3.11.78 \(\int (a+b x)^{10} (A+B x) (d+e x)^{10} \, dx\) [1078]
Optimal. Leaf size=460 \[ \frac {(A b-a B) (b d-a e)^{10} (a+b x)^{11}}{11 b^{12}}+\frac {(b d-a e)^9 (b B d+10 A b e-11 a B e) (a+b x)^{12}}{12 b^{12}}+\frac {5 e (b d-a e)^8 (2 b B d+9 A b e-11 a B e) (a+b x)^{13}}{13 b^{12}}+\frac {15 e^2 (b d-a e)^7 (3 b B d+8 A b e-11 a B e) (a+b x)^{14}}{14 b^{12}}+\frac {2 e^3 (b d-a e)^6 (4 b B d+7 A b e-11 a B e) (a+b x)^{15}}{b^{12}}+\frac {21 e^4 (b d-a e)^5 (5 b B d+6 A b e-11 a B e) (a+b x)^{16}}{8 b^{12}}+\frac {42 e^5 (b d-a e)^4 (6 b B d+5 A b e-11 a B e) (a+b x)^{17}}{17 b^{12}}+\frac {5 e^6 (b d-a e)^3 (7 b B d+4 A b e-11 a B e) (a+b x)^{18}}{3 b^{12}}+\frac {15 e^7 (b d-a e)^2 (8 b B d+3 A b e-11 a B e) (a+b x)^{19}}{19 b^{12}}+\frac {e^8 (b d-a e) (9 b B d+2 A b e-11 a B e) (a+b x)^{20}}{4 b^{12}}+\frac {e^9 (10 b B d+A b e-11 a B e) (a+b x)^{21}}{21 b^{12}}+\frac {B e^{10} (a+b x)^{22}}{22 b^{12}} \]
[Out]
1/11*(A*b-B*a)*(-a*e+b*d)^10*(b*x+a)^11/b^12+1/12*(-a*e+b*d)^9*(10*A*b*e-11*B*a*e+B*b*d)*(b*x+a)^12/b^12+5/13*
e*(-a*e+b*d)^8*(9*A*b*e-11*B*a*e+2*B*b*d)*(b*x+a)^13/b^12+15/14*e^2*(-a*e+b*d)^7*(8*A*b*e-11*B*a*e+3*B*b*d)*(b
*x+a)^14/b^12+2*e^3*(-a*e+b*d)^6*(7*A*b*e-11*B*a*e+4*B*b*d)*(b*x+a)^15/b^12+21/8*e^4*(-a*e+b*d)^5*(6*A*b*e-11*
B*a*e+5*B*b*d)*(b*x+a)^16/b^12+42/17*e^5*(-a*e+b*d)^4*(5*A*b*e-11*B*a*e+6*B*b*d)*(b*x+a)^17/b^12+5/3*e^6*(-a*e
+b*d)^3*(4*A*b*e-11*B*a*e+7*B*b*d)*(b*x+a)^18/b^12+15/19*e^7*(-a*e+b*d)^2*(3*A*b*e-11*B*a*e+8*B*b*d)*(b*x+a)^1
9/b^12+1/4*e^8*(-a*e+b*d)*(2*A*b*e-11*B*a*e+9*B*b*d)*(b*x+a)^20/b^12+1/21*e^9*(A*b*e-11*B*a*e+10*B*b*d)*(b*x+a
)^21/b^12+1/22*B*e^10*(b*x+a)^22/b^12
________________________________________________________________________________________
Rubi [A]
time = 2.10, antiderivative size = 460, 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 {e^9 (a+b x)^{21} (-11 a B e+A b e+10 b B d)}{21 b^{12}}+\frac {e^8 (a+b x)^{20} (b d-a e) (-11 a B e+2 A b e+9 b B d)}{4 b^{12}}+\frac {15 e^7 (a+b x)^{19} (b d-a e)^2 (-11 a B e+3 A b e+8 b B d)}{19 b^{12}}+\frac {5 e^6 (a+b x)^{18} (b d-a e)^3 (-11 a B e+4 A b e+7 b B d)}{3 b^{12}}+\frac {42 e^5 (a+b x)^{17} (b d-a e)^4 (-11 a B e+5 A b e+6 b B d)}{17 b^{12}}+\frac {21 e^4 (a+b x)^{16} (b d-a e)^5 (-11 a B e+6 A b e+5 b B d)}{8 b^{12}}+\frac {2 e^3 (a+b x)^{15} (b d-a e)^6 (-11 a B e+7 A b e+4 b B d)}{b^{12}}+\frac {15 e^2 (a+b x)^{14} (b d-a e)^7 (-11 a B e+8 A b e+3 b B d)}{14 b^{12}}+\frac {5 e (a+b x)^{13} (b d-a e)^8 (-11 a B e+9 A b e+2 b B d)}{13 b^{12}}+\frac {(a+b x)^{12} (b d-a e)^9 (-11 a B e+10 A b e+b B d)}{12 b^{12}}+\frac {(a+b x)^{11} (A b-a B) (b d-a e)^{10}}{11 b^{12}}+\frac {B e^{10} (a+b x)^{22}}{22 b^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(a + b*x)^10*(A + B*x)*(d + e*x)^10,x]
[Out]
((A*b - a*B)*(b*d - a*e)^10*(a + b*x)^11)/(11*b^12) + ((b*d - a*e)^9*(b*B*d + 10*A*b*e - 11*a*B*e)*(a + b*x)^1
2)/(12*b^12) + (5*e*(b*d - a*e)^8*(2*b*B*d + 9*A*b*e - 11*a*B*e)*(a + b*x)^13)/(13*b^12) + (15*e^2*(b*d - a*e)
^7*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^14)/(14*b^12) + (2*e^3*(b*d - a*e)^6*(4*b*B*d + 7*A*b*e - 11*a*B*e
)*(a + b*x)^15)/b^12 + (21*e^4*(b*d - a*e)^5*(5*b*B*d + 6*A*b*e - 11*a*B*e)*(a + b*x)^16)/(8*b^12) + (42*e^5*(
b*d - a*e)^4*(6*b*B*d + 5*A*b*e - 11*a*B*e)*(a + b*x)^17)/(17*b^12) + (5*e^6*(b*d - a*e)^3*(7*b*B*d + 4*A*b*e
- 11*a*B*e)*(a + b*x)^18)/(3*b^12) + (15*e^7*(b*d - a*e)^2*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)^19)/(19*b^
12) + (e^8*(b*d - a*e)*(9*b*B*d + 2*A*b*e - 11*a*B*e)*(a + b*x)^20)/(4*b^12) + (e^9*(10*b*B*d + A*b*e - 11*a*B
*e)*(a + b*x)^21)/(21*b^12) + (B*e^10*(a + b*x)^22)/(22*b^12)
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)^{10} \, dx &=\int \left (\frac {(A b-a B) (b d-a e)^{10} (a+b x)^{10}}{b^{11}}+\frac {(b d-a e)^9 (b B d+10 A b e-11 a B e) (a+b x)^{11}}{b^{11}}+\frac {5 e (b d-a e)^8 (2 b B d+9 A b e-11 a B e) (a+b x)^{12}}{b^{11}}+\frac {15 e^2 (b d-a e)^7 (3 b B d+8 A b e-11 a B e) (a+b x)^{13}}{b^{11}}+\frac {30 e^3 (b d-a e)^6 (4 b B d+7 A b e-11 a B e) (a+b x)^{14}}{b^{11}}+\frac {42 e^4 (b d-a e)^5 (5 b B d+6 A b e-11 a B e) (a+b x)^{15}}{b^{11}}+\frac {42 e^5 (b d-a e)^4 (6 b B d+5 A b e-11 a B e) (a+b x)^{16}}{b^{11}}+\frac {30 e^6 (b d-a e)^3 (7 b B d+4 A b e-11 a B e) (a+b x)^{17}}{b^{11}}+\frac {15 e^7 (b d-a e)^2 (8 b B d+3 A b e-11 a B e) (a+b x)^{18}}{b^{11}}+\frac {5 e^8 (b d-a e) (9 b B d+2 A b e-11 a B e) (a+b x)^{19}}{b^{11}}+\frac {e^9 (10 b B d+A b e-11 a B e) (a+b x)^{20}}{b^{11}}+\frac {B e^{10} (a+b x)^{21}}{b^{11}}\right ) \, dx\\ &=\frac {(A b-a B) (b d-a e)^{10} (a+b x)^{11}}{11 b^{12}}+\frac {(b d-a e)^9 (b B d+10 A b e-11 a B e) (a+b x)^{12}}{12 b^{12}}+\frac {5 e (b d-a e)^8 (2 b B d+9 A b e-11 a B e) (a+b x)^{13}}{13 b^{12}}+\frac {15 e^2 (b d-a e)^7 (3 b B d+8 A b e-11 a B e) (a+b x)^{14}}{14 b^{12}}+\frac {2 e^3 (b d-a e)^6 (4 b B d+7 A b e-11 a B e) (a+b x)^{15}}{b^{12}}+\frac {21 e^4 (b d-a e)^5 (5 b B d+6 A b e-11 a B e) (a+b x)^{16}}{8 b^{12}}+\frac {42 e^5 (b d-a e)^4 (6 b B d+5 A b e-11 a B e) (a+b x)^{17}}{17 b^{12}}+\frac {5 e^6 (b d-a e)^3 (7 b B d+4 A b e-11 a B e) (a+b x)^{18}}{3 b^{12}}+\frac {15 e^7 (b d-a e)^2 (8 b B d+3 A b e-11 a B e) (a+b x)^{19}}{19 b^{12}}+\frac {e^8 (b d-a e) (9 b B d+2 A b e-11 a B e) (a+b x)^{20}}{4 b^{12}}+\frac {e^9 (10 b B d+A b e-11 a B e) (a+b x)^{21}}{21 b^{12}}+\frac {B e^{10} (a+b x)^{22}}{22 b^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(2815\) vs. \(2(460)=920\).
