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3.1062 \(\int (a+b x)^{10} (A+B x) (d+e x)^9 \, dx\)

Optimal. Leaf size=415 \[ \frac{e^8 (a+b x)^{20} (-10 a B e+A b e+9 b B d)}{20 b^{11}}+\frac{9 e^7 (a+b x)^{19} (b d-a e) (-5 a B e+A b e+4 b B d)}{19 b^{11}}+\frac{2 e^6 (a+b x)^{18} (b d-a e)^2 (-10 a B e+3 A b e+7 b B d)}{3 b^{11}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^3 (-5 a B e+2 A b e+3 b B d)}{17 b^{11}}+\frac{63 e^4 (a+b x)^{16} (b d-a e)^4 (-2 a B e+A b e+b B d)}{8 b^{11}}+\frac{14 e^3 (a+b x)^{15} (b d-a e)^5 (-5 a B e+3 A b e+2 b B d)}{5 b^{11}}+\frac{6 e^2 (a+b x)^{14} (b d-a e)^6 (-10 a B e+7 A b e+3 b B d)}{7 b^{11}}+\frac{9 e (a+b x)^{13} (b d-a e)^7 (-5 a B e+4 A b e+b B d)}{13 b^{11}}+\frac{(a+b x)^{12} (b d-a e)^8 (-10 a B e+9 A b e+b B d)}{12 b^{11}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^9}{11 b^{11}}+\frac{B e^9 (a+b x)^{21}}{21 b^{11}} \]

[Out]

((A*b - a*B)*(b*d - a*e)^9*(a + b*x)^11)/(11*b^11) + ((b*d - a*e)^8*(b*B*d + 9*A
*b*e - 10*a*B*e)*(a + b*x)^12)/(12*b^11) + (9*e*(b*d - a*e)^7*(b*B*d + 4*A*b*e -
 5*a*B*e)*(a + b*x)^13)/(13*b^11) + (6*e^2*(b*d - a*e)^6*(3*b*B*d + 7*A*b*e - 10
*a*B*e)*(a + b*x)^14)/(7*b^11) + (14*e^3*(b*d - a*e)^5*(2*b*B*d + 3*A*b*e - 5*a*
B*e)*(a + b*x)^15)/(5*b^11) + (63*e^4*(b*d - a*e)^4*(b*B*d + A*b*e - 2*a*B*e)*(a
 + b*x)^16)/(8*b^11) + (42*e^5*(b*d - a*e)^3*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a +
b*x)^17)/(17*b^11) + (2*e^6*(b*d - a*e)^2*(7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*
x)^18)/(3*b^11) + (9*e^7*(b*d - a*e)*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^19)/(
19*b^11) + (e^8*(9*b*B*d + A*b*e - 10*a*B*e)*(a + b*x)^20)/(20*b^11) + (B*e^9*(a
 + b*x)^21)/(21*b^11)

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Rubi [A]  time = 12.5811, antiderivative size = 415, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{e^8 (a+b x)^{20} (-10 a B e+A b e+9 b B d)}{20 b^{11}}+\frac{9 e^7 (a+b x)^{19} (b d-a e) (-5 a B e+A b e+4 b B d)}{19 b^{11}}+\frac{2 e^6 (a+b x)^{18} (b d-a e)^2 (-10 a B e+3 A b e+7 b B d)}{3 b^{11}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^3 (-5 a B e+2 A b e+3 b B d)}{17 b^{11}}+\frac{63 e^4 (a+b x)^{16} (b d-a e)^4 (-2 a B e+A b e+b B d)}{8 b^{11}}+\frac{14 e^3 (a+b x)^{15} (b d-a e)^5 (-5 a B e+3 A b e+2 b B d)}{5 b^{11}}+\frac{6 e^2 (a+b x)^{14} (b d-a e)^6 (-10 a B e+7 A b e+3 b B d)}{7 b^{11}}+\frac{9 e (a+b x)^{13} (b d-a e)^7 (-5 a B e+4 A b e+b B d)}{13 b^{11}}+\frac{(a+b x)^{12} (b d-a e)^8 (-10 a B e+9 A b e+b B d)}{12 b^{11}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^9}{11 b^{11}}+\frac{B e^9 (a+b x)^{21}}{21 b^{11}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^10*(A + B*x)*(d + e*x)^9,x]

[Out]

((A*b - a*B)*(b*d - a*e)^9*(a + b*x)^11)/(11*b^11) + ((b*d - a*e)^8*(b*B*d + 9*A
*b*e - 10*a*B*e)*(a + b*x)^12)/(12*b^11) + (9*e*(b*d - a*e)^7*(b*B*d + 4*A*b*e -
 5*a*B*e)*(a + b*x)^13)/(13*b^11) + (6*e^2*(b*d - a*e)^6*(3*b*B*d + 7*A*b*e - 10
*a*B*e)*(a + b*x)^14)/(7*b^11) + (14*e^3*(b*d - a*e)^5*(2*b*B*d + 3*A*b*e - 5*a*
B*e)*(a + b*x)^15)/(5*b^11) + (63*e^4*(b*d - a*e)^4*(b*B*d + A*b*e - 2*a*B*e)*(a
 + b*x)^16)/(8*b^11) + (42*e^5*(b*d - a*e)^3*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a +
b*x)^17)/(17*b^11) + (2*e^6*(b*d - a*e)^2*(7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*
x)^18)/(3*b^11) + (9*e^7*(b*d - a*e)*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^19)/(
19*b^11) + (e^8*(9*b*B*d + A*b*e - 10*a*B*e)*(a + b*x)^20)/(20*b^11) + (B*e^9*(a
 + b*x)^21)/(21*b^11)

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Rubi in Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**10*(B*x+A)*(e*x+d)**9,x)

[Out]

Timed out

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Mathematica [B]  time = 2.06357, size = 2553, normalized size = 6.15 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^9,x]

[Out]

