3612, normalized size = 7.78 \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)^12,x, algorithm="fricas")
[Out]
1/12*B*b^10*d^12*x^12 + A*a^10*d^12*x + 1/11*(10*B*a*b^9 + A*b^10)*d^12*x^11 + 1/2*(9*B*a^2*b^8 + 2*A*a*b^9)*d
^12*x^10 + 5/3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^12*x^9 + 15/4*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^12*x^8 + 6*(6*B*a^5*b
^5 + 5*A*a^4*b^6)*d^12*x^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^12*x^6 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^12*x^5 +
15/4*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^12*x^4 + 5/3*(2*B*a^9*b + 9*A*a^8*b^2)*d^12*x^3 + 1/2*(B*a^10 + 10*A*a^9*b
)*d^12*x^2 + 1/356948592*(14872858*B*b^10*x^24 + 27457584*A*a^10*x^13 + 15519504*(10*B*a*b^9 + A*b^10)*x^23 +
81124680*(9*B*a^2*b^8 + 2*A*a*b^9)*x^22 + 254963280*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^21 + 535422888*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*x^20 + 789044256*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^19 + 832880048*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^18
+ 629909280*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^17 + 334639305*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^16 + 118982864*(2*B*a^9
*b + 9*A*a^8*b^2)*x^15 + 25496328*(B*a^10 + 10*A*a^9*b)*x^14)*e^12 + 1/14872858*(7759752*B*b^10*d*x^23 + 14872
858*A*a^10*d*x^12 + 8112468*(10*B*a*b^9 + A*b^10)*d*x^22 + 42493880*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^21 + 1338557
22*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^20 + 281801520*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*x^19 + 416440024*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d*x^18 + 440936496*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^17 + 334639305*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d
*x^16 + 178474296*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^15 + 63740820*(2*B*a^9*b + 9*A*a^8*b^2)*d*x^14 + 13728792*(B
*a^10 + 10*A*a^9*b)*d*x^13)*e^11 + 1/117572*(352716*B*b^10*d^2*x^22 + 705432*A*a^10*d^2*x^11 + 369512*(10*B*a*
b^9 + A*b^10)*d^2*x^21 + 1939938*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^20 + 6126120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*
x^19 + 12932920*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^18 + 19171152*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*x^17 + 2036934
9*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^16 + 15519504*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x^15 + 8314020*(3*B*a^8*b^2
+ 8*A*a^7*b^3)*d^2*x^14 + 2984520*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*x^13 + 646646*(B*a^10 + 10*A*a^9*b)*d^2*x^12)*
e^10 + 1/176358*(1847560*B*b^10*d^3*x^21 + 3879876*A*a^10*d^3*x^10 + 1939938*(10*B*a*b^9 + A*b^10)*d^3*x^20 +