time = 0.77, size = 2815, normalized size = 6.12 \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)^10,x]
[Out]
a^10*A*d^10*x + (a^9*d^9*(a*B*d + 10*A*(b*d + a*e))*x^2)/2 + (5*a^8*d^8*(2*a*B*d*(b*d + a*e) + A*(9*b^2*d^2 +
20*a*b*d*e + 9*a^2*e^2))*x^3)/3 + (5*a^7*d^7*(a*B*d*(9*b^2*d^2 + 20*a*b*d*e + 9*a^2*e^2) + 6*A*(4*b^3*d^3 + 15
*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + 3*a^6*d^6*(2*a*B*d*(4*b^3*d^3 + 15*a*b^2*d^2*e + 15*a^2*b
*d*e^2 + 4*a^3*e^3) + A*(14*b^4*d^4 + 80*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4))*x^5
+ (a^5*d^5*(5*a*B*d*(14*b^4*d^4 + 80*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4) + 4*A*(
21*b^5*d^5 + 175*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b*d*e^4 + 21*a^5*e^5))*x^6)
/2 + (6*a^4*d^4*(2*a*B*d*(21*b^5*d^5 + 175*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b
*d*e^4 + 21*a^5*e^5) + 5*A*(7*b^6*d^6 + 84*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b
^2*d^2*e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6))*x^7)/7 + (15*a^3*d^3*(a*B*d*(7*b^6*d^6 + 84*a*b^5*d^5*e + 315*a^2*b^
4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b^2*d^2*e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6) + A*(4*b^7*d^7 + 70*a*b^6*
d^6*e + 378*a^2*b^5*d^5*e^2 + 840*a^3*b^4*d^4*e^3 + 840*a^4*b^3*d^3*e^4 + 378*a^5*b^2*d^2*e^5 + 70*a^6*b*d*e^6
+ 4*a^7*e^7))*x^8)/4 + (5*a^2*d^2*(4*a*B*d*(2*b^7*d^7 + 35*a*b^6*d^6*e + 189*a^2*b^5*d^5*e^2 + 420*a^3*b^4*d^
4*e^3 + 420*a^4*b^3*d^3*e^4 + 189*a^5*b^2*d^2*e^5 + 35*a^6*b*d*e^6 + 2*a^7*e^7) + A*(3*b^8*d^8 + 80*a*b^7*d^7*
e + 630*a^2*b^6*d^6*e^2 + 2016*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e^5 + 630*a^6*b^2*d^2
*e^6 + 80*a^7*b*d*e^7 + 3*a^8*e^8))*x^9)/3 + (a*d*(3*a*B*d*(3*b^8*d^8 + 80*a*b^7*d^7*e + 630*a^2*b^6*d^6*e^2 +
2016*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e^5 + 630*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + 3
*a^8*e^8) + 2*A*(b^9*d^9 + 45*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d^6*e^3 + 5292*a^4*b^5*d^5*e^4
+ 5292*a^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 540*a^7*b^2*d^2*e^7 + 45*a^8*b*d*e^8 + a^9*e^9))*x^10)/2 + ((1
0*a*B*d*(b^9*d^9 + 45*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d^6*e^3 + 5292*a^4*b^5*d^5*e^4 + 5292*a
^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 540*a^7*b^2*d^2*e^7 + 45*a^8*b*d*e^8 + a^9*e^9) + A*(b^10*d^10 + 100*a
*b^9*d^9*e + 2025*a^2*b^8*d^8*e^2 + 14400*a^3*b^7*d^7*e^3 + 44100*a^4*b^6*d^6*e^4 + 63504*a^5*b^5*d^5*e^5 + 44
100*a^6*b^4*d^4*e^6 + 14400*a^7*b^3*d^3*e^7 + 2025*a^8*b^2*d^2*e^8 + 100*a^9*b*d*e^9 + a^10*e^10))*x^11)/11 +
((a^10*B*e^10 + 10*a^9*b*e^9*(10*B*d + A*e) + 225*a^8*b^2*d*e^8*(9*B*d + 2*A*e) + 1800*a^7*b^3*d^2*e^7*(8*B*d
+ 3*A*e) + 6300*a^6*b^4*d^3*e^6*(7*B*d + 4*A*e) + 10584*a^5*b^5*d^4*e^5*(6*B*d + 5*A*e) + 8820*a^4*b^6*d^5*e^4
*(5*B*d + 6*A*e) + 3600*a^3*b^7*d^6*e^3*(4*B*d + 7*A*e) + 675*a^2*b^8*d^7*e^2*(3*B*d + 8*A*e) + 50*a*b^9*d^8*e
*(2*B*d + 9*A*e) + b^10*d^9*(B*d + 10*A*e))*x^12)/12 + (5*b*e*(2*a^9*B*e^9 + 9*a^8*b*e^8*(10*B*d + A*e) + 120*
a^7*b^2*d*e^7*(9*B*d + 2*A*e) + 630*a^6*b^3*d^2*e^6*(8*B*d + 3*A*e) + 1512*a^5*b^4*d^3*e^5*(7*B*d + 4*A*e) + 1
764*a^4*b^5*d^4*e^4*(6*B*d + 5*A*e) + 1008*a^3*b^6*d^5*e^3*(5*B*d + 6*A*e) + 270*a^2*b^7*d^6*e^2*(4*B*d + 7*A*
e) + 30*a*b^8*d^7*e*(3*B*d + 8*A*e) + b^9*d^8*(2*B*d + 9*A*e))*x^13)/13 + (15*b^2*e^2*(3*a^8*B*e^8 + 8*a^7*b*e
^7*(10*B*d + A*e) + 70*a^6*b^2*d*e^6*(9*B*d + 2*A*e) + 252*a^5*b^3*d^2*e^5*(8*B*d + 3*A*e) + 420*a^4*b^4*d^3*e
^4*(7*B*d + 4*A*e) + 336*a^3*b^5*d^4*e^3*(6*B*d + 5*A*e) + 126*a^2*b^6*d^5*e^2*(5*B*d + 6*A*e) + 20*a*b^7*d^6*
e*(4*B*d + 7*A*e) + b^8*d^7*(3*B*d + 8*A*e))*x^14)/14 + 2*b^3*e^3*(4*a^7*B*e^7 + 7*a^6*b*e^6*(10*B*d + A*e) +
42*a^5*b^2*d*e^5*(9*B*d + 2*A*e) + 105*a^4*b^3*d^2*e^4*(8*B*d + 3*A*e) + 120*a^3*b^4*d^3*e^3*(7*B*d + 4*A*e) +
63*a^2*b^5*d^4*e^2*(6*B*d + 5*A*e) + 14*a*b^6*d^5*e*(5*B*d + 6*A*e) + b^7*d^6*(4*B*d + 7*A*e))*x^15 + (3*b^4*
e^4*(35*a^6*B*e^6 + 42*a^5*b*e^5*(10*B*d + A*e) + 175*a^4*b^2*d*e^4*(9*B*d + 2*A*e) + 300*a^3*b^3*d^2*e^3*(8*B
*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(7*B*d + 4*A*e) + 70*a*b^5*d^4*e*(6*B*d + 5*A*e) + 7*b^6*d^5*(5*B*d + 6*A*e)
)*x^16)/8 + (3*b^5*e^5*(84*a^5*B*e^5 + 70*a^4*b*e^4*(10*B*d + A*e) + 200*a^3*b^2*d*e^3*(9*B*d + 2*A*e) + 225*a
^2*b^3*d^2*e^2*(8*B*d + 3*A*e) + 100*a*b^4*d^3*e*(7*B*d + 4*A*e) + 14*b^5*d^4*(6*B*d + 5*A*e))*x^17)/17 + (5*b
^6*e^6*(14*a^4*B*e^4 + 8*a^3*b*e^3*(10*B*d + A*e) + 15*a^2*b^2*d*e^2*(9*B*d + 2*A*e) + 10*a*b^3*d^2*e*(8*B*d +
3*A*e) + 2*b^4*d^3*(7*B*d + 4*A*e))*x^18)/6 + (5*b^7*e^7*(24*a^3*B*e^3 + 9*a^2*b*e^2*(10*B*d + A*e) + 10*a*b^
2*d*e*(9*B*d + 2*A*e) + 3*b^3*d^2*(8*B*d + 3*A*e))*x^19)/19 + (b^8*e^8*(9*a^2*B*e^2 + 2*a*b*e*(10*B*d + A*e) +
b^2*d*(9*B*d + 2*A*e))*x^20)/4 + (b^9*e^9*(10*b*B*d + A*b*e + 10*a*B*e)*x^21)/21 + (b^10*B*e^10*x^22)/22
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(3040\) vs.
