3.2341 \(\int \frac{(A+B x) \left (a+b x+c x^2\right )^3}{(d+e x)^4} \, dx\)
Optimal. Leaf size=521 \[ -\frac{\log (d+e x) \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{e^8}-\frac{x \left (B (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-A c e \left (-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right )\right )}{e^7}-\frac{c x^2 \left (A c e (4 c d-3 b e)-B \left (-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right )\right )}{2 e^6}+\frac{3 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (d+e x)}+\frac{\left (a e^2-b d e+c d^2\right )^2 \left (3 A e (2 c d-b e)-B \left (7 c d^2-e (4 b d-a e)\right )\right )}{2 e^8 (d+e x)^2}+\frac{(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{3 e^8 (d+e x)^3}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}+\frac{B c^3 x^4}{4 e^4} \]
[Out]
-(((B*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - A*c*e*(10*c
^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x)/e^7) - (c*(A*c*e*(4*c*d - 3*b*e) -
B*(10*c^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x^2)/(2*e^6) - (c^2*(4*B*c*d
- 3*b*B*e - A*c*e)*x^3)/(3*e^5) + (B*c^3*x^4)/(4*e^4) + ((B*d - A*e)*(c*d^2 - b*
d*e + a*e^2)^3)/(3*e^8*(d + e*x)^3) + ((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))))/(2*e^8*(d + e*x)^2) + (3*(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))))/(e^8*(d + e*x)) - ((A*e*(2*c*d - b*e)*(1
0*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)
))*Log[d + e*x])/e^8
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Rubi [A] time = 3.20531, antiderivative size = 519, 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
\[ -\frac{\log (d+e x) \left (A e (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right )\right )}{e^8}-\frac{x \left (B (2 c d-b e) \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )-A c e \left (-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right )\right )}{e^7}-\frac{c x^2 \left (A c e (4 c d-3 b e)-B \left (-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right )\right )}{2 e^6}+\frac{3 \left (a e^2-b d e+c d^2\right ) \left (B \left (-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )\right )}{e^8 (d+e x)}-\frac{\left (a e^2-b d e+c d^2\right )^2 \left (-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right )}{2 e^8 (d+e x)^2}+\frac{(B d-A e) \left (a e^2-b d e+c d^2\right )^3}{3 e^8 (d+e x)^3}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}+\frac{B c^3 x^4}{4 e^4} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]
[Out]
-(((B*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - A*c*e*(10*c
^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x)/e^7) - (c*(A*c*e*(4*c*d - 3*b*e) -
B*(10*c^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x^2)/(2*e^6) - (c^2*(4*B*c*d
- 3*b*B*e - A*c*e)*x^3)/(3*e^5) + (B*c^3*x^4)/(4*e^4) + ((B*d - A*e)*(c*d^2 - b*
d*e + a*e^2)^3)/(3*e^8*(d + e*x)^3) - ((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)))/(2*e^8*(d + e*x)^2) + (3*(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))))/(e^8*(d + e*x)) - ((A*e*(2*c*d - b*e)*(1