10210200*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^19 + 32332300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x^18 + 68468400*(7*B*a^
4*b^6 + 4*A*a^3*b^7)*d^3*x^17 + 101846745*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^16 + 108636528*(5*B*a^6*b^4 + 6*A*
a^5*b^5)*d^3*x^15 + 83140200*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x^14 + 44767800*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*x
^13 + 16166150*(2*B*a^9*b + 9*A*a^8*b^2)*d^3*x^12 + 3527160*(B*a^10 + 10*A*a^9*b)*d^3*x^11)*e^9 + 1/33592*(831
402*B*b^10*d^4*x^20 + 1847560*A*a^10*d^4*x^9 + 875160*(10*B*a*b^9 + A*b^10)*d^4*x^19 + 4618900*(9*B*a^2*b^8 +
2*A*a*b^9)*d^4*x^18 + 14671800*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^17 + 31177575*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4
*x^16 + 46558512*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^15 + 49884120*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x^14 + 383724
00*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*x^13 + 20785050*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*x^12 + 7558200*(2*B*a^9*b +
9*A*a^8*b^2)*d^4*x^11 + 1662804*(B*a^10 + 10*A*a^9*b)*d^4*x^10)*e^8 + 1/8398*(350064*B*b^10*d^5*x^19 + 831402
*A*a^10*d^5*x^8 + 369512*(10*B*a*b^9 + A*b^10)*d^5*x^18 + 1956240*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^17 + 6235515
*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^16 + 13302432*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^15 + 19953648*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d^5*x^14 + 21488544*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*x^13 + 16628040*(4*B*a^7*b^3 + 7*A*a^6*b^4)
*d^5*x^12 + 9069840*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*x^11 + 3325608*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*x^10 + 739024
*(B*a^10 + 10*A*a^9*b)*d^5*x^9)*e^7 + 1/2652*(136136*B*b^10*d^6*x^18 + 350064*A*a^10*d^6*x^7 + 144144*(10*B*a*
b^9 + A*b^10)*d^6*x^17 + 765765*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^16 + 2450448*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x
^15 + 5250960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x^14 + 7916832*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*x^13 + 8576568*(5
*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*x^12 + 6683040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*x^11 + 3675672*(3*B*a^8*b^2 + 8*A
*a^7*b^3)*d^6*x^10 + 1361360*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*x^9 + 306306*(B*a^10 + 10*A*a^9*b)*d^6*x^8)*e^6 + 3
/3094*(48048*B*b^10*d^7*x^17 + 136136*A*a^10*d^7*x^6 + 51051*(10*B*a*b^9 + A*b^10)*d^7*x^16 + 272272*(9*B*a^2*
b^8 + 2*A*a*b^9)*d^7*x^15 + 875160*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x^14 + 1884960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*