\(2(438)=876\).
time = 0.09, size = 3041, normalized size = 6.61
| | |
method |
result |
size |
| | |
default |
\(\text {Expression too large to display}\) |
\(3041\) |
norman |
\(\text {Expression too large to display}\) |
\(3293\) |
gosper |
\(\text {Expression too large to display}\) |
\(3913\) |
risch |
\(\text {Expression too large to display}\) |
\(3913\) |
| | |
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(B*x+A)*(e*x+d)^10,x,method=_RETURNVERBOSE)
[Out]
1/22*b^10*B*e^10*x^22+1/21*((A*b^10+10*B*a*b^9)*e^10+10*b^10*B*d*e^9)*x^21+1/20*((10*A*a*b^9+45*B*a^2*b^8)*e^1
0+10*(A*b^10+10*B*a*b^9)*d*e^9+45*b^10*B*d^2*e^8)*x^20+1/19*((45*A*a^2*b^8+120*B*a^3*b^7)*e^10+10*(10*A*a*b^9+
45*B*a^2*b^8)*d*e^9+45*(A*b^10+10*B*a*b^9)*d^2*e^8+120*b^10*B*d^3*e^7)*x^19+1/18*((120*A*a^3*b^7+210*B*a^4*b^6
)*e^10+10*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^9+45*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^8+120*(A*b^10+10*B*a*b^9)*d^3*
e^7+210*b^10*B*d^4*e^6)*x^18+1/17*((210*A*a^4*b^6+252*B*a^5*b^5)*e^10+10*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^9+4
5*(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^8+120*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^7+210*(A*b^10+10*B*a*b^9)*d^4*e^6+2
52*b^10*B*d^5*e^5)*x^17+1/16*((252*A*a^5*b^5+210*B*a^6*b^4)*e^10+10*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^9+45*(12
0*A*a^3*b^7+210*B*a^4*b^6)*d^2*e^8+120*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^7+210*(10*A*a*b^9+45*B*a^2*b^8)*d^4*
e^6+252*(A*b^10+10*B*a*b^9)*d^5*e^5+210*b^10*B*d^6*e^4)*x^16+1/15*((210*A*a^6*b^4+120*B*a^7*b^3)*e^10+10*(252*
A*a^5*b^5+210*B*a^6*b^4)*d*e^9+45*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^8+120*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*
e^7+210*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*e^6+252*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e^5+210*(A*b^10+10*B*a*b^9)*d^6
*e^4+120*b^10*B*d^7*e^3)*x^15+1/14*((120*A*a^7*b^3+45*B*a^8*b^2)*e^10+10*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^9+4
5*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^8+120*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^7+210*(120*A*a^3*b^7+210*B*a^4
*b^6)*d^4*e^6+252*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e^5+210*(10*A*a*b^9+45*B*a^2*b^8)*d^6*e^4+120*(A*b^10+10*B*
a*b^9)*d^7*e^3+45*b^10*B*d^8*e^2)*x^14+1/13*((45*A*a^8*b^2+10*B*a^9*b)*e^10+10*(120*A*a^7*b^3+45*B*a^8*b^2)*d*
e^9+45*(210*A*a^6*b^4+120*B*a^7*b^3)*d^2*e^8+120*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^7+210*(210*A*a^4*b^6+252*
B*a^5*b^5)*d^4*e^6+252*(120*A*a^3*b^7+210*B*a^4*b^6)*d^5*e^5+210*(45*A*a^2*b^8+120*B*a^3*b^7)*d^6*e^4+120*(10*
A*a*b^9+45*B*a^2*b^8)*d^7*e^3+45*(A*b^10+10*B*a*b^9)*d^8*e^2+10*b^10*B*d^9*e)*x^13+1/12*((10*A*a^9*b+B*a^10)*e
^10+10*(45*A*a^8*b^2+10*B*a^9*b)*d*e^9+45*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^8+120*(210*A*a^6*b^4+120*B*a^7*b^
3)*d^3*e^7+210*(252*A*a^5*b^5+210*B*a^6*b^4)*d^4*e^6+252*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e^5+210*(120*A*a^3*
b^7+210*B*a^4*b^6)*d^6*e^4+120*(45*A*a^2*b^8+120*B*a^3*b^7)*d^7*e^3+45*(10*A*a*b^9+45*B*a^2*b^8)*d^8*e^2+10*(A
*b^10+10*B*a*b^9)*d^9*e+b^10*B*d^10)*x^12+1/11*(a^10*A*e^10+10*(10*A*a^9*b+B*a^10)*d*e^9+45*(45*A*a^8*b^2+10*B
*a^9*b)*d^2*e^8+120*(120*A*a^7*b^3+45*B*a^8*b^2)*d^3*e^7+210*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^6+252*(252*A*
a^5*b^5+210*B*a^6*b^4)*d^5*e^5+210*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^4+120*(120*A*a^3*b^7+210*B*a^4*b^6)*d^7
*e^3+45*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e^2+10*(10*A*a*b^9+45*B*a^2*b^8)*d^9*e+(A*b^10+10*B*a*b^9)*d^10)*x^11
+1/10*(10*a^10*A*d*e^9+45*(10*A*a^9*b+B*a^10)*d^2*e^8+120*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e^7+210*(120*A*a^7*b^3
+45*B*a^8*b^2)*d^4*e^6+252*(210*A*a^6*b^4+120*B*a^7*b^3)*d^5*e^5+210*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^4+120
*(210*A*a^4*b^6+252*B*a^5*b^5)*d^7*e^3+45*(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e^2+10*(45*A*a^2*b^8+120*B*a^3*b^7
)*d^9*e+(10*A*a*b^9+45*B*a^2*b^8)*d^10)*x^10+1/9*(45*a^10*A*d^2*e^8+120*(10*A*a^9*b+B*a^10)*d^3*e^7+210*(45*A*
a^8*b^2+10*B*a^9*b)*d^4*e^6+252*(120*A*a^7*b^3+45*B*a^8*b^2)*d^5*e^5+210*(210*A*a^6*b^4+120*B*a^7*b^3)*d^6*e^4
+120*(252*A*a^5*b^5+210*B*a^6*b^4)*d^7*e^3+45*(210*A*a^4*b^6+252*B*a^5*b^5)*d^8*e^2+10*(120*A*a^3*b^7+210*B*a^
4*b^6)*d^9*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^10)*x^9+1/8*(120*a^10*A*d^3*e^7+210*(10*A*a^9*b+B*a^10)*d^4*e^6+25
2*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e^5+210*(120*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^4+120*(210*A*a^6*b^4+120*B*a^7*b^3)
*d^7*e^3+45*(252*A*a^5*b^5+210*B*a^6*b^4)*d^8*e^2+10*(210*A*a^4*b^6+252*B*a^5*b^5)*d^9*e+(120*A*a^3*b^7+210*B*
a^4*b^6)*d^10)*x^8+1/7*(210*a^10*A*d^4*e^6+252*(10*A*a^9*b+B*a^10)*d^5*e^5+210*(45*A*a^8*b^2+10*B*a^9*b)*d^6*e
^4+120*(120*A*a^7*b^3+45*B*a^8*b^2)*d^7*e^3+45*(210*A*a^6*b^4+120*B*a^7*b^3)*d^8*e^2+10*(252*A*a^5*b^5+210*B*a
^6*b^4)*d^9*e+(210*A*a^4*b^6+252*B*a^5*b^5)*d^10)*x^7+1/6*(252*a^10*A*d^5*e^5+210*(10*A*a^9*b+B*a^10)*d^6*e^4+
120*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^3+45*(120*A*a^7*b^3+45*B*a^8*b^2)*d^8*e^2+10*(210*A*a^6*b^4+120*B*a^7*b^3)
*d^9*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^10)*x^6+1/5*(210*a^10*A*d^6*e^4+120*(10*A*a^9*b+B*a^10)*d^7*e^3+45*(45*
A*a^8*b^2+10*B*a^9*b)*d^8*e^2+10*(120*A*a^7*b^3+45*B*a^8*b^2)*d^9*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^10)*x^5+1/
4*(120*a^10*A*d^7*e^3+45*(10*A*a^9*b+B*a^10)*d^8*e^2+10*(45*A*a^8*b^2+10*B*a^9*b)*d^9*e+(120*A*a^7*b^3+45*B*a^
8*b^2)*d^10)*x^4+1/3*(45*a^10*A*d^8*e^2+10*(10*A*a^9*b+B*a^10)*d^9*e+(45*A*a^8*b^2+10*B*a^9*b)*d^10)*x^3+1/2*(
10*a^10*A*d^9*e+(10*A*a^9*b+B*a^10)*d^10)*x^2+a^10*A*d^10*x
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 3128 vs.