0*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)
))*Log[d + e*x])/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)*(c*x**2+b*x+a)**3/(e*x+d)**4,x)
[Out]
Timed out
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Mathematica [A] time = 0.821223, size = 488, normalized size = 0.94 \[ \frac{12 \log (d+e x) \left (B \left (3 c e^2 \left (a^2 e^2-8 a b d e+10 b^2 d^2\right )+b^2 e^3 (3 a e-4 b d)+30 c^2 d^2 e (a e-2 b d)+35 c^3 d^4\right )+A e (b e-2 c d) \left (2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right )\right )+6 c e^2 x^2 \left (B \left (3 c e (a e-4 b d)+3 b^2 e^2+10 c^2 d^2\right )+A c e (3 b e-4 c d)\right )+12 e x \left (A c e \left (3 c e (a e-4 b d)+3 b^2 e^2+10 c^2 d^2\right )-B (2 c d-b e) \left (2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right )\right )+\frac{36 \left (e (a e-b d)+c d^2\right ) \left (B \left (c d e (3 a e-8 b d)+b e^2 (2 b d-a e)+7 c^2 d^3\right )-A e \left (c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right )\right )}{d+e x}-\frac{6 \left (e (a e-b d)+c d^2\right )^2 \left (B e (a e-4 b d)+3 A e (b e-2 c d)+7 B c d^2\right )}{(d+e x)^2}+\frac{4 (B d-A e) \left (e (a e-b d)+c d^2\right )^3}{(d+e x)^3}+4 c^2 e^3 x^3 (A c e+3 b B e-4 B c d)+3 B c^3 e^4 x^4}{12 e^8} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]
[Out]
(12*e*(A*c*e*(10*c^2*d^2 + 3*b^2*e^2 + 3*c*e*(-4*b*d + a*e)) - B*(2*c*d - b*e)*(
10*c^2*d^2 + b^2*e^2 + 2*c*e*(-5*b*d + 3*a*e)))*x + 6*c*e^2*(A*c*e*(-4*c*d + 3*b
*e) + B*(10*c^2*d^2 + 3*b^2*e^2 + 3*c*e*(-4*b*d + a*e)))*x^2 + 4*c^2*e^3*(-4*B*c
*d + 3*b*B*e + A*c*e)*x^3 + 3*B*c^3*e^4*x^4 + (4*(B*d - A*e)*(c*d^2 + e*(-(b*d)
+ a*e))^3)/(d + e*x)^3 - (6*(c*d^2 + e*(-(b*d) + a*e))^2*(7*B*c*d^2 + B*e*(-4*b*
d + a*e) + 3*A*e*(-2*c*d + b*e)))/(d + e*x)^2 + (36*(c*d^2 + e*(-(b*d) + a*e))*(
-(A*e*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e))) + B*(7*c^2*d^3 + b*e^2*(2*b*d
- a*e) + c*d*e*(-8*b*d + 3*a*e))))/(d + e*x) + 12*(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 + 30*c^2*d^2*e*(-2*b*d + a
*e) + b^2*e^3*(-4*b*d + 3*a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*Lo
g[d + e*x])/(12*e^8)
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Maple [B] time = 0.029, size = 1545, normalized size = 3. \[ \text{result too large to display} \]
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)^4,x)
[Out]
1/4*B*c^3*x^4/e^4-24/e^5*ln(e*x+d)*B*a*b*c*d+18/e^4/(e*x+d)*A*a*b*c*d-36/e^5/(e*
x+d)*B*a*b*c*d^2-9/e^4/(e*x+d)^2*A*a*b*c*d^2-6/e^5*B*x^2*b*c^2*d-12/e^5*A*b*c^2*
d*x+6/e^4*B*a*b*c*x-12/e^5*B*a*c^2*d*x-12/e^5*B*b^2*c*d*x+30/e^6*B*b*c^2*d^2*x+1
/e^2/(e*x+d)^3*A*d*a^2*b-1/e^3/(e*x+d)^3*A*d^2*a^2*c-1/e^5/(e*x+d)^3*A*a*c^2*d^4
-1/e^5/(e*x+d)^3*A*b^2*c*d^4+1/e^6/(e*x+d)^3*A*b*c^2*d^5-1/e^3/(e*x+d)^3*B*d^2*a
^2*b-1/e^3/(e*x+d)^3*A*d^2*a*b^2-12/e^5*ln(e*x+d)*A*a*c^2*d-12/e^5*ln(e*x+d)*A*b
^2*c*d+30/e^6*ln(e*x+d)*A*b*c^2*d^2-1/e^7/(e*x+d)^3*B*b*c^2*d^6+1/e^4/(e*x+d)^3*
B*d^3*a*b^2+1/e^6/(e*x+d)^3*B*a*c^2*d^5+1/e^6/(e*x+d)^3*B*b^2*c*d^5+1/e^4/(e*x+d