a^10*A*d^9*x + (a^9*d^8*(10*A*b*d + a*B*d + 9*a*A*e)*x^2)/2 + (a^8*d^7*(a*B*d*(1
0*b*d + 9*a*e) + 9*A*(5*b^2*d^2 + 10*a*b*d*e + 4*a^2*e^2))*x^3)/3 + (3*a^7*d^6*(
3*a*B*d*(5*b^2*d^2 + 10*a*b*d*e + 4*a^2*e^2) + A*(40*b^3*d^3 + 135*a*b^2*d^2*e +
 120*a^2*b*d*e^2 + 28*a^3*e^3))*x^4)/4 + (3*a^6*d^5*(a*B*d*(40*b^3*d^3 + 135*a*b
^2*d^2*e + 120*a^2*b*d*e^2 + 28*a^3*e^3) + A*(70*b^4*d^4 + 360*a*b^3*d^3*e + 540
*a^2*b^2*d^2*e^2 + 280*a^3*b*d*e^3 + 42*a^4*e^4))*x^5)/5 + a^5*d^4*(a*B*d*(35*b^
4*d^4 + 180*a*b^3*d^3*e + 270*a^2*b^2*d^2*e^2 + 140*a^3*b*d*e^3 + 21*a^4*e^4) +
3*A*(14*b^5*d^5 + 105*a*b^4*d^4*e + 240*a^2*b^3*d^3*e^2 + 210*a^3*b^2*d^2*e^3 +
70*a^4*b*d*e^4 + 7*a^5*e^5))*x^6 + (6*a^4*d^3*(3*a*B*d*(14*b^5*d^5 + 105*a*b^4*d
^4*e + 240*a^2*b^3*d^3*e^2 + 210*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5) +
 7*A*(5*b^6*d^6 + 54*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 240*a^3*b^3*d^3*e^3 + 1
35*a^4*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + 2*a^6*e^6))*x^7)/7 + (3*a^3*d^2*(7*a*B*d*(
5*b^6*d^6 + 54*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 240*a^3*b^3*d^3*e^3 + 135*a^4
*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + 2*a^6*e^6) + A*(20*b^7*d^7 + 315*a*b^6*d^6*e + 1
512*a^2*b^5*d^5*e^2 + 2940*a^3*b^4*d^4*e^3 + 2520*a^4*b^3*d^3*e^4 + 945*a^5*b^2*
d^2*e^5 + 140*a^6*b*d*e^6 + 6*a^7*e^7))*x^8)/4 + (a^2*d*(2*a*B*d*(20*b^7*d^7 + 3
15*a*b^6*d^6*e + 1512*a^2*b^5*d^5*e^2 + 2940*a^3*b^4*d^4*e^3 + 2520*a^4*b^3*d^3*
e^4 + 945*a^5*b^2*d^2*e^5 + 140*a^6*b*d*e^6 + 6*a^7*e^7) + 3*A*(5*b^8*d^8 + 120*
a*b^7*d^7*e + 840*a^2*b^6*d^6*e^2 + 2352*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4
+ 1680*a^5*b^3*d^3*e^5 + 420*a^6*b^2*d^2*e^6 + 40*a^7*b*d*e^7 + a^8*e^8))*x^9)/3
 + (a*(9*a*B*d*(5*b^8*d^8 + 120*a*b^7*d^7*e + 840*a^2*b^6*d^6*e^2 + 2352*a^3*b^5
*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 1680*a^5*b^3*d^3*e^5 + 420*a^6*b^2*d^2*e^6 + 4
0*a^7*b*d*e^7 + a^8*e^8) + A*(10*b^9*d^9 + 405*a*b^8*d^8*e + 4320*a^2*b^7*d^7*e^
2 + 17640*a^3*b^6*d^6*e^3 + 31752*a^4*b^5*d^5*e^4 + 26460*a^5*b^4*d^4*e^5 + 1008
0*a^6*b^3*d^3*e^6 + 1620*a^7*b^2*d^2*e^7 + 90*a^8*b*d*e^8 + a^9*e^9))*x^10)/10 +
 ((a*B*(10*b^9*d^9 + 405*a*b^8*d^8*e + 4320*a^2*b^7*d^7*e^2 + 17640*a^3*b^6*d^6*
e^3 + 31752*a^4*b^5*d^5*e^4 + 26460*a^5*b^4*d^4*e^5 + 10080*a^6*b^3*d^3*e^6 + 16
20*a^7*b^2*d^2*e^7 + 90*a^8*b*d*e^8 + a^9*e^9) + A*b*(b^9*d^9 + 90*a*b^8*d^8*e +
 1620*a^2*b^7*d^7*e^2 + 10080*a^3*b^6*d^6*e^3 + 26460*a^4*b^5*d^5*e^4 + 31752*a^
5*b^4*d^4*e^5 + 17640*a^6*b^3*d^3*e^6 + 4320*a^7*b^2*d^2*e^7 + 405*a^8*b*d*e^8 +
 10*a^9*e^9))*x^11)/11 + (b*(10*a^9*B*e^9 + 26460*a^4*b^5*d^4*e^4*(B*d + A*e) +
1080*a^7*b^2*d*e^7*(4*B*d + A*e) + 45*a^8*b*e^8*(9*B*d + A*e) + 10584*a^5*b^4*d^
3*e^5*(3*B*d + 2*A*e) + 5040*a^3*b^6*d^5*e^3*(2*B*d + 3*A*e) + 2520*a^6*b^3*d^2*
e^6*(7*B*d + 3*A*e) + 90*a*b^8*d^7*e*(B*d + 4*A*e) + 540*a^2*b^7*d^6*e^2*(3*B*d
+ 7*A*e) + b^9*d^8*(B*d + 9*A*e))*x^12)/12 + (3*b^2*e*(15*a^8*B*e^8 + 5040*a^3*b
^5*d^4*e^3*(B*d + A*e) + 630*a^6*b^2*d*e^6*(4*B*d + A*e) + 40*a^7*b*e^7*(9*B*d +
 A*e) + 2940*a^4*b^4*d^3*e^4*(3*B*d + 2*A*e) + 630*a^2*b^6*d^5*e^2*(2*B*d + 3*A*
e) + 1008*a^5*b^3*d^2*e^5*(7*B*d + 3*A*e) + 3*b^8*d^7*(B*d + 4*A*e) + 40*a*b^7*d
^6*e*(3*B*d + 7*A*e))*x^13)/13 + (3*b^3*e^2*(20*a^7*B*e^7 + 945*a^2*b^5*d^4*e^2*
(B*d + A*e) + 378*a^5*b^2*d*e^5*(4*B*d + A*e) + 35*a^6*b*e^6*(9*B*d + A*e) + 840
*a^3*b^4*d^3*e^3*(3*B*d + 2*A*e) + 70*a*b^6*d^5*e*(2*B*d + 3*A*e) + 420*a^4*b^3*
d^2*e^4*(7*B*d + 3*A*e) + 2*b^7*d^6*(3*B*d + 7*A*e))*x^14)/7 + (2*b^4*e^3*(35*a^
6*B*e^6 + 210*a*b^5*d^4*e*(B*d + A*e) + 315*a^4*b^2*d*e^4*(4*B*d + A*e) + 42*a^5
*b*e^5*(9*B*d + A*e) + 315*a^2*b^4*d^3*e^2*(3*B*d + 2*A*e) + 7*b^6*d^5*(2*B*d +
3*A*e) + 240*a^3*b^3*d^2*e^3*(7*B*d + 3*A*e))*x^15)/5 + (3*b^5*e^4*(42*a^5*B*e^5
 + 21*b^5*d^4*(B*d + A*e) + 180*a^3*b^2*d*e^3*(4*B*d + A*e) + 35*a^4*b*e^4*(9*B*
d + A*e) + 70*a*b^4*d^3*e*(3*B*d + 2*A*e) + 90*a^2*b^3*d^2*e^2*(7*B*d + 3*A*e))*
x^16)/8 + (3*b^6*e^5*(70*a^4*B*e^4 + 135*a^2*b^2*d*e^2*(4*B*d + A*e) + 40*a^3*b*
e^3*(9*B*d + A*e) + 14*b^4*d^3*(3*B*d + 2*A*e) + 40*a*b^3*d^2*e*(7*B*d + 3*A*e))
*x^17)/17 + (b^7*e^6*(40*a^3*B*e^3 + 30*a*b^2*d*e*(4*B*d + A*e) + 15*a^2*b*e^2*(
9*B*d + A*e) + 4*b^3*d^2*(7*B*d + 3*A*e))*x^18)/6 + (b^8*e^7*(45*a^2*B*e^2 + 9*b
^2*d*(4*B*d + A*e) + 10*a*b*e*(9*B*d + A*e))*x^19)/19 + (b^9*e^8*(9*b*B*d + A*b*
e + 10*a*B*e)*x^20)/20 + (b^10*B*e^9*x^21)/21