\(2 (460) = 920\).
time = 0.34, size = 3128, normalized size = 6.80 \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)^10,x, algorithm="maxima")
[Out]
1/22*B*b^10*x^22*e^10 + A*a^10*d^10*x + 1/21*(10*B*b^10*d*e^9 + 10*B*a*b^9*e^10 + A*b^10*e^10)*x^21 + 1/4*(9*B
*b^10*d^2*e^8 + 9*B*a^2*b^8*e^10 + 2*A*a*b^9*e^10 + 2*(10*B*a*b^9*e^9 + A*b^10*e^9)*d)*x^20 + 5/19*(24*B*b^10*
d^3*e^7 + 24*B*a^3*b^7*e^10 + 9*A*a^2*b^8*e^10 + 9*(10*B*a*b^9*e^8 + A*b^10*e^8)*d^2 + 10*(9*B*a^2*b^8*e^9 + 2
*A*a*b^9*e^9)*d)*x^19 + 5/6*(14*B*b^10*d^4*e^6 + 14*B*a^4*b^6*e^10 + 8*A*a^3*b^7*e^10 + 8*(10*B*a*b^9*e^7 + A*
b^10*e^7)*d^3 + 15*(9*B*a^2*b^8*e^8 + 2*A*a*b^9*e^8)*d^2 + 10*(8*B*a^3*b^7*e^9 + 3*A*a^2*b^8*e^9)*d)*x^18 + 3/
17*(84*B*b^10*d^5*e^5 + 84*B*a^5*b^5*e^10 + 70*A*a^4*b^6*e^10 + 70*(10*B*a*b^9*e^6 + A*b^10*e^6)*d^4 + 200*(9*
B*a^2*b^8*e^7 + 2*A*a*b^9*e^7)*d^3 + 225*(8*B*a^3*b^7*e^8 + 3*A*a^2*b^8*e^8)*d^2 + 100*(7*B*a^4*b^6*e^9 + 4*A*
a^3*b^7*e^9)*d)*x^17 + 3/8*(35*B*b^10*d^6*e^4 + 35*B*a^6*b^4*e^10 + 42*A*a^5*b^5*e^10 + 42*(10*B*a*b^9*e^5 + A
*b^10*e^5)*d^5 + 175*(9*B*a^2*b^8*e^6 + 2*A*a*b^9*e^6)*d^4 + 300*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d^3 + 225
*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d^2 + 70*(6*B*a^5*b^5*e^9 + 5*A*a^4*b^6*e^9)*d)*x^16 + 2*(4*B*b^10*d^7*e^
3 + 4*B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10 + 7*(10*B*a*b^9*e^4 + A*b^10*e^4)*d^6 + 42*(9*B*a^2*b^8*e^5 + 2*A*a*b^
9*e^5)*d^5 + 105*(8*B*a^3*b^7*e^6 + 3*A*a^2*b^8*e^6)*d^4 + 120*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d^3 + 63*(6
*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^2 + 14*(5*B*a^6*b^4*e^9 + 6*A*a^5*b^5*e^9)*d)*x^15 + 15/14*(3*B*b^10*d^8*e
^2 + 3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10 + 8*(10*B*a*b^9*e^3 + A*b^10*e^3)*d^7 + 70*(9*B*a^2*b^8*e^4 + 2*A*a*b
^9*e^4)*d^6 + 252*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^5 + 420*(7*B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^4 + 336*
(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d^3 + 126*(5*B*a^6*b^4*e^8 + 6*A*a^5*b^5*e^8)*d^2 + 20*(4*B*a^7*b^3*e^9 +
7*A*a^6*b^4*e^9)*d)*x^14 + 5/13*(2*B*b^10*d^9*e + 2*B*a^9*b*e^10 + 9*A*a^8*b^2*e^10 + 9*(10*B*a*b^9*e^2 + A*b^
10*e^2)*d^8 + 120*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^7 + 630*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d^6 + 1512*(
7*B*a^4*b^6*e^5 + 4*A*a^3*b^7*e^5)*d^5 + 1764*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^4 + 1008*(5*B*a^6*b^4*e^7
+ 6*A*a^5*b^5*e^7)*d^3 + 270*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^2 + 30*(3*B*a^8*b^2*e^9 + 8*A*a^7*b^3*e^9)*
d)*x^13 + 1/12*(B*b^10*d^10 + B*a^10*e^10 + 10*A*a^9*b*e^10 + 10*(10*B*a*b^9*e + A*b^10*e)*d^9 + 225*(9*B*a^2*
b^8*e^2 + 2*A*a*b^9*e^2)*d^8 + 1800*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^7 + 6300*(7*B*a^4*b^6*e^4 + 4*A*a^3*
b^7*e^4)*d^6 + 10584*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d^5 + 8820*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^4 +
3600*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^3 + 675*(3*B*a^8*b^2*e^8 + 8*A*a^7*b^3*e^8)*d^2 + 50*(2*B*a^9*b*e^9
+ 9*A*a^8*b^2*e^9)*d)*x^12 + 1/11*(A*a^10*e^10 + (10*B*a*b^9 + A*b^10)*d^10 + 50*(9*B*a^2*b^8*e + 2*A*a*b^9*e
)*d^9 + 675*(8*B*a^3*b^7*e^2 + 3*A*a^2*b^8*e^2)*d^8 + 3600*(7*B*a^4*b^6*e^3 + 4*A*a^3*b^7*e^3)*d^7 + 8820*(6*B
*a^5*b^5*e^4 + 5*A*a^4*b^6*e^4)*d^6 + 10584*(5*B*a^6*b^4*e^5 + 6*A*a^5*b^5*e^5)*d^5 + 6300*(4*B*a^7*b^3*e^6 +
7*A*a^6*b^4*e^6)*d^4 + 1800*(3*B*a^8*b^2*e^7 + 8*A*a^7*b^3*e^7)*d^3 + 225*(2*B*a^9*b*e^8 + 9*A*a^8*b^2*e^8)*d^
2 + 10*(B*a^10*e^9 + 10*A*a^9*b*e^9)*d)*x^11 + 1/2*(2*A*a^10*d*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^10 + 30*(8*B*
a^3*b^7*e + 3*A*a^2*b^8*e)*d^9 + 270*(7*B*a^4*b^6*e^2 + 4*A*a^3*b^7*e^2)*d^8 + 1008*(6*B*a^5*b^5*e^3 + 5*A*a^4
*b^6*e^3)*d^7 + 1764*(5*B*a^6*b^4*e^4 + 6*A*a^5*b^5*e^4)*d^6 + 1512*(4*B*a^7*b^3*e^5 + 7*A*a^6*b^4*e^5)*d^5 +
630*(3*B*a^8*b^2*e^6 + 8*A*a^7*b^3*e^6)*d^4 + 120*(2*B*a^9*b*e^7 + 9*A*a^8*b^2*e^7)*d^3 + 9*(B*a^10*e^8 + 10*A
*a^9*b*e^8)*d^2)*x^10 + 5/3*(3*A*a^10*d^2*e^8 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10 + 20*(7*B*a^4*b^6*e + 4*A*a^3
*b^7*e)*d^9 + 126*(6*B*a^5*b^5*e^2 + 5*A*a^4*b^6*e^2)*d^8 + 336*(5*B*a^6*b^4*e^3 + 6*A*a^5*b^5*e^3)*d^7 + 420*
(4*B*a^7*b^3*e^4 + 7*A*a^6*b^4*e^4)*d^6 + 252*(3*B*a^8*b^2*e^5 + 8*A*a^7*b^3*e^5)*d^5 + 70*(2*B*a^9*b*e^6 + 9*
A*a^8*b^2*e^6)*d^4 + 8*(B*a^10*e^7 + 10*A*a^9*b*e^7)*d^3)*x^9 + 15/4*(4*A*a^10*d^3*e^7 + (7*B*a^4*b^6 + 4*A*a^
3*b^7)*d^10 + 14*(6*B*a^5*b^5*e + 5*A*a^4*b^6*e)*d^9 + 63*(5*B*a^6*b^4*e^2 + 6*A*a^5*b^5*e^2)*d^8 + 120*(4*B*a
^7*b^3*e^3 + 7*A*a^6*b^4*e^3)*d^7 + 105*(3*B*a^8*b^2*e^4 + 8*A*a^7*b^3*e^4)*d^6 + 42*(2*B*a^9*b*e^5 + 9*A*a^8*
b^2*e^5)*d^5 + 7*(B*a^10*e^6 + 10*A*a^9*b*e^6)*d^4)*x^8 + 6/7*(35*A*a^10*d^4*e^6 + 7*(6*B*a^5*b^5 + 5*A*a^4*b^
6)*d^10 + 70*(5*B*a^6*b^4*e + 6*A*a^5*b^5*e)*d^9 + 225*(4*B*a^7*b^3*e^2 + 7*A*a^6*b^4*e^2)*d^8 + 300*(3*B*a^8*
b^2*e^3 + 8*A*a^7*b^3*e^3)*d^7 + 175*(2*B*a^9*b*e^4 + 9*A*a^8*b^2*e^4)*d^6 + 42*(B*a^10*e^5 + 10*A*a^9*b*e^5)*
d^5)*x^7 + 1/2*(84*A*a^10*d^5*e^5 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^10 + 100*(4*B*a^7*b^3*e + 7*A*a^6*b^4*e)*
d^9 + 225*(3*B*a^8*b^2*e^2 + 8*A*a^7*b^3*e^2)*d^8 + 200*(2*B*a^9*b*e^3 + 9*A*a^8*b^2*e^3)*d^7 + 70*(B*a^10*e^4
+ 10*A*a^9*b*e^4)*d^6)*x^6 + 3*(14*A*a^10*d^6*e^4 + 2*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^10 + 10*(3*B*a^8*b^2*e +
8*A*a^7*b^3*e)*d^9 + 15*(2*B*a^9*b*e^2 + 9*A*a^8*b^2*e^2)*d^8 + 8*(B*a^10*e^3 + 10*A*a^9*b*e^3)*d^7)*x^5 + 5/4
*(24*A*a^10*d^7*e^3 + 3*(3*B*a^8*b^2 + 8*A*a^7*...
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 3046 vs.