d^7*x^13 + 2858856*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*x^12 + 3118752*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^7*x^11 + 24504
48*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^7*x^10 + 1361360*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^7*x^9 + 510510*(2*B*a^9*b + 9*
A*a^8*b^2)*d^7*x^8 + 116688*(B*a^10 + 10*A*a^9*b)*d^7*x^7)*e^5 + 3/1456*(15015*B*b^10*d^8*x^16 + 48048*A*a^10*
d^8*x^5 + 16016*(10*B*a*b^9 + A*b^10)*d^8*x^15 + 85800*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x^14 + 277200*(8*B*a^3*b^
7 + 3*A*a^2*b^8)*d^8*x^13 + 600600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*x^12 + 917280*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d
^8*x^11 + 1009008*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*x^10 + 800800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*x^9 + 450450*(
3*B*a^8*b^2 + 8*A*a^7*b^3)*d^8*x^8 + 171600*(2*...
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 4655 vs.
\(2 (478) = 956\).
time = 0.30, size = 4655, normalized size = 10.03 \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)**12,x)
[Out]
A*a**10*d**12*x + B*b**10*e**12*x**24/24 + x**23*(A*b**10*e**12/23 + 10*B*a*b**9*e**12/23 + 12*B*b**10*d*e**11
/23) + x**22*(5*A*a*b**9*e**12/11 + 6*A*b**10*d*e**11/11 + 45*B*a**2*b**8*e**12/22 + 60*B*a*b**9*d*e**11/11 +
3*B*b**10*d**2*e**10) + x**21*(15*A*a**2*b**8*e**12/7 + 40*A*a*b**9*d*e**11/7 + 22*A*b**10*d**2*e**10/7 + 40*B
*a**3*b**7*e**12/7 + 180*B*a**2*b**8*d*e**11/7 + 220*B*a*b**9*d**2*e**10/7 + 220*B*b**10*d**3*e**9/21) + x**20
*(6*A*a**3*b**7*e**12 + 27*A*a**2*b**8*d*e**11 + 33*A*a*b**9*d**2*e**10 + 11*A*b**10*d**3*e**9 + 21*B*a**4*b**
6*e**12/2 + 72*B*a**3*b**7*d*e**11 + 297*B*a**2*b**8*d**2*e**10/2 + 110*B*a*b**9*d**3*e**9 + 99*B*b**10*d**4*e
**8/4) + x**19*(210*A*a**4*b**6*e**12/19 + 1440*A*a**3*b**7*d*e**11/19 + 2970*A*a**2*b**8*d**2*e**10/19 + 2200
*A*a*b**9*d**3*e**9/19 + 495*A*b**10*d**4*e**8/19 + 252*B*a**5*b**5*e**12/19 + 2520*B*a**4*b**6*d*e**11/19 + 7
920*B*a**3*b**7*d**2*e**10/19 + 9900*B*a**2*b**8*d**3*e**9/19 + 4950*B*a*b**9*d**4*e**8/19 + 792*B*b**10*d**5*
e**7/19) + x**18*(14*A*a**5*b**5*e**12 + 140*A*a**4*b**6*d*e**11 + 440*A*a**3*b**7*d**2*e**10 + 550*A*a**2*b**
8*d**3*e**9 + 275*A*a*b**9*d**4*e**8 + 44*A*b**10*d**5*e**7 + 35*B*a**6*b**4*e**12/3 + 168*B*a**5*b**5*d*e**11
+ 770*B*a**4*b**6*d**2*e**10 + 4400*B*a**3*b**7*d**3*e**9/3 + 2475*B*a**2*b**8*d**4*e**8/2 + 440*B*a*b**9*d**
5*e**7 + 154*B*b**10*d**6*e**6/3) + x**17*(210*A*a**6*b**4*e**12/17 + 3024*A*a**5*b**5*d*e**11/17 + 13860*A*a*
*4*b**6*d**2*e**10/17 + 26400*A*a**3*b**7*d**3*e**9/17 + 22275*A*a**2*b**8*d**4*e**8/17 + 7920*A*a*b**9*d**5*e