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Maple [B]  time = 0.006, size = 2757, normalized size = 6.6 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^10*(B*x+A)*(e*x+d)^9,x)

[Out]

1/21*b^10*B*e^9*x^21+1/20*((A*b^10+10*B*a*b^9)*e^9+9*b^10*B*d*e^8)*x^20+1/19*((1
0*A*a*b^9+45*B*a^2*b^8)*e^9+9*(A*b^10+10*B*a*b^9)*d*e^8+36*b^10*B*d^2*e^7)*x^19+
1/18*((45*A*a^2*b^8+120*B*a^3*b^7)*e^9+9*(10*A*a*b^9+45*B*a^2*b^8)*d*e^8+36*(A*b
^10+10*B*a*b^9)*d^2*e^7+84*b^10*B*d^3*e^6)*x^18+1/17*((120*A*a^3*b^7+210*B*a^4*b
^6)*e^9+9*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^8+36*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^
7+84*(A*b^10+10*B*a*b^9)*d^3*e^6+126*b^10*B*d^4*e^5)*x^17+1/16*((210*A*a^4*b^6+2
52*B*a^5*b^5)*e^9+9*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^8+36*(45*A*a^2*b^8+120*B*a
^3*b^7)*d^2*e^7+84*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^6+126*(A*b^10+10*B*a*b^9)*d^4
*e^5+126*b^10*B*d^5*e^4)*x^16+1/15*((252*A*a^5*b^5+210*B*a^6*b^4)*e^9+9*(210*A*a
^4*b^6+252*B*a^5*b^5)*d*e^8+36*(120*A*a^3*b^7+210*B*a^4*b^6)*d^2*e^7+84*(45*A*a^
2*b^8+120*B*a^3*b^7)*d^3*e^6+126*(10*A*a*b^9+45*B*a^2*b^8)*d^4*e^5+126*(A*b^10+1
0*B*a*b^9)*d^5*e^4+84*b^10*B*d^6*e^3)*x^15+1/14*((210*A*a^6*b^4+120*B*a^7*b^3)*e
^9+9*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^8+36*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^
7+84*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*e^6+126*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*
e^5+126*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e^4+84*(A*b^10+10*B*a*b^9)*d^6*e^3+36*b^10
*B*d^7*e^2)*x^14+1/13*((120*A*a^7*b^3+45*B*a^8*b^2)*e^9+9*(210*A*a^6*b^4+120*B*a
^7*b^3)*d*e^8+36*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^7+84*(210*A*a^4*b^6+252*B*a
^5*b^5)*d^3*e^6+126*(120*A*a^3*b^7+210*B*a^4*b^6)*d^4*e^5+126*(45*A*a^2*b^8+120*
B*a^3*b^7)*d^5*e^4+84*(10*A*a*b^9+45*B*a^2*b^8)*d^6*e^3+36*(A*b^10+10*B*a*b^9)*d
^7*e^2+9*b^10*B*d^8*e)*x^13+1/12*((45*A*a^8*b^2+10*B*a^9*b)*e^9+9*(120*A*a^7*b^3
+45*B*a^8*b^2)*d*e^8+36*(210*A*a^6*b^4+120*B*a^7*b^3)*d^2*e^7+84*(252*A*a^5*b^5+
210*B*a^6*b^4)*d^3*e^6+126*(210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^5+126*(120*A*a^3*
b^7+210*B*a^4*b^6)*d^5*e^4+84*(45*A*a^2*b^8+120*B*a^3*b^7)*d^6*e^3+36*(10*A*a*b^
9+45*B*a^2*b^8)*d^7*e^2+9*(A*b^10+10*B*a*b^9)*d^8*e+b^10*B*d^9)*x^12+1/11*((10*A
*a^9*b+B*a^10)*e^9+9*(45*A*a^8*b^2+10*B*a^9*b)*d*e^8+36*(120*A*a^7*b^3+45*B*a^8*
b^2)*d^2*e^7+84*(210*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^6+126*(252*A*a^5*b^5+210*B*a
^6*b^4)*d^4*e^5+126*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e^4+84*(120*A*a^3*b^7+210*
B*a^4*b^6)*d^6*e^3+36*(45*A*a^2*b^8+120*B*a^3*b^7)*d^7*e^2+9*(10*A*a*b^9+45*B*a^
2*b^8)*d^8*e+(A*b^10+10*B*a*b^9)*d^9)*x^11+1/10*(a^10*A*e^9+9*(10*A*a^9*b+B*a^10
)*d*e^8+36*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^7+84*(120*A*a^7*b^3+45*B*a^8*b^2)*d^3
*e^6+126*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^5+126*(252*A*a^5*b^5+210*B*a^6*b^4)
*d^5*e^4+84*(210*A*a^4*b^6+252*B*a^5*b^5)*d^6*e^3+36*(120*A*a^3*b^7+210*B*a^4*b^
6)*d^7*e^2+9*(45*A*a^2*b^8+120*B*a^3*b^7)*d^8*e+(10*A*a*b^9+45*B*a^2*b^8)*d^9)*x
^10+1/9*(9*a^10*A*d*e^8+36*(10*A*a^9*b+B*a^10)*d^2*e^7+84*(45*A*a^8*b^2+10*B*a^9
*b)*d^3*e^6+126*(120*A*a^7*b^3+45*B*a^8*b^2)*d^4*e^5+126*(210*A*a^6*b^4+120*B*a^
7*b^3)*d^5*e^4+84*(252*A*a^5*b^5+210*B*a^6*b^4)*d^6*e^3+36*(210*A*a^4*b^6+252*B*
a^5*b^5)*d^7*e^2+9*(120*A*a^3*b^7+210*B*a^4*b^6)*d^8*e+(45*A*a^2*b^8+120*B*a^3*b
^7)*d^9)*x^9+1/8*(36*a^10*A*d^2*e^7+84*(10*A*a^9*b+B*a^10)*d^3*e^6+126*(45*A*a^8
*b^2+10*B*a^9*b)*d^4*e^5+126*(120*A*a^7*b^3+45*B*a^8*b^2)*d^5*e^4+84*(210*A*a^6*
b^4+120*B*a^7*b^3)*d^6*e^3+36*(252*A*a^5*b^5+210*B*a^6*b^4)*d^7*e^2+9*(210*A*a^4
*b^6+252*B*a^5*b^5)*d^8*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^9)*x^8+1/7*(84*a^10*A*
d^3*e^6+126*(10*A*a^9*b+B*a^10)*d^4*e^5+126*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e^4+84
*(120*A*a^7*b^3+45*B*a^8*b^2)*d^6*e^3+36*(210*A*a^6*b^4+120*B*a^7*b^3)*d^7*e^2+9
*(252*A*a^5*b^5+210*B*a^6*b^4)*d^8*e+(210*A*a^4*b^6+252*B*a^5*b^5)*d^9)*x^7+1/6*
(126*a^10*A*d^4*e^5+126*(10*A*a^9*b+B*a^10)*d^5*e^4+84*(45*A*a^8*b^2+10*B*a^9*b)
*d^6*e^3+36*(120*A*a^7*b^3+45*B*a^8*b^2)*d^7*e^2+9*(210*A*a^6*b^4+120*B*a^7*b^3)
*d^8*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^9)*x^6+1/5*(126*a^10*A*d^5*e^4+84*(10*A*a
^9*b+B*a^10)*d^6*e^3+36*(45*A*a^8*b^2+10*B*a^9*b)*d^7*e^2+9*(120*A*a^7*b^3+45*B*
a^8*b^2)*d^8*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^9)*x^5+1/4*(84*a^10*A*d^6*e^3+36*
(10*A*a^9*b+B*a^10)*d^7*e^2+9*(45*A*a^8*b^2+10*B*a^9*b)*d^8*e+(120*A*a^7*b^3+45*
B*a^8*b^2)*d^9)*x^4+1/3*(36*a^10*A*d^7*e^2+9*(10*A*a^9*b+B*a^10)*d^8*e+(45*A*a^8
*b^2+10*B*a^9*b)*d^9)*x^3+1/2*(9*a^10*A*d^8*e+(10*A*a^9*b+B*a^10)*d^9)*x^2+a^10*
A*d^9*x

