3.2334 \(\int (A+B x) (d+e x)^3 \left (a+b x+c x^2\right )^3 \, dx\)

Optimal. Leaf size=555 \[ -\frac{(d+e x)^7 \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{7 e^8}-\frac{c (d+e x)^9 \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{3 e^8}-\frac{(d+e x)^6 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{2 e^8}-\frac{(d+e x)^8 \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{8 e^8}-\frac{(d+e x)^5 \left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{5 e^8}-\frac{(d+e x)^4 (B d-A e) \left (a e^2-b d e+c d^2\right )^3}{4 e^8}-\frac{c^2 (d+e x)^{10} (-A c e-3 b B e+7 B c d)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8} \]

[Out]

-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/(4*e^8) - ((c*d^2 - b*d*e +
a*e^2)^2*(3*A*e*(2*c*d - b*e) - B*(7*c*d^2 - e*(4*b*d - a*e)))*(d + e*x)^5)/(5*
e^8) - ((c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2
*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^6)/(2*e^
8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*
c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2
*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^7)/(7*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 +
3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^
2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^8)/(8*e^8) - (c*(A*c*e*(2*c*d - b*e) - B*(
7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^9)/(3*e^8) - (c^2*(7*B*c*d -
3*b*B*e - A*c*e)*(d + e*x)^10)/(10*e^8) + (B*c^3*(d + e*x)^11)/(11*e^8)

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Rubi [A]  time = 3.98223, antiderivative size = 553, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ -\frac{(d+e x)^7 \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{7 e^8}-\frac{c (d+e x)^9 \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{3 e^8}-\frac{(d+e x)^6 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{2 e^8}-\frac{(d+e x)^8 \left (B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{8 e^8}+\frac{(d+e x)^5 \left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{5 e^8}-\frac{(d+e x)^4 (B d-A e) \left (a e^2-b d e+c d^2\right )^3}{4 e^8}-\frac{c^2 (d+e x)^{10} (-A c e-3 b B e+7 B c d)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8} \]

Antiderivative was successfully verified.

[In]  Int[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]

[Out]

-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/(4*e^8) + ((c*d^2 - b*d*e +
a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^5)/(5*
e^8) - ((c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2
*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^6)/(2*e^
8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*
c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2
*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^7)/(7*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 +
3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^
2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^8)/(8*e^8) - (c*(A*c*e*(2*c*d - b*e) - B*(
7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^9)/(3*e^8) - (c^2*(7*B*c*d -
3*b*B*e - A*c*e)*(d + e*x)^10)/(10*e^8) + (B*c^3*(d + e*x)^11)/(11*e^8)

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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)*(e*x+d)**3*(c*x**2+b*x+a)**3,x)

[Out]

Timed out

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Mathematica [A]  time = 0.972851, size = 715, normalized size = 1.29 \[ a^3 A d^3 x+\frac{1}{4} x^4 \left (A \left (a^2 e \left (a e^2+9 c d^2\right )+9 a b^2 d^2 e+3 a b d \left (3 a e^2+2 c d^2\right )+b^3 d^3\right )+3 a B d \left (3 a b d e+a \left (a e^2+c d^2\right )+b^2 d^2\right )\right )+\frac{1}{2} a^2 d^2 x^2 (3 A (a e+b d)+a B d)+\frac{1}{3} c e x^9 \left (B \left (c e (a e+3 b d)+b^2 e^2+c^2 d^2\right )+A c e (b e+c d)\right )+a d x^3 \left (A \left (3 a b d e+a \left (a e^2+c d^2\right )+b^2 d^2\right )+a B d (a e+b d)\right )+\frac{1}{8} x^8 \left (3 A c e \left (c e (a e+3 b d)+b^2 e^2+c^2 d^2\right )+B \left (9 c^2 d e (a e+b d)+3 b c e^2 (2 a e+3 b d)+b^3 e^3+c^3 d^3\right )\right )+\frac{1}{7} x^7 \left (3 b^2 e \left (a B e^2+3 A c d e+3 B c d^2\right )+3 b c \left (2 a A e^3+6 a B d e^2+3 A c d^2 e+B c d^3\right )+c \left (A c d \left (9 a e^2+c d^2\right )+3 a B e \left (a e^2+3 c d^2\right )\right )+b^3 e^2 (A e+3 B d)\right )+\frac{1}{2} x^6 \left (b^2 \left (a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right )+A b c d \left (6 a e^2+c d^2\right )+a c \left (a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right )+a b B e \left (a e^2+6 c d^2\right )+b^3 d e (A e+B d)\right )+\frac{1}{5} x^5 \left (3 b^2 d \left (3 a A e^2+3 a B d e+A c d^2\right )+3 a b \left (a A e^3+3 a B d e^2+6 A c d^2 e+2 B c d^3\right )+a \left (3 A c d \left (3 a e^2+c d^2\right )+a B e \left (a e^2+9 c d^2\right )\right )+b^3 d^2 (3 A e+B d)\right )+\frac{1}{10} c^2 e^2 x^{10} (A c e+3 B (b e+c d))+\frac{1}{11} B c^3 e^3 x^{11} \]