**7/17 + 924*A*b**10*d**6*e**6/17 + 120*B*a**7*b**3*e**12/17 + 2520*B*a**6*b**4*d*e**11/17 + 16632*B*a**5*b**5
*d**2*e**10/17 + 46200*B*a**4*b**6*d**3*e**9/17 + 59400*B*a**3*b**7*d**4*e**8/17 + 35640*B*a**2*b**8*d**5*e**7
/17 + 9240*B*a*b**9*d**6*e**6/17 + 792*B*b**10*d**7*e**5/17) + x**16*(15*A*a**7*b**3*e**12/2 + 315*A*a**6*b**4
*d*e**11/2 + 2079*A*a**5*b**5*d**2*e**10/2 + 5775*A*a**4*b**6*d**3*e**9/2 + 7425*A*a**3*b**7*d**4*e**8/2 + 445
5*A*a**2*b**8*d**5*e**7/2 + 1155*A*a*b**9*d**6*e**6/2 + 99*A*b**10*d**7*e**5/2 + 45*B*a**8*b**2*e**12/16 + 90*
B*a**7*b**3*d*e**11 + 3465*B*a**6*b**4*d**2*e**10/4 + 3465*B*a**5*b**5*d**3*e**9 + 51975*B*a**4*b**6*d**4*e**8
/8 + 5940*B*a**3*b**7*d**5*e**7 + 10395*B*a**2*b**8*d**6*e**6/4 + 495*B*a*b**9*d**7*e**5 + 495*B*b**10*d**8*e*
*4/16) + x**15*(3*A*a**8*b**2*e**12 + 96*A*a**7*b**3*d*e**11 + 924*A*a**6*b**4*d**2*e**10 + 3696*A*a**5*b**5*d
**3*e**9 + 6930*A*a**4*b**6*d**4*e**8 + 6336*A*a**3*b**7*d**5*e**7 + 2772*A*a**2*b**8*d**6*e**6 + 528*A*a*b**9
*d**7*e**5 + 33*A*b**10*d**8*e**4 + 2*B*a**9*b*e**12/3 + 36*B*a**8*b**2*d*e**11 + 528*B*a**7*b**3*d**2*e**10 +
3080*B*a**6*b**4*d**3*e**9 + 8316*B*a**5*b**5*d**4*e**8 + 11088*B*a**4*b**6*d**5*e**7 + 7392*B*a**3*b**7*d**6
*e**6 + 2376*B*a**2*b**8*d**7*e**5 + 330*B*a*b**9*d**8*e**4 + 44*B*b**10*d**9*e**3/3) + x**14*(5*A*a**9*b*e**1
2/7 + 270*A*a**8*b**2*d*e**11/7 + 3960*A*a**7*b**3*d**2*e**10/7 + 3300*A*a**6*b**4*d**3*e**9 + 8910*A*a**5*b**
5*d**4*e**8 + 11880*A*a**4*b**6*d**5*e**7 + 7920*A*a**3*b**7*d**6*e**6 + 17820*A*a**2*b**8*d**7*e**5/7 + 2475*
A*a*b**9*d**8*e**4/7 + 110*A*b**10*d**9*e**3/7 + B*a**10*e**12/14 + 60*B*a**9*b*d*e**11/7 + 1485*B*a**8*b**2*d
**2*e**10/7 + 13200*B*a**7*b**3*d**3*e**9/7 + 7425*B*a**6*b**4*d**4*e**8 + 14256*B*a**5*b**5*d**5*e**7 + 13860
*B*a**4*b**6*d**6*e**6 + 47520*B*a**3*b**7*d**7*e**5/7 + 22275*B*a**2*b**8*d**8*e**4/14 + 1100*B*a*b**9*d**9*e
**3/7 + 33*B*b**10*d**10*e**2/7) + x**13*(A*a**10*e**12/13 + 120*A*a**9*b*d*e**11/13 + 2970*A*a**8*b**2*d**2*e
**10/13 + 26400*A*a**7*b**3*d**3*e**9/13 + 103950*A*a**6*b**4*d**4*e**8/13 + 199584*A*a**5*b**5*d**5*e**7/13 +
194040*A*a**4*b**6*d**6*e**6/13 + 95040*A*a**3*b**7*d**7*e**5/13 + 22275*A*a**2*b**8*d**8*e**4/13 + 2200*A*a*
b**9*d**9*e**3/13 + 66*A*b**10*d**10*e**2/13 + 12*B*a**10*d*e**11/13 + 660*B*a**9*b*d**2*e**10/13 + 9900*B*a**
8*b**2*d**3*e**9/13 + 59400*B*a**7*b**3*d**4*e**8/13 + 166320*B*a**6*b**4*d**5*e**7/13 + 232848*B*a**5*b**5*d*
*6*e**6/13 + 166320*B*a**4*b**6*d**7*e**5/13 + 59400*B*a**3*b**7*d**8*e**4/13 + 9900*B*a**2*b**8*d**9*e**3/13
+ 660*B*a*b**9*d**10*e**2/13 + 12*B*b**10*d**11*e/13) + x**12*(A*a**10*d*e**11 + 55*A*a**9*b*d**2*e**10 + 825*
A*a**8*b**2*d**3*e**9 + 4950*A*a**7*b**3*d**4*e**8 + 13860*A*a**6*b**4*d**5*e**7 + 19404*A*a**5*b**5*d**6*e**6
+ 13860*A*a**4*b**6*d**7*e**5 + 4950*A*a**3*b**7*d**8*e**4 + 825*A*a**2*b**8*d**9*e**3 + 55*A*a*b**9*d**10*e*