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Maxima [A]  time = 1.41182, size = 3741, normalized size = 9.01 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^9,x, algorithm="maxima")

[Out]

1/21*B*b^10*e^9*x^21 + A*a^10*d^9*x + 1/20*(9*B*b^10*d*e^8 + (10*B*a*b^9 + A*b^1
0)*e^9)*x^20 + 1/19*(36*B*b^10*d^2*e^7 + 9*(10*B*a*b^9 + A*b^10)*d*e^8 + 5*(9*B*
a^2*b^8 + 2*A*a*b^9)*e^9)*x^19 + 1/6*(28*B*b^10*d^3*e^6 + 12*(10*B*a*b^9 + A*b^1
0)*d^2*e^7 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^8 + 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*
e^9)*x^18 + 3/17*(42*B*b^10*d^4*e^5 + 28*(10*B*a*b^9 + A*b^10)*d^3*e^6 + 60*(9*B
*a^2*b^8 + 2*A*a*b^9)*d^2*e^7 + 45*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^8 + 10*(7*B*a
^4*b^6 + 4*A*a^3*b^7)*e^9)*x^17 + 3/8*(21*B*b^10*d^5*e^4 + 21*(10*B*a*b^9 + A*b^
10)*d^4*e^5 + 70*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^6 + 90*(8*B*a^3*b^7 + 3*A*a^2*b
^8)*d^2*e^7 + 45*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^8 + 7*(6*B*a^5*b^5 + 5*A*a^4*b^
6)*e^9)*x^16 + 2/5*(14*B*b^10*d^6*e^3 + 21*(10*B*a*b^9 + A*b^10)*d^5*e^4 + 105*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^5 + 210*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^6 + 180
*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^7 + 63*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^8 + 7*
(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^9)*x^15 + 3/7*(6*B*b^10*d^7*e^2 + 14*(10*B*a*b^9 +
 A*b^10)*d^6*e^3 + 105*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^4 + 315*(8*B*a^3*b^7 + 3*
A*a^2*b^8)*d^4*e^5 + 420*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^6 + 252*(6*B*a^5*b^5
+ 5*A*a^4*b^6)*d^2*e^7 + 63*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^8 + 5*(4*B*a^7*b^3 +
 7*A*a^6*b^4)*e^9)*x^14 + 3/13*(3*B*b^10*d^8*e + 12*(10*B*a*b^9 + A*b^10)*d^7*e^
2 + 140*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^3 + 630*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*
e^4 + 1260*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^5 + 1176*(6*B*a^5*b^5 + 5*A*a^4*b^6
)*d^3*e^6 + 504*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^7 + 90*(4*B*a^7*b^3 + 7*A*a^6*
b^4)*d*e^8 + 5*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^9)*x^13 + 1/12*(B*b^10*d^9 + 9*(10*
B*a*b^9 + A*b^10)*d^8*e + 180*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^2 + 1260*(8*B*a^3*
b^7 + 3*A*a^2*b^8)*d^6*e^3 + 3780*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^4 + 5292*(6*
B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^5 + 3528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^6 + 10
80*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^7 + 135*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^8 +
 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^9)*x^12 + 1/11*((10*B*a*b^9 + A*b^10)*d^9 + 45*(9
*B*a^2*b^8 + 2*A*a*b^9)*d^8*e + 540*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^2 + 2520*(
7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^3 + 5292*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^4 +
5292*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^5 + 2520*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*
e^6 + 540*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^7 + 45*(2*B*a^9*b + 9*A*a^8*b^2)*d*e
^8 + (B*a^10 + 10*A*a^9*b)*e^9)*x^11 + 1/10*(A*a^10*e^9 + 5*(9*B*a^2*b^8 + 2*A*a
*b^9)*d^9 + 135*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e + 1080*(7*B*a^4*b^6 + 4*A*a^3*
b^7)*d^7*e^2 + 3528*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^3 + 5292*(5*B*a^6*b^4 + 6*
A*a^5*b^5)*d^5*e^4 + 3780*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^5 + 1260*(3*B*a^8*b^
2 + 8*A*a^7*b^3)*d^3*e^6 + 180*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^7 + 9*(B*a^10 + 1
0*A*a^9*b)*d*e^8)*x^10 + 1/3*(3*A*a^10*d*e^8 + 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^9
 + 90*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^8*e + 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^7*e^
2 + 1176*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*e^3 + 1260*(4*B*a^7*b^3 + 7*A*a^6*b^4)*
d^5*e^4 + 630*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^4*e^5 + 140*(2*B*a^9*b + 9*A*a^8*b^2
)*d^3*e^6 + 12*(B*a^10 + 10*A*a^9*b)*d^2*e^7)*x^9 + 3/4*(6*A*a^10*d^2*e^7 + 5*(7
*B*a^4*b^6 + 4*A*a^3*b^7)*d^9 + 63*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^8*e + 252*(5*B*
a^6*b^4 + 6*A*a^5*b^5)*d^7*e^2 + 420*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*e^3 + 315*(
3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*e^4 + 105*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*e^5 + 14*
(B*a^10 + 10*A*a^9*b)*d^3*e^6)*x^8 + 6/7*(14*A*a^10*d^3*e^6 + 7*(6*B*a^5*b^5 + 5
*A*a^4*b^6)*d^9 + 63*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^8*e + 180*(4*B*a^7*b^3 + 7*A*
a^6*b^4)*d^7*e^2 + 210*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6*e^3 + 105*(2*B*a^9*b + 9*
A*a^8*b^2)*d^5*e^4 + 21*(B*a^10 + 10*A*a^9*b)*d^4*e^5)*x^7 + (21*A*a^10*d^4*e^5
+ 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^9 + 45*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^8*e + 90*
(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^7*e^2 + 70*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*e^3 + 21*
(B*a^10 + 10*A*a^9*b)*d^5*e^4)*x^6 + 3/5*(42*A*a^10*d^5*e^4 + 10*(4*B*a^7*b^3 +
7*A*a^6*b^4)*d^9 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^8*e + 60*(2*B*a^9*b + 9*A*a^
8*b^2)*d^7*e^2 + 28*(B*a^10 + 10*A*a^9*b)*d^6*e^3)*x^5 + 3/4*(28*A*a^10*d^6*e^3
+ 5*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^9 + 15*(2*B*a^9*b + 9*A*a^8*b^2)*d^8*e + 12*(B
*a^10 + 10*A*a^9*b)*d^7*e^2)*x^4 + 1/3*(36*A*a^10*d^7*e^2 + 5*(2*B*a^9*b + 9*A*a
^8*b^2)*d^9 + 9*(B*a^10 + 10*A*a^9*b)*d^8*e)*x^3 + 1/2*(9*A*a^10*d^8*e + (B*a^10
 + 10*A*a^9*b)*d^9)*x^2