\(2 (460) = 920\).
time = 0.64, size = 3046, normalized size = 6.62 \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)^10,x, algorithm="fricas")
[Out]
1/12*B*b^10*d^10*x^12 + A*a^10*d^10*x + 1/11*(10*B*a*b^9 + A*b^10)*d^10*x^11 + 1/2*(9*B*a^2*b^8 + 2*A*a*b^9)*d
^10*x^10 + 5/3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^10*x^9 + 15/4*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^10*x^8 + 6*(6*B*a^5*b
^5 + 5*A*a^4*b^6)*d^10*x^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^10*x^6 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^10*x^5 +
15/4*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^10*x^4 + 5/3*(2*B*a^9*b + 9*A*a^8*b^2)*d^10*x^3 + 1/2*(B*a^10 + 10*A*a^9*b
)*d^10*x^2 + 1/7759752*(352716*B*b^10*x^22 + 705432*A*a^10*x^11 + 369512*(10*B*a*b^9 + A*b^10)*x^21 + 1939938*
(9*B*a^2*b^8 + 2*A*a*b^9)*x^20 + 6126120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^19 + 12932920*(7*B*a^4*b^6 + 4*A*a^3*b^
7)*x^18 + 19171152*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^17 + 20369349*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^16 + 15519504*(4*
B*a^7*b^3 + 7*A*a^6*b^4)*x^15 + 8314020*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^14 + 2984520*(2*B*a^9*b + 9*A*a^8*b^2)*x
^13 + 646646*(B*a^10 + 10*A*a^9*b)*x^12)*e^10 + 1/3879876*(1847560*B*b^10*d*x^21 + 3879876*A*a^10*d*x^10 + 193
9938*(10*B*a*b^9 + A*b^10)*d*x^20 + 10210200*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^19 + 32332300*(8*B*a^3*b^7 + 3*A*a^
2*b^8)*d*x^18 + 68468400*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*x^17 + 101846745*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^16 + 1
08636528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^15 + 83140200*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*x^14 + 44767800*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d*x^13 + 16166150*(2*B*a^9*b + 9*A*a^8*b^2)*d*x^12 + 3527160*(B*a^10 + 10*A*a^9*b)*d*x^11)*
e^9 + 1/369512*(831402*B*b^10*d^2*x^20 + 1847560*A*a^10*d^2*x^9 + 875160*(10*B*a*b^9 + A*b^10)*d^2*x^19 + 4618
900*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^18 + 14671800*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^17 + 31177575*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^2*x^16 + 46558512*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*x^15 + 49884120*(5*B*a^6*b^4 + 6*A*a^5*b^5
)*d^2*x^14 + 38372400*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x^13 + 20785050*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x^12 + 7
558200*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*x^11 + 1662804*(B*a^10 + 10*A*a^9*b)*d^2*x^10)*e^8 + 5/277134*(350064*B*b
^10*d^3*x^19 + 831402*A*a^10*d^3*x^8 + 369512*(10*B*a*b^9 + A*b^10)*d^3*x^18 + 1956240*(9*B*a^2*b^8 + 2*A*a*b^
9)*d^3*x^17 + 6235515*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x^16 + 13302432*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*x^15 + 1
9953648*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^14 + 21488544*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^13 + 16628040*(4*B*a
^7*b^3 + 7*A*a^6*b^4)*d^3*x^12 + 9069840*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*x^11 + 3325608*(2*B*a^9*b + 9*A*a^8*b
^2)*d^3*x^10 + 739024*(B*a^10 + 10*A*a^9*b)*d^3*x^9)*e^7 + 5/58344*(136136*B*b^10*d^4*x^18 + 350064*A*a^10*d^4
*x^7 + 144144*(10*B*a*b^9 + A*b^10)*d^4*x^17 + 765765*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^16 + 2450448*(8*B*a^3*b^
7 + 3*A*a^2*b^8)*d^4*x^15 + 5250960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^14 + 7916832*(6*B*a^5*b^5 + 5*A*a^4*b^6)
*d^4*x^13 + 8576568*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x^12 + 6683040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*x^11 + 3675
672*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*x^10 + 1361360*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*x^9 + 306306*(B*a^10 + 10*A*a
^9*b)*d^4*x^8)*e^6 + 3/9724*(48048*B*b^10*d^5*x^17 + 136136*A*a^10*d^5*x^6 + 51051*(10*B*a*b^9 + A*b^10)*d^5*x
^16 + 272272*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^15 + 875160*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^14 + 1884960*(7*B*a
^4*b^6 + 4*A*a^3*b^7)*d^5*x^13 + 2858856*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x^12 + 3118752*(5*B*a^6*b^4 + 6*A*a^5
*b^5)*d^5*x^11 + 2450448*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^5*x^10 + 1361360*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*x^9 +
510510*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*x^8 + 116688*(B*a^10 + 10*A*a^9*b)*d^5*x^7)*e^5 + 1/1144*(15015*B*b^10*d^
6*x^16 + 48048*A*a^10*d^6*x^5 + 16016*(10*B*a*b^9 + A*b^10)*d^6*x^15 + 85800*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^1
4 + 277200*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^13 + 600600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x^12 + 917280*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*d^6*x^11 + 1009008*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*x^10 + 800800*(4*B*a^7*b^3 + 7*A*a^6*b
^4)*d^6*x^9 + 450450*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*x^8 + 171600*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*x^7 + 40040*(B
*a^10 + 10*A*a^9*b)*d^6*x^6)*e^4 + 2/1001*(4004*B*b^10*d^7*x^15 + 15015*A*a^10*d^7*x^4 + 4290*(10*B*a*b^9 + A*
b^10)*d^7*x^14 + 23100*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^13 + 75075*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x^12 + 16380
0*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*x^11 + 252252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*x^10 + 280280*(5*B*a^6*b^4 + 6