Antiderivative was successfully verified.

[In]  Integrate[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]

[Out]

a^3*A*d^3*x + (a^2*d^2*(a*B*d + 3*A*(b*d + a*e))*x^2)/2 + a*d*(a*B*d*(b*d + a*e)
+ A*(b^2*d^2 + 3*a*b*d*e + a*(c*d^2 + a*e^2)))*x^3 + ((3*a*B*d*(b^2*d^2 + 3*a*b
*d*e + a*(c*d^2 + a*e^2)) + A*(b^3*d^3 + 9*a*b^2*d^2*e + a^2*e*(9*c*d^2 + a*e^2)
+ 3*a*b*d*(2*c*d^2 + 3*a*e^2)))*x^4)/4 + ((b^3*d^2*(B*d + 3*A*e) + 3*b^2*d*(A*c
*d^2 + 3*a*B*d*e + 3*a*A*e^2) + 3*a*b*(2*B*c*d^3 + 6*A*c*d^2*e + 3*a*B*d*e^2 + a
*A*e^3) + a*(a*B*e*(9*c*d^2 + a*e^2) + 3*A*c*d*(c*d^2 + 3*a*e^2)))*x^5)/5 + ((b^
3*d*e*(B*d + A*e) + a*b*B*e*(6*c*d^2 + a*e^2) + A*b*c*d*(c*d^2 + 6*a*e^2) + b^2*
(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3) + a*c*(B*c*d^3 + 3*A*c*d^2*e + 3
*a*B*d*e^2 + a*A*e^3))*x^6)/2 + ((b^3*e^2*(3*B*d + A*e) + 3*b^2*e*(3*B*c*d^2 + 3
*A*c*d*e + a*B*e^2) + 3*b*c*(B*c*d^3 + 3*A*c*d^2*e + 6*a*B*d*e^2 + 2*a*A*e^3) +
c*(3*a*B*e*(3*c*d^2 + a*e^2) + A*c*d*(c*d^2 + 9*a*e^2)))*x^7)/7 + ((3*A*c*e*(c^2
*d^2 + b^2*e^2 + c*e*(3*b*d + a*e)) + B*(c^3*d^3 + b^3*e^3 + 9*c^2*d*e*(b*d + a*
e) + 3*b*c*e^2*(3*b*d + 2*a*e)))*x^8)/8 + (c*e*(A*c*e*(c*d + b*e) + B*(c^2*d^2 +
b^2*e^2 + c*e*(3*b*d + a*e)))*x^9)/3 + (c^2*e^2*(A*c*e + 3*B*(c*d + b*e))*x^10)
/10 + (B*c^3*e^3*x^11)/11

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Maple [A]  time = 0., size = 819, normalized size = 1.5 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a)^3,x)

[Out]