*2 + A*b**10*d**11*e + 11*B*a**10*d**2*e**10/2 + 550*B*a**9*b*d**3*e**9/3 + 7425*B*a**8*b**2*d**4*e**8/4 + 792
0*B*a**7*b**3*d**5*e**7 + 16170*B*a**6*b**4*d**6*e**6 + 16632*B*a**5*b**5*d**7*e**5 + 17325*B*a**4*b**6*d**8*e
**4/2 + 2200*B*a**3*b**7*d**9*e**3 + 495*B*a**2*b**8*d**10*e**2/2 + 10*B*a*b**9*d**11*e + B*b**10*d**12/12) +
x**11*(6*A*a**10*d**2*e**10 + 200*A*a**9*b*d**3*e**9 + 2025*A*a**8*b**2*d**4*e**8 + 8640*A*a**7*b**3*d**5*e**7
+ 17640*A*a**6*b**4*d**6*e**6 + 18144*A*a**5*b**5*d**7*e**5 + 9450*A*a**4*b**6*d**8*e**4 + 2400*A*a**3*b**7*d
**9*e**3 + 270*A*a**2*b**8*d**10*e**2 + 120*A*a...
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 4443 vs.
\(2 (471) = 942\).
time = 1.10, size = 4443, normalized size = 9.58 \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)^12,x, algorithm="giac")
[Out]
1/24*B*b^10*x^24*e^12 + 12/23*B*b^10*d*x^23*e^11 + 3*B*b^10*d^2*x^22*e^10 + 220/21*B*b^10*d^3*x^21*e^9 + 99/4*
B*b^10*d^4*x^20*e^8 + 792/19*B*b^10*d^5*x^19*e^7 + 154/3*B*b^10*d^6*x^18*e^6 + 792/17*B*b^10*d^7*x^17*e^5 + 49
5/16*B*b^10*d^8*x^16*e^4 + 44/3*B*b^10*d^9*x^15*e^3 + 33/7*B*b^10*d^10*x^14*e^2 + 12/13*B*b^10*d^11*x^13*e + 1
/12*B*b^10*d^12*x^12 + 10/23*B*a*b^9*x^23*e^12 + 1/23*A*b^10*x^23*e^12 + 60/11*B*a*b^9*d*x^22*e^11 + 6/11*A*b^
10*d*x^22*e^11 + 220/7*B*a*b^9*d^2*x^21*e^10 + 22/7*A*b^10*d^2*x^21*e^10 + 110*B*a*b^9*d^3*x^20*e^9 + 11*A*b^1
0*d^3*x^20*e^9 + 4950/19*B*a*b^9*d^4*x^19*e^8 + 495/19*A*b^10*d^4*x^19*e^8 + 440*B*a*b^9*d^5*x^18*e^7 + 44*A*b
^10*d^5*x^18*e^7 + 9240/17*B*a*b^9*d^6*x^17*e^6 + 924/17*A*b^10*d^6*x^17*e^6 + 495*B*a*b^9*d^7*x^16*e^5 + 99/2
*A*b^10*d^7*x^16*e^5 + 330*B*a*b^9*d^8*x^15*e^4 + 33*A*b^10*d^8*x^15*e^4 + 1100/7*B*a*b^9*d^9*x^14*e^3 + 110/7
*A*b^10*d^9*x^14*e^3 + 660/13*B*a*b^9*d^10*x^13*e^2 + 66/13*A*b^10*d^10*x^13*e^2 + 10*B*a*b^9*d^11*x^12*e + A*
b^10*d^11*x^12*e + 10/11*B*a*b^9*d^12*x^11 + 1/11*A*b^10*d^12*x^11 + 45/22*B*a^2*b^8*x^22*e^12 + 5/11*A*a*b^9*
x^22*e^12 + 180/7*B*a^2*b^8*d*x^21*e^11 + 40/7*A*a*b^9*d*x^21*e^11 + 297/2*B*a^2*b^8*d^2*x^20*e^10 + 33*A*a*b^
9*d^2*x^20*e^10 + 9900/19*B*a^2*b^8*d^3*x^19*e^9 + 2200/19*A*a*b^9*d^3*x^19*e^9 + 2475/2*B*a^2*b^8*d^4*x^18*e^
8 + 275*A*a*b^9*d^4*x^18*e^8 + 35640/17*B*a^2*b^8*d^5*x^17*e^7 + 7920/17*A*a*b^9*d^5*x^17*e^7 + 10395/4*B*a^2*
b^8*d^6*x^16*e^6 + 1155/2*A*a*b^9*d^6*x^16*e^6 + 2376*B*a^2*b^8*d^7*x^15*e^5 + 528*A*a*b^9*d^7*x^15*e^5 + 2227
5/14*B*a^2*b^8*d^8*x^14*e^4 + 2475/7*A*a*b^9*d^8*x^14*e^4 + 9900/13*B*a^2*b^8*d^9*x^13*e^3 + 2200/13*A*a*b^9*d
^9*x^13*e^3 + 495/2*B*a^2*b^8*d^10*x^12*e^2 + 55*A*a*b^9*d^10*x^12*e^2 + 540/11*B*a^2*b^8*d^11*x^11*e + 120/11
*A*a*b^9*d^11*x^11*e + 9/2*B*a^2*b^8*d^12*x^10 + A*a*b^9*d^12*x^10 + 40/7*B*a^3*b^7*x^21*e^12 + 15/7*A*a^2*b^8
*x^21*e^12 + 72*B*a^3*b^7*d*x^20*e^11 + 27*A*a^2*b^8*d*x^20*e^11 + 7920/19*B*a^3*b^7*d^2*x^19*e^10 + 2970/19*A