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Fricas [A]  time = 0.20035, size = 1, normalized size = 0. \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^9,x, algorithm="fricas")

[Out]

1/21*x^21*e^9*b^10*B + 9/20*x^20*e^8*d*b^10*B + 1/2*x^20*e^9*b^9*a*B + 1/20*x^20
*e^9*b^10*A + 36/19*x^19*e^7*d^2*b^10*B + 90/19*x^19*e^8*d*b^9*a*B + 45/19*x^19*
e^9*b^8*a^2*B + 9/19*x^19*e^8*d*b^10*A + 10/19*x^19*e^9*b^9*a*A + 14/3*x^18*e^6*
d^3*b^10*B + 20*x^18*e^7*d^2*b^9*a*B + 45/2*x^18*e^8*d*b^8*a^2*B + 20/3*x^18*e^9
*b^7*a^3*B + 2*x^18*e^7*d^2*b^10*A + 5*x^18*e^8*d*b^9*a*A + 5/2*x^18*e^9*b^8*a^2
*A + 126/17*x^17*e^5*d^4*b^10*B + 840/17*x^17*e^6*d^3*b^9*a*B + 1620/17*x^17*e^7
*d^2*b^8*a^2*B + 1080/17*x^17*e^8*d*b^7*a^3*B + 210/17*x^17*e^9*b^6*a^4*B + 84/1
7*x^17*e^6*d^3*b^10*A + 360/17*x^17*e^7*d^2*b^9*a*A + 405/17*x^17*e^8*d*b^8*a^2*
A + 120/17*x^17*e^9*b^7*a^3*A + 63/8*x^16*e^4*d^5*b^10*B + 315/4*x^16*e^5*d^4*b^
9*a*B + 945/4*x^16*e^6*d^3*b^8*a^2*B + 270*x^16*e^7*d^2*b^7*a^3*B + 945/8*x^16*e
^8*d*b^6*a^4*B + 63/4*x^16*e^9*b^5*a^5*B + 63/8*x^16*e^5*d^4*b^10*A + 105/2*x^16
*e^6*d^3*b^9*a*A + 405/4*x^16*e^7*d^2*b^8*a^2*A + 135/2*x^16*e^8*d*b^7*a^3*A + 1
05/8*x^16*e^9*b^6*a^4*A + 28/5*x^15*e^3*d^6*b^10*B + 84*x^15*e^4*d^5*b^9*a*B + 3
78*x^15*e^5*d^4*b^8*a^2*B + 672*x^15*e^6*d^3*b^7*a^3*B + 504*x^15*e^7*d^2*b^6*a^
4*B + 756/5*x^15*e^8*d*b^5*a^5*B + 14*x^15*e^9*b^4*a^6*B + 42/5*x^15*e^4*d^5*b^1
0*A + 84*x^15*e^5*d^4*b^9*a*A + 252*x^15*e^6*d^3*b^8*a^2*A + 288*x^15*e^7*d^2*b^
7*a^3*A + 126*x^15*e^8*d*b^6*a^4*A + 84/5*x^15*e^9*b^5*a^5*A + 18/7*x^14*e^2*d^7
*b^10*B + 60*x^14*e^3*d^6*b^9*a*B + 405*x^14*e^4*d^5*b^8*a^2*B + 1080*x^14*e^5*d
^4*b^7*a^3*B + 1260*x^14*e^6*d^3*b^6*a^4*B + 648*x^14*e^7*d^2*b^5*a^5*B + 135*x^
14*e^8*d*b^4*a^6*B + 60/7*x^14*e^9*b^3*a^7*B + 6*x^14*e^3*d^6*b^10*A + 90*x^14*e
^4*d^5*b^9*a*A + 405*x^14*e^5*d^4*b^8*a^2*A + 720*x^14*e^6*d^3*b^7*a^3*A + 540*x
^14*e^7*d^2*b^6*a^4*A + 162*x^14*e^8*d*b^5*a^5*A + 15*x^14*e^9*b^4*a^6*A + 9/13*
x^13*e*d^8*b^10*B + 360/13*x^13*e^2*d^7*b^9*a*B + 3780/13*x^13*e^3*d^6*b^8*a^2*B
 + 15120/13*x^13*e^4*d^5*b^7*a^3*B + 26460/13*x^13*e^5*d^4*b^6*a^4*B + 21168/13*
x^13*e^6*d^3*b^5*a^5*B + 7560/13*x^13*e^7*d^2*b^4*a^6*B + 1080/13*x^13*e^8*d*b^3
*a^7*B + 45/13*x^13*e^9*b^2*a^8*B + 36/13*x^13*e^2*d^7*b^10*A + 840/13*x^13*e^3*
d^6*b^9*a*A + 5670/13*x^13*e^4*d^5*b^8*a^2*A + 15120/13*x^13*e^5*d^4*b^7*a^3*A +
 17640/13*x^13*e^6*d^3*b^6*a^4*A + 9072/13*x^13*e^7*d^2*b^5*a^5*A + 1890/13*x^13
*e^8*d*b^4*a^6*A + 120/13*x^13*e^9*b^3*a^7*A + 1/12*x^12*d^9*b^10*B + 15/2*x^12*
e*d^8*b^9*a*B + 135*x^12*e^2*d^7*b^8*a^2*B + 840*x^12*e^3*d^6*b^7*a^3*B + 2205*x
^12*e^4*d^5*b^6*a^4*B + 2646*x^12*e^5*d^4*b^5*a^5*B + 1470*x^12*e^6*d^3*b^4*a^6*
B + 360*x^12*e^7*d^2*b^3*a^7*B + 135/4*x^12*e^8*d*b^2*a^8*B + 5/6*x^12*e^9*b*a^9
*B + 3/4*x^12*e*d^8*b^10*A + 30*x^12*e^2*d^7*b^9*a*A + 315*x^12*e^3*d^6*b^8*a^2*
A + 1260*x^12*e^4*d^5*b^7*a^3*A + 2205*x^12*e^5*d^4*b^6*a^4*A + 1764*x^12*e^6*d^
3*b^5*a^5*A + 630*x^12*e^7*d^2*b^4*a^6*A + 90*x^12*e^8*d*b^3*a^7*A + 15/4*x^12*e
^9*b^2*a^8*A + 10/11*x^11*d^9*b^9*a*B + 405/11*x^11*e*d^8*b^8*a^2*B + 4320/11*x^
11*e^2*d^7*b^7*a^3*B + 17640/11*x^11*e^3*d^6*b^6*a^4*B + 31752/11*x^11*e^4*d^5*b
