3.2346 \(\int \frac{(A+B x) \left (a+b x+c x^2\right )^3}{(d+e x)^9} \, dx\)

Optimal. Leaf size=550 \[ \frac{A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )}{5 e^8 (d+e x)^5}+\frac{c \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{e^8 (d+e x)^3}+\frac{\left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{2 e^8 (d+e x)^6}+\frac{B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )}{4 e^8 (d+e x)^4}+\frac{\left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{7 e^8 (d+e x)^7}+\frac{(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{8 e^8 (d+e x)^8}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)} \]

[Out]

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

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Rubi [A]  time = 3.58001, antiderivative size = 548, 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 \[ \frac{A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )}{5 e^8 (d+e x)^5}+\frac{c \left (A c e (2 c d-b e)-B \left (-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right )\right )}{e^8 (d+e x)^3}+\frac{\left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{2 e^8 (d+e x)^6}+\frac{B \left (-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right )-3 A c e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )}{4 e^8 (d+e x)^4}-\frac{\left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{7 e^8 (d+e x)^7}+\frac{(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{8 e^8 (d+e x)^8}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)} \]

Antiderivative was successfully verified.

[In]  Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^9,x]

[Out]

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

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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)*(c*x**2+b*x+a)**3/(e*x+d)**9,x)

[Out]

Timed out

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Mathematica [A]  time = 3.83033, size = 847, normalized size = 1.54 \[ -\frac{A e \left (5 \left (d^6+8 e x d^5+28 e^2 x^2 d^4+56 e^3 x^3 d^3+70 e^4 x^4 d^2+56 e^5 x^5 d+28 e^6 x^6\right ) c^3+e \left (3 a e \left (d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right )+5 b \left (d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right )\right ) c^2+e^2 \left (3 \left (d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right ) b^2+6 a e \left (d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right ) b+5 a^2 e^2 \left (d^2+8 e x d+28 e^2 x^2\right )\right ) c+e^3 \left (\left (d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right ) b^3+5 a e \left (d^2+8 e x d+28 e^2 x^2\right ) b^2+15 a^2 e^2 (d+8 e x) b+35 a^3 e^3\right )\right )+B \left (35 \left (d^7+8 e x d^6+28 e^2 x^2 d^5+56 e^3 x^3 d^4+70 e^4 x^4 d^3+56 e^5 x^5 d^2+28 e^6 x^6 d+8 e^7 x^7\right ) c^3+5 e \left (a e \left (d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right )+3 b \left (d^6+8 e x d^5+28 e^2 x^2 d^4+56 e^3 x^3 d^3+70 e^4 x^4 d^2+56 e^5 x^5 d+28 e^6 x^6\right )\right ) c^2+e^2 \left (5 \left (d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right ) b^2+6 a e \left (d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right ) b+3 a^2 e^2 \left (d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right )\right ) c+e^3 \left (\left (d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right ) b^3+3 a e \left (d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right ) b^2+5 a^2 e^2 \left (d^2+8 e x d+28 e^2 x^2\right ) b+5 a^3 e^3 (d+8 e x)\right )\right )}{280 e^8 (d+e x)^8} \]

Antiderivative was successfully verified.

[In]  Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^9,x]

[Out]

-(A*e*(5*c^3*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4
+ 56*d*e^5*x^5 + 28*e^6*x^6) + e^3*(35*a^3*e^3 + 15*a^2*b*e^2*(d + 8*e*x) + 5*a
*b^2*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + b^3*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e
^3*x^3)) + c*e^2*(5*a^2*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 6*a*b*e*(d^3 + 8*d^2*
e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 3*b^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*
d*e^3*x^3 + 70*e^4*x^4)) + c^2*e*(3*a*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d
*e^3*x^3 + 70*e^4*x^4) + 5*b*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3
+ 70*d*e^4*x^4 + 56*e^5*x^5))) + B*(35*c^3*(d^7 + 8*d^6*e*x + 28*d^5*e^2*x^2 + 5
6*d^4*e^3*x^3 + 70*d^3*e^4*x^4 + 56*d^2*e^5*x^5 + 28*d*e^6*x^6 + 8*e^7*x^7) + e^
3*(5*a^3*e^3*(d + 8*e*x) + 5*a^2*b*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*a*b^2*e*
(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + b^3*(d^4 + 8*d^3*e*x + 28*d^2*e^
2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + c*e^2*(3*a^2*e^2*(d^3 + 8*d^2*e*x + 28*d*e
^2*x^2 + 56*e^3*x^3) + 6*a*b*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3
+ 70*e^4*x^4) + 5*b^2*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*
e^4*x^4 + 56*e^5*x^5)) + 5*c^2*e*(a*e*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2
*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + 3*b*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 +
56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6))))/(280*e^8*(d + e*
x)^8)