*a^2*b^8*d^2*x^19*e^10 + 4400/3*B*a^3*b^7*d^3*x^18*e^9 + 550*A*a^2*b^8*d^3*x^18*e^9 + 59400/17*B*a^3*b^7*d^4*x
^17*e^8 + 22275/17*A*a^2*b^8*d^4*x^17*e^8 + 5940*B*a^3*b^7*d^5*x^16*e^7 + 4455/2*A*a^2*b^8*d^5*x^16*e^7 + 7392
*B*a^3*b^7*d^6*x^15*e^6 + 2772*A*a^2*b^8*d^6*x^15*e^6 + 47520/7*B*a^3*b^7*d^7*x^14*e^5 + 17820/7*A*a^2*b^8*d^7
*x^14*e^5 + 59400/13*B*a^3*b^7*d^8*x^13*e^4 + 22275/13*A*a^2*b^8*d^8*x^13*e^4 + 2200*B*a^3*b^7*d^9*x^12*e^3 +
825*A*a^2*b^8*d^9*x^12*e^3 + 720*B*a^3*b^7*d^10*x^11*e^2 + 270*A*a^2*b^8*d^10*x^11*e^2 + 144*B*a^3*b^7*d^11*x^
10*e + 54*A*a^2*b^8*d^11*x^10*e + 40/3*B*a^3*b^7*d^12*x^9 + 5*A*a^2*b^8*d^12*x^9 + 21/2*B*a^4*b^6*x^20*e^12 +
6*A*a^3*b^7*x^20*e^12 + 2520/19*B*a^4*b^6*d*x^19*e^11 + 1440/19*A*a^3*b^7*d*x^19*e^11 + 770*B*a^4*b^6*d^2*x^18
*e^10 + 440*A*a^3*b^7*d^2*x^18*e^10 + 46200/17*B*a^4*b^6*d^3*x^17*e^9 + 26400/17*A*a^3*b^7*d^3*x^17*e^9 + 5197
5/8*B*a^4*b^6*d^4*x^16*e^8 + 7425/2*A*a^3*b^7*d^4*x^16*e^8 + 11088*B*a^4*b^6*d^5*x^15*e^7 + 6336*A*a^3*b^7*d^5
*x^15*e^7 + 13860*B*a^4*b^6*d^6*x^14*e^6 + 7920*A*a^3*b^7*d^6*x^14*e^6 + 166320/13*B*a^4*b^6*d^7*x^13*e^5 + 95
040/13*A*a^3*b^7*d^7*x^13*e^5 + 17325/2*B*a^4*b^6*d^8*x^12*e^4 + 4950*A*a^3*b^7*d^8*x^12*e^4 + 4200*B*a^4*b^6*
d^9*x^11*e^3 + 2400*A*a^3*b^7*d^9*x^11*e^3 + 1386*B*a^4*b^6*d^10*x^10*e^2 + 792*A*a^3*b^7*d^10*x^10*e^2 + 280*
B*a^4*b^6*d^11*x^9*e + 160*A*a^3*b^7*d^11*x^9*e + 105/4*B*a^4*b^6*d^12*x^8 + 15*A*a^3*b^7*d^12*x^8 + 252/19*B*
a^5*b^5*x^19*e^12 + 210/19*A*a^4*b^6*x^19*e^12 + 168*B*a^5*b^5*d*x^18*e^11 + 140*A*a^4*b^6*d*x^18*e^11 + 16632
/17*B*a^5*b^5*d^2*x^17*e^10 + 13860/17*A*a^4*b^6*d^2*x^17*e^10 + 3465*B*a^5*b^5*d^3*x^16*e^9 + 5775/2*A*a^4*b^
6*d^3*x^16*e^9 + 8316*B*a^5*b^5*d^4*x^15*e^8 + 6930*A*a^4*b^6*d^4*x^15*e^8 + 14256*B*a^5*b^5*d^5*x^14*e^7 + 11
880*A*a^4*b^6*d^5*x^14*e^7 + 232848/13*B*a^5*b^5*d^6*x^13*e^6 + 194040/13*A*a^4*b^6*d^6*x^13*e^6 + 16632*B*a^5
*b^5*d^7*x^12*e^5 + 13860*A*a^4*b^6*d^7*x^12*e^5 + 11340*B*a^5*b^5*d^8*x^11*e^4 + 9450*A*a^4*b^6*d^8*x^11*e^4
+ 5544*B*a^5*b^5*d^9*x^10*e^3 + 4620*A*a^4*b^6*d^9*x^10*e^3 + 1848*B*a^5*b^5*d^10*x^9*e^2 + 1540*A*a^4*b^6*d^1
0*x^9*e^2 + 378*B*a^5*b^5*d^11*x^8*e + 315*A*a^4*b^6*d^11*x^8*e + 36*B*a^5*b^5*d^12*x^7 + 30*A*a^4*b^6*d^12*x^
7 + 35/3*B*a^6*b^4*x^18*e^12 + 14*A*a^5*b^5*x^18*e^12 + 2520/17*B*a^6*b^4*d*x^17*e^11 + 3024/17*A*a^5*b^5*d*x^
17*e^11 + 3465/4*B*a^6*b^4*d^2*x^16*e^10 + 2079/2*A*a^5*b^5*d^2*x^16*e^10 + 3080*B*a^6*b^4*d^3*x^15*e^9 + 3696
*A*a^5*b^5*d^3*x^15*e^9 + 7425*B*a^6*b^4*d^4*x^14*e^8 + 8910*A*a^5*b^5*d^4*x^14*e^8 + 166320/13*B*a^6*b^4*d^5*
x^13*e^7 + 199584/13*A*a^5*b^5*d^5*x^13*e^7 + 16170*B*a^6*b^4*d^6*x^12*e^6 + 19404*A*a^5*b^5*d^6*x^12*e^6 + 15
120*B*a^6*b^4*d^7*x^11*e^5 + 18144*A*a^5*b^5*d^7*x^11*e^5 + 10395*B*a^6*b^4*d^8*x^10*e^4 + 12474*A*a^5*b^5*d^8