^5*a^5*B + 26460/11*x^11*e^5*d^4*b^4*a^6*B + 10080/11*x^11*e^6*d^3*b^3*a^7*B + 1
620/11*x^11*e^7*d^2*b^2*a^8*B + 90/11*x^11*e^8*d*b*a^9*B + 1/11*x^11*e^9*a^10*B
+ 1/11*x^11*d^9*b^10*A + 90/11*x^11*e*d^8*b^9*a*A + 1620/11*x^11*e^2*d^7*b^8*a^2
*A + 10080/11*x^11*e^3*d^6*b^7*a^3*A + 26460/11*x^11*e^4*d^5*b^6*a^4*A + 31752/1
1*x^11*e^5*d^4*b^5*a^5*A + 17640/11*x^11*e^6*d^3*b^4*a^6*A + 4320/11*x^11*e^7*d^
2*b^3*a^7*A + 405/11*x^11*e^8*d*b^2*a^8*A + 10/11*x^11*e^9*b*a^9*A + 9/2*x^10*d^
9*b^8*a^2*B + 108*x^10*e*d^8*b^7*a^3*B + 756*x^10*e^2*d^7*b^6*a^4*B + 10584/5*x^
10*e^3*d^6*b^5*a^5*B + 2646*x^10*e^4*d^5*b^4*a^6*B + 1512*x^10*e^5*d^4*b^3*a^7*B
 + 378*x^10*e^6*d^3*b^2*a^8*B + 36*x^10*e^7*d^2*b*a^9*B + 9/10*x^10*e^8*d*a^10*B
 + x^10*d^9*b^9*a*A + 81/2*x^10*e*d^8*b^8*a^2*A + 432*x^10*e^2*d^7*b^7*a^3*A + 1
764*x^10*e^3*d^6*b^6*a^4*A + 15876/5*x^10*e^4*d^5*b^5*a^5*A + 2646*x^10*e^5*d^4*
b^4*a^6*A + 1008*x^10*e^6*d^3*b^3*a^7*A + 162*x^10*e^7*d^2*b^2*a^8*A + 9*x^10*e^
8*d*b*a^9*A + 1/10*x^10*e^9*a^10*A + 40/3*x^9*d^9*b^7*a^3*B + 210*x^9*e*d^8*b^6*
a^4*B + 1008*x^9*e^2*d^7*b^5*a^5*B + 1960*x^9*e^3*d^6*b^4*a^6*B + 1680*x^9*e^4*d
^5*b^3*a^7*B + 630*x^9*e^5*d^4*b^2*a^8*B + 280/3*x^9*e^6*d^3*b*a^9*B + 4*x^9*e^7
*d^2*a^10*B + 5*x^9*d^9*b^8*a^2*A + 120*x^9*e*d^8*b^7*a^3*A + 840*x^9*e^2*d^7*b^
6*a^4*A + 2352*x^9*e^3*d^6*b^5*a^5*A + 2940*x^9*e^4*d^5*b^4*a^6*A + 1680*x^9*e^5
*d^4*b^3*a^7*A + 420*x^9*e^6*d^3*b^2*a^8*A + 40*x^9*e^7*d^2*b*a^9*A + x^9*e^8*d*
a^10*A + 105/4*x^8*d^9*b^6*a^4*B + 567/2*x^8*e*d^8*b^5*a^5*B + 945*x^8*e^2*d^7*b
^4*a^6*B + 1260*x^8*e^3*d^6*b^3*a^7*B + 2835/4*x^8*e^4*d^5*b^2*a^8*B + 315/2*x^8
*e^5*d^4*b*a^9*B + 21/2*x^8*e^6*d^3*a^10*B + 15*x^8*d^9*b^7*a^3*A + 945/4*x^8*e*
d^8*b^6*a^4*A + 1134*x^8*e^2*d^7*b^5*a^5*A + 2205*x^8*e^3*d^6*b^4*a^6*A + 1890*x
^8*e^4*d^5*b^3*a^7*A + 2835/4*x^8*e^5*d^4*b^2*a^8*A + 105*x^8*e^6*d^3*b*a^9*A +
9/2*x^8*e^7*d^2*a^10*A + 36*x^7*d^9*b^5*a^5*B + 270*x^7*e*d^8*b^4*a^6*B + 4320/7
*x^7*e^2*d^7*b^3*a^7*B + 540*x^7*e^3*d^6*b^2*a^8*B + 180*x^7*e^4*d^5*b*a^9*B + 1
8*x^7*e^5*d^4*a^10*B + 30*x^7*d^9*b^6*a^4*A + 324*x^7*e*d^8*b^5*a^5*A + 1080*x^7
*e^2*d^7*b^4*a^6*A + 1440*x^7*e^3*d^6*b^3*a^7*A + 810*x^7*e^4*d^5*b^2*a^8*A + 18
0*x^7*e^5*d^4*b*a^9*A + 12*x^7*e^6*d^3*a^10*A + 35*x^6*d^9*b^4*a^6*B + 180*x^6*e
*d^8*b^3*a^7*B + 270*x^6*e^2*d^7*b^2*a^8*B + 140*x^6*e^3*d^6*b*a^9*B + 21*x^6*e^
4*d^5*a^10*B + 42*x^6*d^9*b^5*a^5*A + 315*x^6*e*d^8*b^4*a^6*A + 720*x^6*e^2*d^7*
b^3*a^7*A + 630*x^6*e^3*d^6*b^2*a^8*A + 210*x^6*e^4*d^5*b*a^9*A + 21*x^6*e^5*d^4
*a^10*A + 24*x^5*d^9*b^3*a^7*B + 81*x^5*e*d^8*b^2*a^8*B + 72*x^5*e^2*d^7*b*a^9*B
 + 84/5*x^5*e^3*d^6*a^10*B + 42*x^5*d^9*b^4*a^6*A + 216*x^5*e*d^8*b^3*a^7*A + 32
4*x^5*e^2*d^7*b^2*a^8*A + 168*x^5*e^3*d^6*b*a^9*A + 126/5*x^5*e^4*d^5*a^10*A + 4
5/4*x^4*d^9*b^2*a^8*B + 45/2*x^4*e*d^8*b*a^9*B + 9*x^4*e^2*d^7*a^10*B + 30*x^4*d
^9*b^3*a^7*A + 405/4*x^4*e*d^8*b^2*a^8*A + 90*x^4*e^2*d^7*b*a^9*A + 21*x^4*e^3*d
^6*a^10*A + 10/3*x^3*d^9*b*a^9*B + 3*x^3*e*d^8*a^10*B + 15*x^3*d^9*b^2*a^8*A + 3
0*x^3*e*d^8*b*a^9*A + 12*x^3*e^2*d^7*a^10*A + 1/2*x^2*d^9*a^10*B + 5*x^2*d^9*b*a
^9*A + 9/2*x^2*e*d^8*a^10*A + x*d^9*a^10*A