1/11*B*c^3*e^3*x^11+1/10*((A*e^3+3*B*d*e^2)*c^3+3*B*e^3*b*c^2)*x^10+1/9*((3*A*d*
e^2+3*B*d^2*e)*c^3+3*(A*e^3+3*B*d*e^2)*b*c^2+B*e^3*(a*c^2+2*b^2*c+c*(2*a*c+b^2))
)*x^9+1/8*((3*A*d^2*e+B*d^3)*c^3+3*(3*A*d*e^2+3*B*d^2*e)*b*c^2+(A*e^3+3*B*d*e^2)
*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+B*e^3*(4*a*b*c+b*(2*a*c+b^2)))*x^8+1/7*(A*c^3*d^3
+3*(3*A*d^2*e+B*d^3)*b*c^2+(3*A*d*e^2+3*B*d^2*e)*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+(
A*e^3+3*B*d*e^2)*(4*a*b*c+b*(2*a*c+b^2))+B*e^3*(a*(2*a*c+b^2)+2*b^2*a+c*a^2))*x^
7+1/6*(3*A*d^3*b*c^2+(3*A*d^2*e+B*d^3)*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+(3*A*d*e^2+
3*B*d^2*e)*(4*a*b*c+b*(2*a*c+b^2))+(A*e^3+3*B*d*e^2)*(a*(2*a*c+b^2)+2*b^2*a+c*a^
2)+3*B*e^3*a^2*b)*x^6+1/5*(A*d^3*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+(3*A*d^2*e+B*d^3)
*(4*a*b*c+b*(2*a*c+b^2))+(3*A*d*e^2+3*B*d^2*e)*(a*(2*a*c+b^2)+2*b^2*a+c*a^2)+3*(
A*e^3+3*B*d*e^2)*a^2*b+B*e^3*a^3)*x^5+1/4*(A*d^3*(4*a*b*c+b*(2*a*c+b^2))+(3*A*d^
2*e+B*d^3)*(a*(2*a*c+b^2)+2*b^2*a+c*a^2)+3*(3*A*d*e^2+3*B*d^2*e)*a^2*b+(A*e^3+3*
B*d*e^2)*a^3)*x^4+1/3*(A*d^3*(a*(2*a*c+b^2)+2*b^2*a+c*a^2)+3*(3*A*d^2*e+B*d^3)*a
^2*b+(3*A*d*e^2+3*B*d^2*e)*a^3)*x^3+1/2*(3*A*d^3*a^2*b+(3*A*d^2*e+B*d^3)*a^3)*x^
2+A*d^3*a^3*x

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Maxima [A]  time = 0.695128, size = 963, normalized size = 1.74 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + b*x + a)^3*(B*x + A)*(e*x + d)^3,x, algorithm="maxima")

[Out]

1/11*B*c^3*e^3*x^11 + 1/10*(3*B*c^3*d*e^2 + (3*B*b*c^2 + A*c^3)*e^3)*x^10 + 1/3*
(B*c^3*d^2*e + (3*B*b*c^2 + A*c^3)*d*e^2 + (B*b^2*c + (B*a + A*b)*c^2)*e^3)*x^9
+ 1/8*(B*c^3*d^3 + 3*(3*B*b*c^2 + A*c^3)*d^2*e + 9*(B*b^2*c + (B*a + A*b)*c^2)*d
*e^2 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^3)*x^8 + A*a^3*d^3*x + 1/7*
((3*B*b*c^2 + A*c^3)*d^3 + 9*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e + 3*(B*b^3 + 3*A*
a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^2 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*
c)*e^3)*x^7 + 1/2*((B*b^2*c + (B*a + A*b)*c^2)*d^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B
*a*b + A*b^2)*c)*d^2*e + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^2 + (B*
a^2*b + A*a*b^2 + A*a^2*c)*e^3)*x^6 + 1/5*((B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b
^2)*c)*d^3 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e + 9*(B*a^2*b +
A*a*b^2 + A*a^2*c)*d*e^2 + (B*a^3 + 3*A*a^2*b)*e^3)*x^5 + 1/4*(A*a^3*e^3 + (3*B*
a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3 + 9*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2
*e + 3*(B*a^3 + 3*A*a^2*b)*d*e^2)*x^4 + (A*a^3*d*e^2 + (B*a^2*b + A*a*b^2 + A*a^
2*c)*d^3 + (B*a^3 + 3*A*a^2*b)*d^2*e)*x^3 + 1/2*(3*A*a^3*d^2*e + (B*a^3 + 3*A*a^
2*b)*d^3)*x^2