*A*a^5*b^5)*d^7*x^9 + 225225*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^7*x^8 + 128700*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^7*x^7
+ 50050*(2*B*a^9*b + 9*A*a^8*b^2)*d^7*x^6 + 12012*(B*a^10 + 10*A*a^9*b)*d^7*x^5)*e^3 + 15/4004*(858*B*b^10*d^8
*x^14 + 4004*A*a^10*d^8*x^3 + 924*(10*B*a*b^9 + A*b^10)*d^8*x^13 + 5005*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x^12 + 1
6380*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*x^11 + 36036*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*x^10 + 56056*(6*B*a^5*b^5 +
5*A*a^4*b^6)*d^8*x^9 + 63063*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*x^8 + 51480*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*x^7 +
30030*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^8*x^6 + 12012*(2*B*a^9*b + 9*A*a^8*b^2)*d^8*x^5 + 3003*(B*a^10 + 10*A*a^9
*b)*d^8*x^4)*e^2 + 5/858*(132*B*b^10*d^9*x^13 +...
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 3936 vs.
\(2 (478) = 956\).
time = 0.29, size = 3936, normalized size = 8.56 \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)**10,x)
[Out]
A*a**10*d**10*x + B*b**10*e**10*x**22/22 + x**21*(A*b**10*e**10/21 + 10*B*a*b**9*e**10/21 + 10*B*b**10*d*e**9/
21) + x**20*(A*a*b**9*e**10/2 + A*b**10*d*e**9/2 + 9*B*a**2*b**8*e**10/4 + 5*B*a*b**9*d*e**9 + 9*B*b**10*d**2*
e**8/4) + x**19*(45*A*a**2*b**8*e**10/19 + 100*A*a*b**9*d*e**9/19 + 45*A*b**10*d**2*e**8/19 + 120*B*a**3*b**7*
e**10/19 + 450*B*a**2*b**8*d*e**9/19 + 450*B*a*b**9*d**2*e**8/19 + 120*B*b**10*d**3*e**7/19) + x**18*(20*A*a**
3*b**7*e**10/3 + 25*A*a**2*b**8*d*e**9 + 25*A*a*b**9*d**2*e**8 + 20*A*b**10*d**3*e**7/3 + 35*B*a**4*b**6*e**10
/3 + 200*B*a**3*b**7*d*e**9/3 + 225*B*a**2*b**8*d**2*e**8/2 + 200*B*a*b**9*d**3*e**7/3 + 35*B*b**10*d**4*e**6/
3) + x**17*(210*A*a**4*b**6*e**10/17 + 1200*A*a**3*b**7*d*e**9/17 + 2025*A*a**2*b**8*d**2*e**8/17 + 1200*A*a*b
**9*d**3*e**7/17 + 210*A*b**10*d**4*e**6/17 + 252*B*a**5*b**5*e**10/17 + 2100*B*a**4*b**6*d*e**9/17 + 5400*B*a
**3*b**7*d**2*e**8/17 + 5400*B*a**2*b**8*d**3*e**7/17 + 2100*B*a*b**9*d**4*e**6/17 + 252*B*b**10*d**5*e**5/17)
+ x**16*(63*A*a**5*b**5*e**10/4 + 525*A*a**4*b**6*d*e**9/4 + 675*A*a**3*b**7*d**2*e**8/2 + 675*A*a**2*b**8*d*
*3*e**7/2 + 525*A*a*b**9*d**4*e**6/4 + 63*A*b**10*d**5*e**5/4 + 105*B*a**6*b**4*e**10/8 + 315*B*a**5*b**5*d*e*
*9/2 + 4725*B*a**4*b**6*d**2*e**8/8 + 900*B*a**3*b**7*d**3*e**7 + 4725*B*a**2*b**8*d**4*e**6/8 + 315*B*a*b**9*
d**5*e**5/2 + 105*B*b**10*d**6*e**4/8) + x**15*(14*A*a**6*b**4*e**10 + 168*A*a**5*b**5*d*e**9 + 630*A*a**4*b**
6*d**2*e**8 + 960*A*a**3*b**7*d**3*e**7 + 630*A*a**2*b**8*d**4*e**6 + 168*A*a*b**9*d**5*e**5 + 14*A*b**10*d**6
*e**4 + 8*B*a**7*b**3*e**10 + 140*B*a**6*b**4*d*e**9 + 756*B*a**5*b**5*d**2*e**8 + 1680*B*a**4*b**6*d**3*e**7
+ 1680*B*a**3*b**7*d**4*e**6 + 756*B*a**2*b**8*d**5*e**5 + 140*B*a*b**9*d**6*e**4 + 8*B*b**10*d**7*e**3) + x**
14*(60*A*a**7*b**3*e**10/7 + 150*A*a**6*b**4*d*e**9 + 810*A*a**5*b**5*d**2*e**8 + 1800*A*a**4*b**6*d**3*e**7 +
1800*A*a**3*b**7*d**4*e**6 + 810*A*a**2*b**8*d**5*e**5 + 150*A*a*b**9*d**6*e**4 + 60*A*b**10*d**7*e**3/7 + 45
*B*a**8*b**2*e**10/14 + 600*B*a**7*b**3*d*e**9/7 + 675*B*a**6*b**4*d**2*e**8 + 2160*B*a**5*b**5*d**3*e**7 + 31
50*B*a**4*b**6*d**4*e**6 + 2160*B*a**3*b**7*d**5*e**5 + 675*B*a**2*b**8*d**6*e**4 + 600*B*a*b**9*d**7*e**3/7 +
45*B*b**10*d**8*e**2/14) + x**13*(45*A*a**8*b**2*e**10/13 + 1200*A*a**7*b**3*d*e**9/13 + 9450*A*a**6*b**4*d**
2*e**8/13 + 30240*A*a**5*b**5*d**3*e**7/13 + 44100*A*a**4*b**6*d**4*e**6/13 + 30240*A*a**3*b**7*d**5*e**5/13 +
9450*A*a**2*b**8*d**6*e**4/13 + 1200*A*a*b**9*d**7*e**3/13 + 45*A*b**10*d**8*e**2/13 + 10*B*a**9*b*e**10/13 +
450*B*a**8*b**2*d*e**9/13 + 5400*B*a**7*b**3*d**2*e**8/13 + 25200*B*a**6*b**4*d**3*e**7/13 + 52920*B*a**5*b**
5*d**4*e**6/13 + 52920*B*a**4*b**6*d**5*e**5/13 + 25200*B*a**3*b**7*d**6*e**4/13 + 5400*B*a**2*b**8*d**7*e**3/
13 + 450*B*a*b**9*d**8*e**2/13 + 10*B*b**10*d**9*e/13) + x**12*(5*A*a**9*b*e**10/6 + 75*A*a**8*b**2*d*e**9/2 +
450*A*a**7*b**3*d**2*e**8 + 2100*A*a**6*b**4*d**3*e**7 + 4410*A*a**5*b**5*d**4*e**6 + 4410*A*a**4*b**6*d**5*e
**5 + 2100*A*a**3*b**7*d**6*e**4 + 450*A*a**2*b**8*d**7*e**3 + 75*A*a*b**9*d**8*e**2/2 + 5*A*b**10*d**9*e/6 +
B*a**10*e**10/12 + 25*B*a**9*b*d*e**9/3 + 675*B*a**8*b**2*d**2*e**8/4 + 1200*B*a**7*b**3*d**3*e**7 + 3675*B*a*
*6*b**4*d**4*e**6 + 5292*B*a**5*b**5*d**5*e**5 + 3675*B*a**4*b**6*d**6*e**4 + 1200*B*a**3*b**7*d**7*e**3 + 675
*B*a**2*b**8*d**8*e**2/4 + 25*B*a*b**9*d**9*e/3 + B*b**10*d**10/12) + x**11*(A*a**10*e**10/11 + 100*A*a**9*b*d
*e**9/11 + 2025*A*a**8*b**2*d**2*e**8/11 + 14400*A*a**7*b**3*d**3*e**7/11 + 44100*A*a**6*b**4*d**4*e**6/11 + 6
3504*A*a**5*b**5*d**5*e**5/11 + 44100*A*a**4*b**6*d**6*e**4/11 + 14400*A*a**3*b**7*d**7*e**3/11 + 2025*A*a**2*
b**8*d**8*e**2/11 + 100*A*a*b**9*d**9*e/11 + A*b**10*d**10/11 + 10*B*a**10*d*e**9/11 + 450*B*a**9*b*d**2*e**8/
11 + 5400*B*a**8*b**2*d**3*e**7/11 + 25200*B*a**7*b**3*d**4*e**6/11 + 52920*B*a**6*b**4*d**5*e**5/11 + 52920*B
*a**5*b**5*d**6*e**4/11 + 25200*B*a**4*b**6*d**7*e**3/11 + 5400*B*a**3*b**7*d**8*e**2/11 + 450*B*a**2*b**8*d**
9*e/11 + 10*B*a*b**9*d**10/11) + x**10*(A*a**10*d*e**9 + 45*A*a**9*b*d**2*e**8 + 540*A*a**8*b**2*d**3*e**7 + 2
520*A*a**7*b**3*d**4*e**6 + 5292*A*a**6*b**4*d**5*e**5 + 5292*A*a**5*b**5*d**6*e**4 + 2520*A*a**4*b**6*d**7*e*
*3 + 540*A*a**3*b**7*d**8*e**2 + 45*A*a**2*b**8*d**9*e + A*a*b**9*d**10 + 9*B*a**10*d**2*e**8/2 + 120*B*a**9*b
*d**3*e**7 + 945*B*a**8*b**2*d**4*e**6 + 3024*B*a**7*b**3*d**5*e**5 + 4410*B*a**6*b**4*d**6*e**4 + 3024*B*a**5
*b**5*d**7*e**3 + 945*B*a**4*b**6*d**8*e**2 + 120*B*a**3*b**7*d**9*e + 9*B*a**2*b**8*d**10/2) + x**9*(5*A*a**1
0*d**2*e**8 + 400*A*a**9*b*d**3*e**7/3 + 1050*A*a**8*b**2*d**4*e**6 + 3360*A*a**7*b**3*d**5*e**5 + 4900*A*a**6