_______________________________________________________________________________________

Sympy [A]  time = 1.45604, size = 3541, normalized size = 8.53 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**10*(B*x+A)*(e*x+d)**9,x)

[Out]

A*a**10*d**9*x + B*b**10*e**9*x**21/21 + x**20*(A*b**10*e**9/20 + B*a*b**9*e**9/
2 + 9*B*b**10*d*e**8/20) + x**19*(10*A*a*b**9*e**9/19 + 9*A*b**10*d*e**8/19 + 45
*B*a**2*b**8*e**9/19 + 90*B*a*b**9*d*e**8/19 + 36*B*b**10*d**2*e**7/19) + x**18*
(5*A*a**2*b**8*e**9/2 + 5*A*a*b**9*d*e**8 + 2*A*b**10*d**2*e**7 + 20*B*a**3*b**7
*e**9/3 + 45*B*a**2*b**8*d*e**8/2 + 20*B*a*b**9*d**2*e**7 + 14*B*b**10*d**3*e**6
/3) + x**17*(120*A*a**3*b**7*e**9/17 + 405*A*a**2*b**8*d*e**8/17 + 360*A*a*b**9*
d**2*e**7/17 + 84*A*b**10*d**3*e**6/17 + 210*B*a**4*b**6*e**9/17 + 1080*B*a**3*b
**7*d*e**8/17 + 1620*B*a**2*b**8*d**2*e**7/17 + 840*B*a*b**9*d**3*e**6/17 + 126*
B*b**10*d**4*e**5/17) + x**16*(105*A*a**4*b**6*e**9/8 + 135*A*a**3*b**7*d*e**8/2
 + 405*A*a**2*b**8*d**2*e**7/4 + 105*A*a*b**9*d**3*e**6/2 + 63*A*b**10*d**4*e**5
/8 + 63*B*a**5*b**5*e**9/4 + 945*B*a**4*b**6*d*e**8/8 + 270*B*a**3*b**7*d**2*e**
7 + 945*B*a**2*b**8*d**3*e**6/4 + 315*B*a*b**9*d**4*e**5/4 + 63*B*b**10*d**5*e**
4/8) + x**15*(84*A*a**5*b**5*e**9/5 + 126*A*a**4*b**6*d*e**8 + 288*A*a**3*b**7*d
**2*e**7 + 252*A*a**2*b**8*d**3*e**6 + 84*A*a*b**9*d**4*e**5 + 42*A*b**10*d**5*e
**4/5 + 14*B*a**6*b**4*e**9 + 756*B*a**5*b**5*d*e**8/5 + 504*B*a**4*b**6*d**2*e*
*7 + 672*B*a**3*b**7*d**3*e**6 + 378*B*a**2*b**8*d**4*e**5 + 84*B*a*b**9*d**5*e*
*4 + 28*B*b**10*d**6*e**3/5) + x**14*(15*A*a**6*b**4*e**9 + 162*A*a**5*b**5*d*e*
*8 + 540*A*a**4*b**6*d**2*e**7 + 720*A*a**3*b**7*d**3*e**6 + 405*A*a**2*b**8*d**
4*e**5 + 90*A*a*b**9*d**5*e**4 + 6*A*b**10*d**6*e**3 + 60*B*a**7*b**3*e**9/7 + 1
35*B*a**6*b**4*d*e**8 + 648*B*a**5*b**5*d**2*e**7 + 1260*B*a**4*b**6*d**3*e**6 +
 1080*B*a**3*b**7*d**4*e**5 + 405*B*a**2*b**8*d**5*e**4 + 60*B*a*b**9*d**6*e**3
+ 18*B*b**10*d**7*e**2/7) + x**13*(120*A*a**7*b**3*e**9/13 + 1890*A*a**6*b**4*d*
e**8/13 + 9072*A*a**5*b**5*d**2*e**7/13 + 17640*A*a**4*b**6*d**3*e**6/13 + 15120
*A*a**3*b**7*d**4*e**5/13 + 5670*A*a**2*b**8*d**5*e**4/13 + 840*A*a*b**9*d**6*e*
*3/13 + 36*A*b**10*d**7*e**2/13 + 45*B*a**8*b**2*e**9/13 + 1080*B*a**7*b**3*d*e*
*8/13 + 7560*B*a**6*b**4*d**2*e**7/13 + 21168*B*a**5*b**5*d**3*e**6/13 + 26460*B
*a**4*b**6*d**4*e**5/13 + 15120*B*a**3*b**7*d**5*e**4/13 + 3780*B*a**2*b**8*d**6
*e**3/13 + 360*B*a*b**9*d**7*e**2/13 + 9*B*b**10*d**8*e/13) + x**12*(15*A*a**8*b
**2*e**9/4 + 90*A*a**7*b**3*d*e**8 + 630*A*a**6*b**4*d**2*e**7 + 1764*A*a**5*b**
5*d**3*e**6 + 2205*A*a**4*b**6*d**4*e**5 + 1260*A*a**3*b**7*d**5*e**4 + 315*A*a*
*2*b**8*d**6*e**3 + 30*A*a*b**9*d**7*e**2 + 3*A*b**10*d**8*e/4 + 5*B*a**9*b*e**9
/6 + 135*B*a**8*b**2*d*e**8/4 + 360*B*a**7*b**3*d**2*e**7 + 1470*B*a**6*b**4*d**
3*e**6 + 2646*B*a**5*b**5*d**4*e**5 + 2205*B*a**4*b**6*d**5*e**4 + 840*B*a**3*b*
*7*d**6*e**3 + 135*B*a**2*b**8*d**7*e**2 + 15*B*a*b**9*d**8*e/2 + B*b**10*d**9/1
2) + x**11*(10*A*a**9*b*e**9/11 + 405*A*a**8*b**2*d*e**8/11 + 4320*A*a**7*b**3*d
**2*e**7/11 + 17640*A*a**6*b**4*d**3*e**6/11 + 31752*A*a**5*b**5*d**4*e**5/11 +
26460*A*a**4*b**6*d**5*e**4/11 + 10080*A*a**3*b**7*d**6*e**3/11 + 1620*A*a**2*b*