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Maple [A]  time = 0.013, size = 1067, normalized size = 1.9 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^9,x)

[Out]

-c*(A*b*c*e^2-2*A*c^2*d*e+B*a*c*e^2+B*b^2*e^2-6*B*b*c*d*e+7*B*c^2*d^2)/e^8/(e*x+
d)^3-1/8*(A*a^3*e^7-3*A*a^2*b*d*e^6+3*A*a^2*c*d^2*e^5+3*A*a*b^2*d^2*e^5-6*A*a*b*
c*d^3*e^4+3*A*a*c^2*d^4*e^3-A*b^3*d^3*e^4+3*A*b^2*c*d^4*e^3-3*A*b*c^2*d^5*e^2+A*
c^3*d^6*e-B*a^3*d*e^6+3*B*a^2*b*d^2*e^5-3*B*a^2*c*d^3*e^4-3*B*a*b^2*d^3*e^4+6*B*
a*b*c*d^4*e^3-3*B*a*c^2*d^5*e^2+B*b^3*d^4*e^3-3*B*b^2*c*d^5*e^2+3*B*b*c^2*d^6*e-
B*c^3*d^7)/e^8/(e*x+d)^8-B*c^3/e^8/(e*x+d)-1/4*(3*A*a*c^2*e^3+3*A*b^2*c*e^3-15*A
*b*c^2*d*e^2+15*A*c^3*d^2*e+6*B*a*b*c*e^3-15*B*a*c^2*d*e^2+B*b^3*e^3-15*B*b^2*c*
d*e^2+45*B*b*c^2*d^2*e-35*B*c^3*d^3)/e^8/(e*x+d)^4-1/2*c^2*(A*c*e+3*B*b*e-7*B*c*
d)/e^8/(e*x+d)^2-1/5*(6*A*a*b*c*e^4-12*A*a*c^2*d*e^3+A*b^3*e^4-12*A*b^2*c*d*e^3+
30*A*b*c^2*d^2*e^2-20*A*c^3*d^3*e+3*B*a^2*c*e^4+3*B*a*b^2*e^4-24*B*a*b*c*d*e^3+3
0*B*a*c^2*d^2*e^2-4*B*b^3*d*e^3+30*B*b^2*c*d^2*e^2-60*B*b*c^2*d^3*e+35*B*c^3*d^4
)/e^8/(e*x+d)^5-1/6*(3*A*a^2*c*e^5+3*A*a*b^2*e^5-18*A*a*b*c*d*e^4+18*A*a*c^2*d^2
*e^3-3*A*b^3*d*e^4+18*A*b^2*c*d^2*e^3-30*A*b*c^2*d^3*e^2+15*A*c^3*d^4*e+3*B*a^2*
b*e^5-9*B*a^2*c*d*e^4-9*B*a*b^2*d*e^4+36*B*a*b*c*d^2*e^3-30*B*a*c^2*d^3*e^2+6*B*
b^3*d^2*e^3-30*B*b^2*c*d^3*e^2+45*B*b*c^2*d^4*e-21*B*c^3*d^5)/e^8/(e*x+d)^6-1/7*
(3*A*a^2*b*e^6-6*A*a^2*c*d*e^5-6*A*a*b^2*d*e^5+18*A*a*b*c*d^2*e^4-12*A*a*c^2*d^3
*e^3+3*A*b^3*d^2*e^4-12*A*b^2*c*d^3*e^3+15*A*b*c^2*d^4*e^2-6*A*c^3*d^5*e+B*a^3*e
^6-6*B*a^2*b*d*e^5+9*B*a^2*c*d^2*e^4+9*B*a*b^2*d^2*e^4-24*B*a*b*c*d^3*e^3+15*B*a
*c^2*d^4*e^2-4*B*b^3*d^3*e^3+15*B*b^2*c*d^4*e^2-18*B*b*c^2*d^5*e+7*B*c^3*d^6)/e^
8/(e*x+d)^7