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Fricas [A]  time = 0.242892, size = 1, normalized size = 0. \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + b*x + a)^3*(B*x + A)*(e*x + d)^3,x, algorithm="fricas")

[Out]

1/11*x^11*e^3*c^3*B + 3/10*x^10*e^2*d*c^3*B + 3/10*x^10*e^3*c^2*b*B + 1/10*x^10*
e^3*c^3*A + 1/3*x^9*e*d^2*c^3*B + x^9*e^2*d*c^2*b*B + 1/3*x^9*e^3*c*b^2*B + 1/3*
x^9*e^3*c^2*a*B + 1/3*x^9*e^2*d*c^3*A + 1/3*x^9*e^3*c^2*b*A + 1/8*x^8*d^3*c^3*B
+ 9/8*x^8*e*d^2*c^2*b*B + 9/8*x^8*e^2*d*c*b^2*B + 1/8*x^8*e^3*b^3*B + 9/8*x^8*e^
2*d*c^2*a*B + 3/4*x^8*e^3*c*b*a*B + 3/8*x^8*e*d^2*c^3*A + 9/8*x^8*e^2*d*c^2*b*A
+ 3/8*x^8*e^3*c*b^2*A + 3/8*x^8*e^3*c^2*a*A + 3/7*x^7*d^3*c^2*b*B + 9/7*x^7*e*d^
2*c*b^2*B + 3/7*x^7*e^2*d*b^3*B + 9/7*x^7*e*d^2*c^2*a*B + 18/7*x^7*e^2*d*c*b*a*B
+ 3/7*x^7*e^3*b^2*a*B + 3/7*x^7*e^3*c*a^2*B + 1/7*x^7*d^3*c^3*A + 9/7*x^7*e*d^2
*c^2*b*A + 9/7*x^7*e^2*d*c*b^2*A + 1/7*x^7*e^3*b^3*A + 9/7*x^7*e^2*d*c^2*a*A + 6
/7*x^7*e^3*c*b*a*A + 1/2*x^6*d^3*c*b^2*B + 1/2*x^6*e*d^2*b^3*B + 1/2*x^6*d^3*c^2
*a*B + 3*x^6*e*d^2*c*b*a*B + 3/2*x^6*e^2*d*b^2*a*B + 3/2*x^6*e^2*d*c*a^2*B + 1/2
*x^6*e^3*b*a^2*B + 1/2*x^6*d^3*c^2*b*A + 3/2*x^6*e*d^2*c*b^2*A + 1/2*x^6*e^2*d*b
^3*A + 3/2*x^6*e*d^2*c^2*a*A + 3*x^6*e^2*d*c*b*a*A + 1/2*x^6*e^3*b^2*a*A + 1/2*x
^6*e^3*c*a^2*A + 1/5*x^5*d^3*b^3*B + 6/5*x^5*d^3*c*b*a*B + 9/5*x^5*e*d^2*b^2*a*B
+ 9/5*x^5*e*d^2*c*a^2*B + 9/5*x^5*e^2*d*b*a^2*B + 1/5*x^5*e^3*a^3*B + 3/5*x^5*d
^3*c*b^2*A + 3/5*x^5*e*d^2*b^3*A + 3/5*x^5*d^3*c^2*a*A + 18/5*x^5*e*d^2*c*b*a*A
+ 9/5*x^5*e^2*d*b^2*a*A + 9/5*x^5*e^2*d*c*a^2*A + 3/5*x^5*e^3*b*a^2*A + 3/4*x^4*
d^3*b^2*a*B + 3/4*x^4*d^3*c*a^2*B + 9/4*x^4*e*d^2*b*a^2*B + 3/4*x^4*e^2*d*a^3*B
+ 1/4*x^4*d^3*b^3*A + 3/2*x^4*d^3*c*b*a*A + 9/4*x^4*e*d^2*b^2*a*A + 9/4*x^4*e*d^
2*c*a^2*A + 9/4*x^4*e^2*d*b*a^2*A + 1/4*x^4*e^3*a^3*A + x^3*d^3*b*a^2*B + x^3*e*
d^2*a^3*B + x^3*d^3*b^2*a*A + x^3*d^3*c*a^2*A + 3*x^3*e*d^2*b*a^2*A + x^3*e^2*d*
a^3*A + 1/2*x^2*d^3*a^3*B + 3/2*x^2*d^3*b*a^2*A + 3/2*x^2*e*d^2*a^3*A + x*d^3*a^
3*A