*x^10*e^4 + 15400/3*B*a^6*b^4*d^9*x^9*e^3 + 6160*A*a^5*b^5*d^9*x^9*e^3 + 3465/2*B*a^6*b^4*d^10*x^8*e^2 + 2079*
A*a^5*b^5*d^10*x^8*e^2 + 360*B*a^6*b^4*d^11*x^7*e + 432*A*a^5*b^5*d^11*x^7*e + 35*B*a^6*b^4*d^12*x^6 + 42*A*a^
5*b^5*d^12*x^6 + 120/17*B*a^7*b^3*x^17*e^12 + 2...
________________________________________________________________________________________
Mupad [B]
time = 2.46, 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)^12,x)
[Out]
x^5*(42*A*a^6*b^4*d^12 + 24*B*a^7*b^3*d^12 + 99*A*a^10*d^8*e^4 + 44*B*a^10*d^9*e^3 + 288*A*a^7*b^3*d^11*e + 44
0*A*a^9*b*d^9*e^3 + 108*B*a^8*b^2*d^11*e + 132*B*a^9*b*d^10*e^2 + 594*A*a^8*b^2*d^10*e^2) + x^8*(15*A*a^3*b^7*
d^12 + (105*B*a^4*b^6*d^12)/4 + 99*A*a^10*d^5*e^7 + (231*B*a^10*d^6*e^6)/2 + 315*A*a^4*b^6*d^11*e + 1155*A*a^9
*b*d^6*e^6 + 378*B*a^5*b^5*d^11*e + 990*B*a^9*b*d^7*e^5 + 2079*A*a^5*b^5*d^10*e^2 + 5775*A*a^6*b^4*d^9*e^3 + 7
425*A*a^7*b^3*d^8*e^4 + 4455*A*a^8*b^2*d^7*e^5 + (3465*B*a^6*b^4*d^10*e^2)/2 + 3300*B*a^7*b^3*d^9*e^3 + (22275
*B*a^8*b^2*d^8*e^4)/8) + x^20*(6*A*a^3*b^7*e^12 + (21*B*a^4*b^6*e^12)/2 + 11*A*b^10*d^3*e^9 + (99*B*b^10*d^4*e
^8)/4 + 33*A*a*b^9*d^2*e^10 + 27*A*a^2*b^8*d*e^11 + 110*B*a*b^9*d^3*e^9 + 72*B*a^3*b^7*d*e^11 + (297*B*a^2*b^8
*d^2*e^10)/2) + x^17*((210*A*a^6*b^4*e^12)/17 + (120*B*a^7*b^3*e^12)/17 + (924*A*b^10*d^6*e^6)/17 + (792*B*b^1
0*d^7*e^5)/17 + (7920*A*a*b^9*d^5*e^7)/17 + (3024*A*a^5*b^5*d*e^11)/17 + (9240*B*a*b^9*d^6*e^6)/17 + (2520*B*a
^6*b^4*d*e^11)/17 + (22275*A*a^2*b^8*d^4*e^8)/17 + (26400*A*a^3*b^7*d^3*e^9)/17 + (13860*A*a^4*b^6*d^2*e^10)/1
7 + (35640*B*a^2*b^8*d^5*e^7)/17 + (59400*B*a^3*b^7*d^4*e^8)/17 + (46200*B*a^4*b^6*d^3*e^9)/17 + (16632*B*a^5*
b^5*d^2*e^10)/17) + x^10*(A*a*b^9*d^12 + (9*B*a^2*b^8*d^12)/2 + 22*A*a^10*d^3*e^9 + (99*B*a^10*d^4*e^8)/2 + 54
*A*a^2*b^8*d^11*e + 495*A*a^9*b*d^4*e^8 + 144*B*a^3*b^7*d^11*e + 792*B*a^9*b*d^5*e^7 + 792*A*a^3*b^7*d^10*e^2
+ 4620*A*a^4*b^6*d^9*e^3 + 12474*A*a^5*b^5*d^8*e^4 + 16632*A*a^6*b^4*d^7*e^5 + 11088*A*a^7*b^3*d^6*e^6 + 3564*
A*a^8*b^2*d^5*e^7 + 1386*B*a^4*b^6*d^10*e^2 + 5544*B*a^5*b^5*d^9*e^3 + 10395*B*a^6*b^4*d^8*e^4 + 9504*B*a^7*b^
3*d^7*e^5 + 4158*B*a^8*b^2*d^6*e^6) + x^15*((2*B*a^9*b*e^12)/3 + 3*A*a^8*b^2*e^12 + 33*A*b^10*d^8*e^4 + (44*B*
b^10*d^9*e^3)/3 + 528*A*a*b^9*d^7*e^5 + 96*A*a^7*b^3*d*e^11 + 330*B*a*b^9*d^8*e^4 + 36*B*a^8*b^2*d*e^11 + 2772
*A*a^2*b^8*d^6*e^6 + 6336*A*a^3*b^7*d^5*e^7 + 6930*A*a^4*b^6*d^4*e^8 + 3696*A*a^5*b^5*d^3*e^9 + 924*A*a^6*b^4*
d^2*e^10 + 2376*B*a^2*b^8*d^7*e^5 + 7392*B*a^3*b^7*d^6*e^6 + 11088*B*a^4*b^6*d^5*e^7 + 8316*B*a^5*b^5*d^4*e^8
+ 3080*B*a^6*b^4*d^3*e^9 + 528*B*a^7*b^3*d^2*e^10) + x^6*(42*A*a^5*b^5*d^12 + 35*B*a^6*b^4*d^12 + 132*A*a^10*d
^7*e^5 + (165*B*a^10*d^8*e^4)/2 + 420*A*a^6*b^4*d^11*e + 825*A*a^9*b*d^8*e^4 + 240*B*a^7*b^3*d^11*e + (1100*B*