*b**4*d**6*e**4 + 3360*A*a**5*b**5*d**7*e**3 + 1050*A*a**4*b**6*d**8*e**2 + 400*A*a**3*b**7*d**9*e/3 + 5*A*a**
2*b**8*d**10 + 40*B*a**10*d**3*e**7/3 + 700*B*a**9*b*d**4*e**6/3 + 1260*B*a**8*b**2*d**5*e**5 + 2800*B*a**7*b*
*3*d**6*e**4 + 2800*B*a**6*b**4*d**7*e**3 + 1260*B*a**5*b**5*d**8*e**2 + 700*B*a**4*b**6*d**9*e/3 + 40*B*a**3*
b**7*d**10/3) + x**8*(15*A*a**10*d**3*e**7 + 52...
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 3736 vs.
\(2 (460) = 920\).
time = 1.23, size = 3736, normalized size = 8.12 \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)^10,x, algorithm="giac")
[Out]
1/22*B*b^10*x^22*e^10 + 10/21*B*b^10*d*x^21*e^9 + 9/4*B*b^10*d^2*x^20*e^8 + 120/19*B*b^10*d^3*x^19*e^7 + 35/3*
B*b^10*d^4*x^18*e^6 + 252/17*B*b^10*d^5*x^17*e^5 + 105/8*B*b^10*d^6*x^16*e^4 + 8*B*b^10*d^7*x^15*e^3 + 45/14*B
*b^10*d^8*x^14*e^2 + 10/13*B*b^10*d^9*x^13*e + 1/12*B*b^10*d^10*x^12 + 10/21*B*a*b^9*x^21*e^10 + 1/21*A*b^10*x
^21*e^10 + 5*B*a*b^9*d*x^20*e^9 + 1/2*A*b^10*d*x^20*e^9 + 450/19*B*a*b^9*d^2*x^19*e^8 + 45/19*A*b^10*d^2*x^19*
e^8 + 200/3*B*a*b^9*d^3*x^18*e^7 + 20/3*A*b^10*d^3*x^18*e^7 + 2100/17*B*a*b^9*d^4*x^17*e^6 + 210/17*A*b^10*d^4
*x^17*e^6 + 315/2*B*a*b^9*d^5*x^16*e^5 + 63/4*A*b^10*d^5*x^16*e^5 + 140*B*a*b^9*d^6*x^15*e^4 + 14*A*b^10*d^6*x
^15*e^4 + 600/7*B*a*b^9*d^7*x^14*e^3 + 60/7*A*b^10*d^7*x^14*e^3 + 450/13*B*a*b^9*d^8*x^13*e^2 + 45/13*A*b^10*d
^8*x^13*e^2 + 25/3*B*a*b^9*d^9*x^12*e + 5/6*A*b^10*d^9*x^12*e + 10/11*B*a*b^9*d^10*x^11 + 1/11*A*b^10*d^10*x^1
1 + 9/4*B*a^2*b^8*x^20*e^10 + 1/2*A*a*b^9*x^20*e^10 + 450/19*B*a^2*b^8*d*x^19*e^9 + 100/19*A*a*b^9*d*x^19*e^9
+ 225/2*B*a^2*b^8*d^2*x^18*e^8 + 25*A*a*b^9*d^2*x^18*e^8 + 5400/17*B*a^2*b^8*d^3*x^17*e^7 + 1200/17*A*a*b^9*d^
3*x^17*e^7 + 4725/8*B*a^2*b^8*d^4*x^16*e^6 + 525/4*A*a*b^9*d^4*x^16*e^6 + 756*B*a^2*b^8*d^5*x^15*e^5 + 168*A*a
*b^9*d^5*x^15*e^5 + 675*B*a^2*b^8*d^6*x^14*e^4 + 150*A*a*b^9*d^6*x^14*e^4 + 5400/13*B*a^2*b^8*d^7*x^13*e^3 + 1
200/13*A*a*b^9*d^7*x^13*e^3 + 675/4*B*a^2*b^8*d^8*x^12*e^2 + 75/2*A*a*b^9*d^8*x^12*e^2 + 450/11*B*a^2*b^8*d^9*
x^11*e + 100/11*A*a*b^9*d^9*x^11*e + 9/2*B*a^2*b^8*d^10*x^10 + A*a*b^9*d^10*x^10 + 120/19*B*a^3*b^7*x^19*e^10
+ 45/19*A*a^2*b^8*x^19*e^10 + 200/3*B*a^3*b^7*d*x^18*e^9 + 25*A*a^2*b^8*d*x^18*e^9 + 5400/17*B*a^3*b^7*d^2*x^1
7*e^8 + 2025/17*A*a^2*b^8*d^2*x^17*e^8 + 900*B*a^3*b^7*d^3*x^16*e^7 + 675/2*A*a^2*b^8*d^3*x^16*e^7 + 1680*B*a^
3*b^7*d^4*x^15*e^6 + 630*A*a^2*b^8*d^4*x^15*e^6 + 2160*B*a^3*b^7*d^5*x^14*e^5 + 810*A*a^2*b^8*d^5*x^14*e^5 + 2
5200/13*B*a^3*b^7*d^6*x^13*e^4 + 9450/13*A*a^2*b^8*d^6*x^13*e^4 + 1200*B*a^3*b^7*d^7*x^12*e^3 + 450*A*a^2*b^8*
d^7*x^12*e^3 + 5400/11*B*a^3*b^7*d^8*x^11*e^2 + 2025/11*A*a^2*b^8*d^8*x^11*e^2 + 120*B*a^3*b^7*d^9*x^10*e + 45
*A*a^2*b^8*d^9*x^10*e + 40/3*B*a^3*b^7*d^10*x^9 + 5*A*a^2*b^8*d^10*x^9 + 35/3*B*a^4*b^6*x^18*e^10 + 20/3*A*a^3
*b^7*x^18*e^10 + 2100/17*B*a^4*b^6*d*x^17*e^9 + 1200/17*A*a^3*b^7*d*x^17*e^9 + 4725/8*B*a^4*b^6*d^2*x^16*e^8 +
675/2*A*a^3*b^7*d^2*x^16*e^8 + 1680*B*a^4*b^6*d^3*x^15*e^7 + 960*A*a^3*b^7*d^3*x^15*e^7 + 3150*B*a^4*b^6*d^4*
x^14*e^6 + 1800*A*a^3*b^7*d^4*x^14*e^6 + 52920/13*B*a^4*b^6*d^5*x^13*e^5 + 30240/13*A*a^3*b^7*d^5*x^13*e^5 + 3
675*B*a^4*b^6*d^6*x^12*e^4 + 2100*A*a^3*b^7*d^6*x^12*e^4 + 25200/11*B*a^4*b^6*d^7*x^11*e^3 + 14400/11*A*a^3*b^
7*d^7*x^11*e^3 + 945*B*a^4*b^6*d^8*x^10*e^2 + 540*A*a^3*b^7*d^8*x^10*e^2 + 700/3*B*a^4*b^6*d^9*x^9*e + 400/3*A
*a^3*b^7*d^9*x^9*e + 105/4*B*a^4*b^6*d^10*x^8 + 15*A*a^3*b^7*d^10*x^8 + 252/17*B*a^5*b^5*x^17*e^10 + 210/17*A*
a^4*b^6*x^17*e^10 + 315/2*B*a^5*b^5*d*x^16*e^9 + 525/4*A*a^4*b^6*d*x^16*e^9 + 756*B*a^5*b^5*d^2*x^15*e^8 + 630
*A*a^4*b^6*d^2*x^15*e^8 + 2160*B*a^5*b^5*d^3*x^14*e^7 + 1800*A*a^4*b^6*d^3*x^14*e^7 + 52920/13*B*a^5*b^5*d^4*x
^13*e^6 + 44100/13*A*a^4*b^6*d^4*x^13*e^6 + 5292*B*a^5*b^5*d^5*x^12*e^5 + 4410*A*a^4*b^6*d^5*x^12*e^5 + 52920/
11*B*a^5*b^5*d^6*x^11*e^4 + 44100/11*A*a^4*b^6*d^6*x^11*e^4 + 3024*B*a^5*b^5*d^7*x^10*e^3 + 2520*A*a^4*b^6*d^7
*x^10*e^3 + 1260*B*a^5*b^5*d^8*x^9*e^2 + 1050*A*a^4*b^6*d^8*x^9*e^2 + 315*B*a^5*b^5*d^9*x^8*e + 525/2*A*a^4*b^
6*d^9*x^8*e + 36*B*a^5*b^5*d^10*x^7 + 30*A*a^4*b^6*d^10*x^7 + 105/8*B*a^6*b^4*x^16*e^10 + 63/4*A*a^5*b^5*x^16*
e^10 + 140*B*a^6*b^4*d*x^15*e^9 + 168*A*a^5*b^5*d*x^15*e^9 + 675*B*a^6*b^4*d^2*x^14*e^8 + 810*A*a^5*b^5*d^2*x^
14*e^8 + 25200/13*B*a^6*b^4*d^3*x^13*e^7 + 30240/13*A*a^5*b^5*d^3*x^13*e^7 + 3675*B*a^6*b^4*d^4*x^12*e^6 + 441
0*A*a^5*b^5*d^4*x^12*e^6 + 52920/11*B*a^6*b^4*d^5*x^11*e^5 + 63504/11*A*a^5*b^5*d^5*x^11*e^5 + 4410*B*a^6*b^4*
d^6*x^10*e^4 + 5292*A*a^5*b^5*d^6*x^10*e^4 + 2800*B*a^6*b^4*d^7*x^9*e^3 + 3360*A*a^5*b^5*d^7*x^9*e^3 + 4725/4*
B*a^6*b^4*d^8*x^8*e^2 + 2835/2*A*a^5*b^5*d^8*x^8*e^2 + 300*B*a^6*b^4*d^9*x^7*e + 360*A*a^5*b^5*d^9*x^7*e + 35*
B*a^6*b^4*d^10*x^6 + 42*A*a^5*b^5*d^10*x^6 + 8*B*a^7*b^3*x^15*e^10 + 14*A*a^6*b^4*x^15*e^10 + 600/7*B*a^7*b^3*
d*x^14*e^9 + 150*A*a^6*b^4*d*x^14*e^9 + 5400/13*B*a^7*b^3*d^2*x^13*e^8 + 9450/13*A*a^6*b^4*d^2*x^13*e^8 + 1200
*B*a^7*b^3*d^3*x^12*e^7 + 2100*A*a^6*b^4*d^3*x^12*e^7 + 25200/11*B*a^7*b^3*d^4*x^11*e^6 + 44100/11*A*a^6*b^4*d
^4*x^11*e^6 + 3024*B*a^7*b^3*d^5*x^10*e^5 + 5292*A*a^6*b^4*d^5*x^10*e^5 + 2800*B*a^7*b^3*d^6*x^9*e^4 + 4900*A*
a^6*b^4*d^6*x^9*e^4 + 1800*B*a^7*b^3*d^7*x^8*e^3 + 3150*A*a^6*b^4*d^7*x^8*e^3 + 5400/7*B*a^7*b^3*d^8*x^7*e^2 +
1350*A*a^6*b^4*d^8*x^7*e^2 + 200*B*a^7*b^3*d^9*x^6*e + 350*A*a^6*b^4*d^9*x^6*e + 24*B*a^7*b^3*d^10*x^5 + 42*A
*a^6*b^4*d^10*x^5 + 45/14*B*a^8*b^2*x^14*e^10 + 60/7*A*a^7*b^3*x^14*e^10 + 450/13*B*a^8*b^2*d*x^13*e^9 + 1200/
13*A*a^7*b^3*d*x^13*e^9 + 675/4*B*a^8*b^2*d^2*x^12*e^8 + 450*A*a^7*b^3*d^2*x^12*e^8 + 5400/11*B*a^8*b^2*d^3*x^
11*e^7 + 14400/11*A*a^7*b^3*d^3*x^11*e^7 + 945*...