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Maxima [A]  time = 0.744781, size = 1245, normalized size = 2.26 \[ \text{result too large to display} \]

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)^9,x, algorithm="maxima")

[Out]

-1/280*(280*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 35*A*a^3*e^7 + 5*(3*B*b*c^2 + A*c^3)*
d^6*e + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b
+ A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 5*(B
*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 5*(B*a^3 + 3*A*a^2*b)*d*e^6 + 140*(7*B*c^3
*d*e^6 + (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 280*(7*B*c^3*d^2*e^5 + (3*B*b*c^2 + A*c^
3)*d*e^6 + (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 70*(35*B*c^3*d^3*e^4 + 5*(3*B*
b*c^2 + A*c^3)*d^2*e^5 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + (B*b^3 + 3*A*a*c^
2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 56*(35*B*c^3*d^4*e^3 + 5*(3*B*b*c^2 + A*c^
3)*d^3*e^4 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + (B*b^3 + 3*A*a*c^2 + 3*(2*B
*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 +
28*(35*B*c^3*d^5*e^2 + 5*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 5*(B*b^2*c + (B*a + A*b)*
c^2)*d^3*e^4 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2
+ A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^
2 + 8*(35*B*c^3*d^6*e + 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 5*(B*b^2*c + (B*a + A*b)
*c^2)*d^4*e^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2
+ A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^
6 + 5*(B*a^3 + 3*A*a^2*b)*e^7)*x)/(e^16*x^8 + 8*d*e^15*x^7 + 28*d^2*e^14*x^6 + 5
6*d^3*e^13*x^5 + 70*d^4*e^12*x^4 + 56*d^5*e^11*x^3 + 28*d^6*e^10*x^2 + 8*d^7*e^9
*x + d^8*e^8)

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Fricas [A]  time = 0.263543, size = 1245, normalized size = 2.26 \[ \text{result too large to display} \]

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)^9,x, algorithm="fricas")

[Out]

-1/280*(280*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 35*A*a^3*e^7 + 5*(3*B*b*c^2 + A*c^3)*
d^6*e + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b
+ A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 5*(B
*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 5*(B*a^3 + 3*A*a^2*b)*d*e^6 + 140*(7*B*c^3
*d*e^6 + (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 280*(7*B*c^3*d^2*e^5 + (3*B*b*c^2 + A*c^
3)*d*e^6 + (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 70*(35*B*c^3*d^3*e^4 + 5*(3*B*
b*c^2 + A*c^3)*d^2*e^5 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + (B*b^3 + 3*A*a*c^
2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 56*(35*B*c^3*d^4*e^3 + 5*(3*B*b*c^2 + A*c^
3)*d^3*e^4 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + (B*b^3 + 3*A*a*c^2 + 3*(2*B
*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 +
28*(35*B*c^3*d^5*e^2 + 5*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 5*(B*b^2*c + (B*a + A*b)*
c^2)*d^3*e^4 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2
+ A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^
2 + 8*(35*B*c^3*d^6*e + 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 5*(B*b^2*c + (B*a + A*b)
*c^2)*d^4*e^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2
+ A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^
6 + 5*(B*a^3 + 3*A*a^2*b)*e^7)*x)/(e^16*x^8 + 8*d*e^15*x^7 + 28*d^2*e^14*x^6 + 5
6*d^3*e^13*x^5 + 70*d^4*e^12*x^4 + 56*d^5*e^11*x^3 + 28*d^6*e^10*x^2 + 8*d^7*e^9
*x + d^8*e^8)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**9,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.278959, 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)^9,x, algorithm="giac")

[Out]

Done