a^9*b*d^9*e^3)/3 + 1320*A*a^7*b^3*d^10*e^2 + 1650*A*a^8*b^2*d^9*e^3 + 495*B*a^8*b^2*d^10*e^2) + x^9*(5*A*a^2*b
^8*d^12 + (40*B*a^3*b^7*d^12)/3 + 55*A*a^10*d^4*e^8 + 88*B*a^10*d^5*e^7 + 160*A*a^3*b^7*d^11*e + 880*A*a^9*b*d
^5*e^7 + 280*B*a^4*b^6*d^11*e + (3080*B*a^9*b*d^6*e^6)/3 + 1540*A*a^4*b^6*d^10*e^2 + 6160*A*a^5*b^5*d^9*e^3 +
11550*A*a^6*b^4*d^8*e^4 + 10560*A*a^7*b^3*d^7*e^5 + 4620*A*a^8*b^2*d^6*e^6 + 1848*B*a^5*b^5*d^10*e^2 + (15400*
B*a^6*b^4*d^9*e^3)/3 + 6600*B*a^7*b^3*d^8*e^4 + 3960*B*a^8*b^2*d^7*e^5) + x^19*((210*A*a^4*b^6*e^12)/19 + (252
*B*a^5*b^5*e^12)/19 + (495*A*b^10*d^4*e^8)/19 + (792*B*b^10*d^5*e^7)/19 + (2200*A*a*b^9*d^3*e^9)/19 + (1440*A*
a^3*b^7*d*e^11)/19 + (4950*B*a*b^9*d^4*e^8)/19 + (2520*B*a^4*b^6*d*e^11)/19 + (2970*A*a^2*b^8*d^2*e^10)/19 + (
9900*B*a^2*b^8*d^3*e^9)/19 + (7920*B*a^3*b^7*d^2*e^10)/19) + x^16*((15*A*a^7*b^3*e^12)/2 + (45*B*a^8*b^2*e^12)
/16 + (99*A*b^10*d^7*e^5)/2 + (495*B*b^10*d^8*e^4)/16 + (1155*A*a*b^9*d^6*e^6)/2 + (315*A*a^6*b^4*d*e^11)/2 +
495*B*a*b^9*d^7*e^5 + 90*B*a^7*b^3*d*e^11 + (4455*A*a^2*b^8*d^5*e^7)/2 + (7425*A*a^3*b^7*d^4*e^8)/2 + (5775*A*
a^4*b^6*d^3*e^9)/2 + (2079*A*a^5*b^5*d^2*e^10)/2 + (10395*B*a^2*b^8*d^6*e^6)/4 + 5940*B*a^3*b^7*d^5*e^7 + (519
75*B*a^4*b^6*d^4*e^8)/8 + 3465*B*a^5*b^5*d^3*e^9 + (3465*B*a^6*b^4*d^2*e^10)/4) + x^11*((A*b^10*d^12)/11 + (10
*B*a*b^9*d^12)/11 + 6*A*a^10*d^2*e^10 + 20*B*a^10*d^3*e^9 + 200*A*a^9*b*d^3*e^9 + (540*B*a^2*b^8*d^11*e)/11 +
450*B*a^9*b*d^4*e^8 + 270*A*a^2*b^8*d^10*e^2 + 2400*A*a^3*b^7*d^9*e^3 + 9450*A*a^4*b^6*d^8*e^4 + 18144*A*a^5*b
^5*d^7*e^5 + 17640*A*a^6*b^4*d^6*e^6 + 8640*A*a^7*b^3*d^5*e^7 + 2025*A*a^8*b^2*d^4*e^8 + 720*B*a^3*b^7*d^10*e^
2 + 4200*B*a^4*b^6*d^9*e^3 + 11340*B*a^5*b^5*d^8*e^4 + 15120*B*a^6*b^4*d^7*e^5 + 10080*B*a^7*b^3*d^6*e^6 + 324
0*B*a^8*b^2*d^5*e^7 + (120*A*a*b^9*d^11*e)/11) + x^14*((B*a^10*e^12)/14 + (5*A*a^9*b*e^12)/7 + (110*A*b^10*d^9
*e^3)/7 + (33*B*b^10*d^10*e^2)/7 + (2475*A*a*b^9*d^8*e^4)/7 + (270*A*a^8*b^2*d*e^11)/7 + (1100*B*a*b^9*d^9*e^3
)/7 + (17820*A*a^2*b^8*d^7*e^5)/7 + 7920*A*a^3*b^7*d^6*e^6 + 11880*A*a^4*b^6*d^5*e^7 + 8910*A*a^5*b^5*d^4*e^8
+ 3300*A*a^6*b^4*d^3*e^9 + (3960*A*a^7*b^3*d^2*e^10)/7 + (22275*B*a^2*b^8*d^8*e^4)/14 + (47520*B*a^3*b^7*d^7*e
^5)/7 + 13860*B*a^4*b^6*d^6*e^6 + 14256*B*a^5*b^5*d^5*e^7 + 7425*B*a^6*b^4*d^4*e^8 + (13200*B*a^7*b^3*d^3*e^9)
/7 + (1485*B*a^8*b^2*d^2*e^10)/7 + (60*B*a^9*b*d*e^11)/7) + x^4*(30*A*a^7*b^3*d^12 + (45*B*a^8*b^2*d^12)/4 + 5
5*A*a^10*d^9*e^3 + (33*B*a^10*d^10*e^2)/2 + 135*A*a^8*b^2*d^11*e + 165*A*a^9*b*d^10*e^2 + 30*B*a^9*b*d^11*e) +
x^7*(30*A*a^4*b^6*d^12 + 36*B*a^5*b^5*d^12 + 132*A*a^10*d^6*e^6 + (792*B*a^10*d^7*e^5)/7 + 432*A*a^5*b^5*d^11
*e + (7920*A*a^9*b*d^7*e^5)/7 + 360*B*a^6*b^4*d...
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