)^3*B*d^3*a^2*c+30/e^6*ln(e*x+d)*B*a*c^2*d^2+30/e^6*ln(e*x+d)*B*b^2*c*d^2-60/e^7
*ln(e*x+d)*B*b*c^2*d^3-18/e^5/(e*x+d)*A*a*c^2*d^2-18/e^5/(e*x+d)*A*b^2*c*d^2+6/e
^4*ln(e*x+d)*A*a*b*c+30/e^6/(e*x+d)*B*b^2*c*d^3-45/e^7/(e*x+d)*B*b*c^2*d^4+30/e^
6/(e*x+d)*A*b*c^2*d^3+9/e^4/(e*x+d)*B*a^2*c*d+9/e^4/(e*x+d)*B*a*b^2*d+30/e^6/(e*
x+d)*B*a*c^2*d^3-15/2/e^6/(e*x+d)^2*A*b*c^2*d^4+3/e^3/(e*x+d)^2*A*a*b^2*d+6/e^5/
(e*x+d)^2*A*a*c^2*d^3+6/e^5/(e*x+d)^2*A*b^2*c*d^3+3/e^3/(e*x+d)^2*A*a^2*c*d+3/e^
3/(e*x+d)^2*B*a^2*b*d-9/2/e^4/(e*x+d)^2*B*a^2*c*d^2-9/2/e^4/(e*x+d)^2*B*a*b^2*d^
2-15/2/e^6/(e*x+d)^2*B*b^2*c*d^4+9/e^7/(e*x+d)^2*B*b*c^2*d^5-15/2/e^6/(e*x+d)^2*
B*a*c^2*d^4-1/3/e/(e*x+d)^3*A*a^3+1/e^4*ln(e*x+d)*A*b^3-1/2/e^2/(e*x+d)^2*B*a^3+
1/3/e^4*A*x^3*c^3+1/e^4*B*b^3*x+3/e^7/(e*x+d)^2*A*c^3*d^5+2/e^5/(e*x+d)^2*B*b^3*
d^3-7/2/e^8/(e*x+d)^2*B*c^3*d^6+3/2/e^4*A*x^2*b*c^2-2/e^5*A*x^2*c^3*d+3/2/e^4*B*
x^2*a*c^2+3/2/e^4*B*x^2*b^2*c+5/e^6*B*x^2*c^3*d^2+3/e^4*A*a*c^2*x+3/e^4*A*b^2*c*
x+10/e^6*A*c^3*d^2*x-20/e^7*B*c^3*d^3*x+1/3/e^4/(e*x+d)^3*A*d^3*b^3-1/3/e^7/(e*x
+d)^3*A*c^3*d^6+1/3/e^2/(e*x+d)^3*B*d*a^3-1/3/e^5/(e*x+d)^3*B*b^3*d^4+1/3/e^8/(e
*x+d)^3*B*c^3*d^7+1/e^4*B*x^3*b*c^2-4/3/e^5*B*x^3*c^3*d+3/e^4*ln(e*x+d)*B*a*b^2-
4/e^5*ln(e*x+d)*B*b^3*d+35/e^8*ln(e*x+d)*B*c^3*d^4-3/e^3/(e*x+d)*A*a^2*c-3/e^3/(
e*x+d)*A*a*b^2+3/e^4/(e*x+d)*A*b^3*d-15/e^7/(e*x+d)*A*c^3*d^4-3/e^3/(e*x+d)*B*a^
2*b-6/e^5/(e*x+d)*B*b^3*d^2+21/e^8/(e*x+d)*B*c^3*d^5-3/2/e^2/(e*x+d)^2*A*a^2*b-3
/2/e^4/(e*x+d)^2*A*b^3*d^2-20/e^7*ln(e*x+d)*A*c^3*d^3+3/e^4*ln(e*x+d)*B*a^2*c+12
/e^5/(e*x+d)^2*B*a*b*c*d^3+2/e^4/(e*x+d)^3*A*d^3*a*b*c-2/e^5/(e*x+d)^3*B*a*b*c*d
^4
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Maxima [A] time = 0.722797, size = 1181, normalized size = 2.27 \[ \text{result too large to display} \]
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)^4,x, algorithm="maxima")
[Out]
1/6*(107*B*c^3*d^7 - 2*A*a^3*e^7 - 74*(3*B*b*c^2 + A*c^3)*d^6*e + 141*(B*b^2*c +
(B*a + A*b)*c^2)*d^5*e^2 - 26*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e
^3 + 11*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 6*(B*a^2*b + A*a*b
^2 + A*a^2*c)*d^2*e^5 - (B*a^3 + 3*A*a^2*b)*d*e^6 + 18*(7*B*c^3*d^5*e^2 - 5*(3*B
*b*c^2 + A*c^3)*d^4*e^3 + 10*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 2*(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 - (B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 3*(77*B*c^3*d^6*e - 54*(
3*B*b*c^2 + A*c^3)*d^5*e^2 + 105*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 20*(B*b^3
+ 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 9*(3*B*a*b^2 + A*b^3 + 3*(B*a^2
+ 2*A*a*b)*c)*d^2*e^5 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - (B*a^3 + 3*A*a^2
*b)*e^7)*x)/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8) + 1/12*(3*B*c^3*e^
3*x^4 - 4*(4*B*c^3*d*e^2 - (3*B*b*c^2 + A*c^3)*e^3)*x^3 + 6*(10*B*c^3*d^2*e - 4*
(3*B*b*c^2 + A*c^3)*d*e^2 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^3)*x^2 - 12*(20*B*c^