________________________________________________________________________________________
Mupad [B]
time = 2.18, size = 2500, normalized size = 5.43 \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)^10,x)
[Out]
x^11*((A*a^10*e^10)/11 + (A*b^10*d^10)/11 + (10*B*a*b^9*d^10)/11 + (10*B*a^10*d*e^9)/11 + (450*B*a^2*b^8*d^9*e
)/11 + (450*B*a^9*b*d^2*e^8)/11 + (2025*A*a^2*b^8*d^8*e^2)/11 + (14400*A*a^3*b^7*d^7*e^3)/11 + (44100*A*a^4*b^
6*d^6*e^4)/11 + (63504*A*a^5*b^5*d^5*e^5)/11 + (44100*A*a^6*b^4*d^4*e^6)/11 + (14400*A*a^7*b^3*d^3*e^7)/11 + (
2025*A*a^8*b^2*d^2*e^8)/11 + (5400*B*a^3*b^7*d^8*e^2)/11 + (25200*B*a^4*b^6*d^7*e^3)/11 + (52920*B*a^5*b^5*d^6
*e^4)/11 + (52920*B*a^6*b^4*d^5*e^5)/11 + (25200*B*a^7*b^3*d^4*e^6)/11 + (5400*B*a^8*b^2*d^3*e^7)/11 + (100*A*
a*b^9*d^9*e)/11 + (100*A*a^9*b*d*e^9)/11) + x^5*(42*A*a^6*b^4*d^10 + 24*B*a^7*b^3*d^10 + 42*A*a^10*d^6*e^4 + 2
4*B*a^10*d^7*e^3 + 240*A*a^7*b^3*d^9*e + 240*A*a^9*b*d^7*e^3 + 90*B*a^8*b^2*d^9*e + 90*B*a^9*b*d^8*e^2 + 405*A
*a^8*b^2*d^8*e^2) + x^8*(15*A*a^3*b^7*d^10 + (105*B*a^4*b^6*d^10)/4 + 15*A*a^10*d^3*e^7 + (105*B*a^10*d^4*e^6)
/4 + (525*A*a^4*b^6*d^9*e)/2 + (525*A*a^9*b*d^4*e^6)/2 + 315*B*a^5*b^5*d^9*e + 315*B*a^9*b*d^5*e^5 + (2835*A*a
^5*b^5*d^8*e^2)/2 + 3150*A*a^6*b^4*d^7*e^3 + 3150*A*a^7*b^3*d^6*e^4 + (2835*A*a^8*b^2*d^5*e^5)/2 + (4725*B*a^6
*b^4*d^8*e^2)/4 + 1800*B*a^7*b^3*d^7*e^3 + (4725*B*a^8*b^2*d^6*e^4)/4) + x^12*((B*a^10*e^10)/12 + (B*b^10*d^10
)/12 + (5*A*a^9*b*e^10)/6 + (5*A*b^10*d^9*e)/6 + (75*A*a*b^9*d^8*e^2)/2 + (75*A*a^8*b^2*d*e^9)/2 + 450*A*a^2*b
^8*d^7*e^3 + 2100*A*a^3*b^7*d^6*e^4 + 4410*A*a^4*b^6*d^5*e^5 + 4410*A*a^5*b^5*d^4*e^6 + 2100*A*a^6*b^4*d^3*e^7
+ 450*A*a^7*b^3*d^2*e^8 + (675*B*a^2*b^8*d^8*e^2)/4 + 1200*B*a^3*b^7*d^7*e^3 + 3675*B*a^4*b^6*d^6*e^4 + 5292*
B*a^5*b^5*d^5*e^5 + 3675*B*a^6*b^4*d^4*e^6 + 1200*B*a^7*b^3*d^3*e^7 + (675*B*a^8*b^2*d^2*e^8)/4 + (25*B*a*b^9*
d^9*e)/3 + (25*B*a^9*b*d*e^9)/3) + x^18*((20*A*a^3*b^7*e^10)/3 + (35*B*a^4*b^6*e^10)/3 + (20*A*b^10*d^3*e^7)/3
+ (35*B*b^10*d^4*e^6)/3 + 25*A*a*b^9*d^2*e^8 + 25*A*a^2*b^8*d*e^9 + (200*B*a*b^9*d^3*e^7)/3 + (200*B*a^3*b^7*
d*e^9)/3 + (225*B*a^2*b^8*d^2*e^8)/2) + x^15*(14*A*a^6*b^4*e^10 + 8*B*a^7*b^3*e^10 + 14*A*b^10*d^6*e^4 + 8*B*b
^10*d^7*e^3 + 168*A*a*b^9*d^5*e^5 + 168*A*a^5*b^5*d*e^9 + 140*B*a*b^9*d^6*e^4 + 140*B*a^6*b^4*d*e^9 + 630*A*a^
2*b^8*d^4*e^6 + 960*A*a^3*b^7*d^3*e^7 + 630*A*a^4*b^6*d^2*e^8 + 756*B*a^2*b^8*d^5*e^5 + 1680*B*a^3*b^7*d^4*e^6
+ 1680*B*a^4*b^6*d^3*e^7 + 756*B*a^5*b^5*d^2*e^8) + x^6*(42*A*a^5*b^5*d^10 + 35*B*a^6*b^4*d^10 + 42*A*a^10*d^
5*e^5 + 35*B*a^10*d^6*e^4 + 350*A*a^6*b^4*d^9*e + 350*A*a^9*b*d^6*e^4 + 200*B*a^7*b^3*d^9*e + 200*B*a^9*b*d^7*
e^3 + 900*A*a^7*b^3*d^8*e^2 + 900*A*a^8*b^2*d^7*e^3 + (675*B*a^8*b^2*d^8*e^2)/2) + x^9*(5*A*a^2*b^8*d^10 + (40
*B*a^3*b^7*d^10)/3 + 5*A*a^10*d^2*e^8 + (40*B*a^10*d^3*e^7)/3 + (400*A*a^3*b^7*d^9*e)/3 + (400*A*a^9*b*d^3*e^7
)/3 + (700*B*a^4*b^6*d^9*e)/3 + (700*B*a^9*b*d^4*e^6)/3 + 1050*A*a^4*b^6*d^8*e^2 + 3360*A*a^5*b^5*d^7*e^3 + 49
00*A*a^6*b^4*d^6*e^4 + 3360*A*a^7*b^3*d^5*e^5 + 1050*A*a^8*b^2*d^4*e^6 + 1260*B*a^5*b^5*d^8*e^2 + 2800*B*a^6*b
^4*d^7*e^3 + 2800*B*a^7*b^3*d^6*e^4 + 1260*B*a^8*b^2*d^5*e^5) + x^17*((210*A*a^4*b^6*e^10)/17 + (252*B*a^5*b^5
*e^10)/17 + (210*A*b^10*d^4*e^6)/17 + (252*B*b^10*d^5*e^5)/17 + (1200*A*a*b^9*d^3*e^7)/17 + (1200*A*a^3*b^7*d*
e^9)/17 + (2100*B*a*b^9*d^4*e^6)/17 + (2100*B*a^4*b^6*d*e^9)/17 + (2025*A*a^2*b^8*d^2*e^8)/17 + (5400*B*a^2*b^
8*d^3*e^7)/17 + (5400*B*a^3*b^7*d^2*e^8)/17) + x^14*((60*A*a^7*b^3*e^10)/7 + (45*B*a^8*b^2*e^10)/14 + (60*A*b^
10*d^7*e^3)/7 + (45*B*b^10*d^8*e^2)/14 + 150*A*a*b^9*d^6*e^4 + 150*A*a^6*b^4*d*e^9 + (600*B*a*b^9*d^7*e^3)/7 +
(600*B*a^7*b^3*d*e^9)/7 + 810*A*a^2*b^8*d^5*e^5 + 1800*A*a^3*b^7*d^4*e^6 + 1800*A*a^4*b^6*d^3*e^7 + 810*A*a^5
*b^5*d^2*e^8 + 675*B*a^2*b^8*d^6*e^4 + 2160*B*a^3*b^7*d^5*e^5 + 3150*B*a^4*b^6*d^4*e^6 + 2160*B*a^5*b^5*d^3*e^
7 + 675*B*a^6*b^4*d^2*e^8) + x^4*(30*A*a^7*b^3*d^10 + (45*B*a^8*b^2*d^10)/4 + 30*A*a^10*d^7*e^3 + (45*B*a^10*d
^8*e^2)/4 + (225*A*a^8*b^2*d^9*e)/2 + (225*A*a^9*b*d^8*e^2)/2 + 25*B*a^9*b*d^9*e) + x^7*(30*A*a^4*b^6*d^10 + 3
6*B*a^5*b^5*d^10 + 30*A*a^10*d^4*e^6 + 36*B*a^10*d^5*e^5 + 360*A*a^5*b^5*d^9*e + 360*A*a^9*b*d^5*e^5 + 300*B*a
^6*b^4*d^9*e + 300*B*a^9*b*d^6*e^4 + 1350*A*a^6*b^4*d^8*e^2 + (14400*A*a^7*b^3*d^7*e^3)/7 + 1350*A*a^8*b^2*d^6
*e^4 + (5400*B*a^7*b^3*d^8*e^2)/7 + (5400*B*a^8*b^2*d^7*e^3)/7) + x^19*((45*A*a^2*b^8*e^10)/19 + (120*B*a^3*b^
7*e^10)/19 + (45*A*b^10*d^2*e^8)/19 + (120*B*b^10*d^3*e^7)/19 + (450*B*a*b^9*d^2*e^8)/19 + (450*B*a^2*b^8*d*e^
9)/19 + (100*A*a*b^9*d*e^9)/19) + x^16*((63*A*a^5*b^5*e^10)/4 + (105*B*a^6*b^4*e^10)/8 + (63*A*b^10*d^5*e^5)/4
+ (105*B*b^10*d^6*e^4)/8 + (525*A*a*b^9*d^4*e^6)/4 + (525*A*a^4*b^6*d*e^9)/4 + (315*B*a*b^9*d^5*e^5)/2 + (315
*B*a^5*b^5*d*e^9)/2 + (675*A*a^2*b^8*d^3*e^7)/2 + (675*A*a^3*b^7*d^2*e^8)/2 + (4725*B*a^2*b^8*d^4*e^6)/8 + 900
*B*a^3*b^7*d^3*e^7 + (4725*B*a^4*b^6*d^2*e^8)/8) + x^10*(A*a*b^9*d^10 + A*a^10*d*e^9 + (9*B*a^2*b^8*d^10)/2 +
(9*B*a^10*d^2*e^8)/2 + 45*A*a^2*b^8*d^9*e + 45*A*a^9*b*d^2*e^8 + 120*B*a^3*b^7*d^9*e + 120*B*a^9*b*d^3*e^7 + 5
40*A*a^3*b^7*d^8*e^2 + 2520*A*a^4*b^6*d^7*e^3 + 5292*A*a^5*b^5*d^6*e^4 + 5292*A*a^6*b^4*d^5*e^5 + 2520*A*a^7*b
^3*d^4*e^6 + 540*A*a^8*b^2*d^3*e^7 + 945*B*a^4*...
________________________________________________________________________________________