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Sympy [A]  time = 0.53916, size = 1080, normalized size = 1.95 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x+a)**3,x)

[Out]

A*a**3*d**3*x + B*c**3*e**3*x**11/11 + x**10*(A*c**3*e**3/10 + 3*B*b*c**2*e**3/1
0 + 3*B*c**3*d*e**2/10) + x**9*(A*b*c**2*e**3/3 + A*c**3*d*e**2/3 + B*a*c**2*e**
3/3 + B*b**2*c*e**3/3 + B*b*c**2*d*e**2 + B*c**3*d**2*e/3) + x**8*(3*A*a*c**2*e*
*3/8 + 3*A*b**2*c*e**3/8 + 9*A*b*c**2*d*e**2/8 + 3*A*c**3*d**2*e/8 + 3*B*a*b*c*e
**3/4 + 9*B*a*c**2*d*e**2/8 + B*b**3*e**3/8 + 9*B*b**2*c*d*e**2/8 + 9*B*b*c**2*d
**2*e/8 + B*c**3*d**3/8) + x**7*(6*A*a*b*c*e**3/7 + 9*A*a*c**2*d*e**2/7 + A*b**3
*e**3/7 + 9*A*b**2*c*d*e**2/7 + 9*A*b*c**2*d**2*e/7 + A*c**3*d**3/7 + 3*B*a**2*c
*e**3/7 + 3*B*a*b**2*e**3/7 + 18*B*a*b*c*d*e**2/7 + 9*B*a*c**2*d**2*e/7 + 3*B*b*
*3*d*e**2/7 + 9*B*b**2*c*d**2*e/7 + 3*B*b*c**2*d**3/7) + x**6*(A*a**2*c*e**3/2 +
A*a*b**2*e**3/2 + 3*A*a*b*c*d*e**2 + 3*A*a*c**2*d**2*e/2 + A*b**3*d*e**2/2 + 3*
A*b**2*c*d**2*e/2 + A*b*c**2*d**3/2 + B*a**2*b*e**3/2 + 3*B*a**2*c*d*e**2/2 + 3*
B*a*b**2*d*e**2/2 + 3*B*a*b*c*d**2*e + B*a*c**2*d**3/2 + B*b**3*d**2*e/2 + B*b**
2*c*d**3/2) + x**5*(3*A*a**2*b*e**3/5 + 9*A*a**2*c*d*e**2/5 + 9*A*a*b**2*d*e**2/
5 + 18*A*a*b*c*d**2*e/5 + 3*A*a*c**2*d**3/5 + 3*A*b**3*d**2*e/5 + 3*A*b**2*c*d**
3/5 + B*a**3*e**3/5 + 9*B*a**2*b*d*e**2/5 + 9*B*a**2*c*d**2*e/5 + 9*B*a*b**2*d**
2*e/5 + 6*B*a*b*c*d**3/5 + B*b**3*d**3/5) + x**4*(A*a**3*e**3/4 + 9*A*a**2*b*d*e
**2/4 + 9*A*a**2*c*d**2*e/4 + 9*A*a*b**2*d**2*e/4 + 3*A*a*b*c*d**3/2 + A*b**3*d*
*3/4 + 3*B*a**3*d*e**2/4 + 9*B*a**2*b*d**2*e/4 + 3*B*a**2*c*d**3/4 + 3*B*a*b**2*
d**3/4) + x**3*(A*a**3*d*e**2 + 3*A*a**2*b*d**2*e + A*a**2*c*d**3 + A*a*b**2*d**
3 + B*a**3*d**2*e + B*a**2*b*d**3) + x**2*(3*A*a**3*d**2*e/2 + 3*A*a**2*b*d**3/2
+ B*a**3*d**3/2)

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GIAC/XCAS [A]  time = 0.28072, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + b*x + a)^3*(B*x + A)*(e*x + d)^3,x, algorithm="giac")

[Out]

Done