3*d^3 - 10*(3*B*b*c^2 + A*c^3)*d^2*e + 12*(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)/e^7 + (35*B*c^3*d^4 - 20*(3*B*
b*c^2 + A*c^3)*d^3*e + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^2 - 4*(B*b^3 + 3*A*a
*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c
)*e^4)*log(e*x + d)/e^8
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Fricas [A] time = 0.272552, size = 1848, normalized size = 3.55 \[ \text{result too large to display} \]
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)^4,x, algorithm="fricas")
[Out]
1/12*(3*B*c^3*e^7*x^7 + 214*B*c^3*d^7 - 4*A*a^3*e^7 - 148*(3*B*b*c^2 + A*c^3)*d^
6*e + 282*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 52*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a
*b + A*b^2)*c)*d^4*e^3 + 22*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4
- 12*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - 2*(B*a^3 + 3*A*a^2*b)*d*e^6 - (7*B*
c^3*d*e^6 - 4*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 4*(3*B*b*c^2 +
A*c^3)*d*e^6 + 6*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 3*(35*B*c^3*d^3*e^4 - 2
0*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - 4*(B*b^3
+ 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 - 2*(278*B*c^3*d^4*e^3 - 146*(3*B*
b*c^2 + A*c^3)*d^3*e^4 + 189*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 18*(B*b^3 + 3
*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6)*x^3 - 6*(68*B*c^3*d^5*e^2 - 26*(3*B*b*c
^2 + A*c^3)*d^4*e^3 + 9*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + 6*(B*b^3 + 3*A*a*c
^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 - 6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)
*c)*d*e^6 + 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 6*(37*B*c^3*d^6*e - 34*(3
*B*b*c^2 + A*c^3)*d^5*e^2 + 81*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 18*(B*b^3 +
3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 9*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 +
2*A*a*b)*c)*d^2*e^5 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - (B*a^3 + 3*A*a^2*b
)*e^7)*x + 12*(35*B*c^3*d^7 - 20*(3*B*b*c^2 + A*c^3)*d^6*e + 30*(B*b^2*c + (B*a
+ A*b)*c^2)*d^5*e^2 - 4*(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 + (35*B*c^3*d^4*e^3 - 20*(3*B*
b*c^2 + A*c^3)*d^3*e^4 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 4*(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 + 3*(35*B*c^3*d^5*e^2 - 20*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 30*(B*b^2*
c + (B*a + A*b)*c^2)*d^3*e^4 - 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)*x^2 + 3*(35*B*c^3*d^6*
e - 20*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 4*
(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)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9
*x + d^3*e^8)
_______________________________________________________________________________________
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)**4,x)
[Out]
Timed out
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.257419, 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)^4,x, algorithm="giac")
[Out]
Done