*8*d**7*e**2/11 + 90*A*a*b**9*d**8*e/11 + A*b**10*d**9/11 + B*a**10*e**9/11 + 90
*B*a**9*b*d*e**8/11 + 1620*B*a**8*b**2*d**2*e**7/11 + 10080*B*a**7*b**3*d**3*e**
6/11 + 26460*B*a**6*b**4*d**4*e**5/11 + 31752*B*a**5*b**5*d**5*e**4/11 + 17640*B
*a**4*b**6*d**6*e**3/11 + 4320*B*a**3*b**7*d**7*e**2/11 + 405*B*a**2*b**8*d**8*e
/11 + 10*B*a*b**9*d**9/11) + x**10*(A*a**10*e**9/10 + 9*A*a**9*b*d*e**8 + 162*A*
a**8*b**2*d**2*e**7 + 1008*A*a**7*b**3*d**3*e**6 + 2646*A*a**6*b**4*d**4*e**5 +
15876*A*a**5*b**5*d**5*e**4/5 + 1764*A*a**4*b**6*d**6*e**3 + 432*A*a**3*b**7*d**
7*e**2 + 81*A*a**2*b**8*d**8*e/2 + A*a*b**9*d**9 + 9*B*a**10*d*e**8/10 + 36*B*a*
*9*b*d**2*e**7 + 378*B*a**8*b**2*d**3*e**6 + 1512*B*a**7*b**3*d**4*e**5 + 2646*B
*a**6*b**4*d**5*e**4 + 10584*B*a**5*b**5*d**6*e**3/5 + 756*B*a**4*b**6*d**7*e**2
 + 108*B*a**3*b**7*d**8*e + 9*B*a**2*b**8*d**9/2) + x**9*(A*a**10*d*e**8 + 40*A*
a**9*b*d**2*e**7 + 420*A*a**8*b**2*d**3*e**6 + 1680*A*a**7*b**3*d**4*e**5 + 2940
*A*a**6*b**4*d**5*e**4 + 2352*A*a**5*b**5*d**6*e**3 + 840*A*a**4*b**6*d**7*e**2
+ 120*A*a**3*b**7*d**8*e + 5*A*a**2*b**8*d**9 + 4*B*a**10*d**2*e**7 + 280*B*a**9
*b*d**3*e**6/3 + 630*B*a**8*b**2*d**4*e**5 + 1680*B*a**7*b**3*d**5*e**4 + 1960*B
*a**6*b**4*d**6*e**3 + 1008*B*a**5*b**5*d**7*e**2 + 210*B*a**4*b**6*d**8*e + 40*
B*a**3*b**7*d**9/3) + x**8*(9*A*a**10*d**2*e**7/2 + 105*A*a**9*b*d**3*e**6 + 283
5*A*a**8*b**2*d**4*e**5/4 + 1890*A*a**7*b**3*d**5*e**4 + 2205*A*a**6*b**4*d**6*e
**3 + 1134*A*a**5*b**5*d**7*e**2 + 945*A*a**4*b**6*d**8*e/4 + 15*A*a**3*b**7*d**
9 + 21*B*a**10*d**3*e**6/2 + 315*B*a**9*b*d**4*e**5/2 + 2835*B*a**8*b**2*d**5*e*
*4/4 + 1260*B*a**7*b**3*d**6*e**3 + 945*B*a**6*b**4*d**7*e**2 + 567*B*a**5*b**5*
d**8*e/2 + 105*B*a**4*b**6*d**9/4) + x**7*(12*A*a**10*d**3*e**6 + 180*A*a**9*b*d
**4*e**5 + 810*A*a**8*b**2*d**5*e**4 + 1440*A*a**7*b**3*d**6*e**3 + 1080*A*a**6*
b**4*d**7*e**2 + 324*A*a**5*b**5*d**8*e + 30*A*a**4*b**6*d**9 + 18*B*a**10*d**4*
e**5 + 180*B*a**9*b*d**5*e**4 + 540*B*a**8*b**2*d**6*e**3 + 4320*B*a**7*b**3*d**
7*e**2/7 + 270*B*a**6*b**4*d**8*e + 36*B*a**5*b**5*d**9) + x**6*(21*A*a**10*d**4
*e**5 + 210*A*a**9*b*d**5*e**4 + 630*A*a**8*b**2*d**6*e**3 + 720*A*a**7*b**3*d**
7*e**2 + 315*A*a**6*b**4*d**8*e + 42*A*a**5*b**5*d**9 + 21*B*a**10*d**5*e**4 + 1
40*B*a**9*b*d**6*e**3 + 270*B*a**8*b**2*d**7*e**2 + 180*B*a**7*b**3*d**8*e + 35*
B*a**6*b**4*d**9) + x**5*(126*A*a**10*d**5*e**4/5 + 168*A*a**9*b*d**6*e**3 + 324
*A*a**8*b**2*d**7*e**2 + 216*A*a**7*b**3*d**8*e + 42*A*a**6*b**4*d**9 + 84*B*a**
10*d**6*e**3/5 + 72*B*a**9*b*d**7*e**2 + 81*B*a**8*b**2*d**8*e + 24*B*a**7*b**3*
d**9) + x**4*(21*A*a**10*d**6*e**3 + 90*A*a**9*b*d**7*e**2 + 405*A*a**8*b**2*d**
8*e/4 + 30*A*a**7*b**3*d**9 + 9*B*a**10*d**7*e**2 + 45*B*a**9*b*d**8*e/2 + 45*B*
a**8*b**2*d**9/4) + x**3*(12*A*a**10*d**7*e**2 + 30*A*a**9*b*d**8*e + 15*A*a**8*
b**2*d**9 + 3*B*a**10*d**8*e + 10*B*a**9*b*d**9/3) + x**2*(9*A*a**10*d**8*e/2 +
5*A*a**9*b*d**9 + B*a**10*d**9/2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211624, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^10*(e*x + d)^9,x, algorithm="giac")

[Out]

Done

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