3.2147 \(\int \frac{\left (a+b x+c x^2\right )^4}{(d+e x)^8} \, dx\)

Optimal. Leaf size=424 \[ -\frac{6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{3 e^9 (d+e x)^3}-\frac{2 c^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (d+e x)}+\frac{2 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^2}+\frac{(2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^4}-\frac{2 \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{5 e^9 (d+e x)^5}+\frac{2 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{3 e^9 (d+e x)^6}-\frac{\left (a e^2-b d e+c d^2\right )^4}{7 e^9 (d+e x)^7}-\frac{4 c^3 (2 c d-b e) \log (d+e x)}{e^9}+\frac{c^4 x}{e^8} \]

[Out]

(c^4*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(
c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^6) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14
*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e
)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d +
e*x)^4) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7
*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(3*e^9*(d + e*x)^
3) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e
*x)^2) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x))
- (4*c^3*(2*c*d - b*e)*Log[d + e*x])/e^9

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Rubi [A]  time = 1.69771, antiderivative size = 424, 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 \[ -\frac{6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{3 e^9 (d+e x)^3}-\frac{2 c^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (d+e x)}+\frac{2 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^2}+\frac{(2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^4}-\frac{2 \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{5 e^9 (d+e x)^5}+\frac{2 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{3 e^9 (d+e x)^6}-\frac{\left (a e^2-b d e+c d^2\right )^4}{7 e^9 (d+e x)^7}-\frac{4 c^3 (2 c d-b e) \log (d+e x)}{e^9}+\frac{c^4 x}{e^8} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x + c*x^2)^4/(d + e*x)^8,x]

[Out]

(c^4*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(
c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^6) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14
*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e
)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d +
e*x)^4) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7
*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(3*e^9*(d + e*x)^
3) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e
*x)^2) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x))
- (4*c^3*(2*c*d - b*e)*Log[d + e*x])/e^9

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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((c*x**2+b*x+a)**4/(e*x+d)**8,x)

[Out]

Timed out

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Mathematica [A]  time = 4.7061, size = 748, normalized size = 1.76 \[ -\frac{6 c^2 e^2 \left (a^2 e^2 \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )+5 a b e \left (d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right )+15 b^2 \left (d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right )\right )+c e^3 \left (4 a^3 e^3 \left (d^2+7 d e x+21 e^2 x^2\right )+9 a^2 b e^2 \left (d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right )+12 a b^2 e \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )+10 b^3 \left (d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right )\right )+e^4 \left (15 a^4 e^4+10 a^3 b e^3 (d+7 e x)+6 a^2 b^2 e^2 \left (d^2+7 d e x+21 e^2 x^2\right )+3 a b^3 e \left (d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right )+b^4 \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )\right )+c^3 e \left (60 a e \left (d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right )-b d \left (1089 d^6+7203 d^5 e x+20139 d^4 e^2 x^2+30625 d^3 e^3 x^3+26950 d^2 e^4 x^4+13230 d e^5 x^5+2940 e^6 x^6\right )\right )+420 c^3 (d+e x)^7 (2 c d-b e) \log (d+e x)+c^4 \left (1443 d^8+9261 d^7 e x+24843 d^6 e^2 x^2+35525 d^5 e^3 x^3+28175 d^4 e^4 x^4+11025 d^3 e^5 x^5+735 d^2 e^6 x^6-735 d e^7 x^7-105 e^8 x^8\right )}{105 e^9 (d+e x)^7} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x + c*x^2)^4/(d + e*x)^8,x]

[Out]

-(c^4*(1443*d^8 + 9261*d^7*e*x + 24843*d^6*e^2*x^2 + 35525*d^5*e^3*x^3 + 28175*d
^4*e^4*x^4 + 11025*d^3*e^5*x^5 + 735*d^2*e^6*x^6 - 735*d*e^7*x^7 - 105*e^8*x^8)
+ e^4*(15*a^4*e^4 + 10*a^3*b*e^3*(d + 7*e*x) + 6*a^2*b^2*e^2*(d^2 + 7*d*e*x + 21
*e^2*x^2) + 3*a*b^3*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + b^4*(d^4 +
7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + c*e^3*(4*a^3*e^3*(d^
2 + 7*d*e*x + 21*e^2*x^2) + 9*a^2*b*e^2*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3
*x^3) + 12*a*b^2*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4
) + 10*b^3*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 2
1*e^5*x^5)) + 6*c^2*e^2*(a^2*e^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^
3 + 35*e^4*x^4) + 5*a*b*e*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 3
5*d*e^4*x^4 + 21*e^5*x^5) + 15*b^2*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^
3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6)) + c^3*e*(60*a*e*(d^6 + 7*d^5
*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x
^6) - b*d*(1089*d^6 + 7203*d^5*e*x + 20139*d^4*e^2*x^2 + 30625*d^3*e^3*x^3 + 269
50*d^2*e^4*x^4 + 13230*d*e^5*x^5 + 2940*e^6*x^6)) + 420*c^3*(2*c*d - b*e)*(d + e
*x)^7*Log[d + e*x])/(105*e^9*(d + e*x)^7)

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Maple [B]  time = 0.021, size = 1374, normalized size = 3.2 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^2+b*x+a)^4/(e*x+d)^8,x)

[Out]

-10/3/e^6/(e*x+d)^6*b^3*c*d^4-30/e^7/(e*x+d)^3*b^2*c^2*d^2+140/3/e^8/(e*x+d)^3*b
*c^3*d^3-36/5/e^5/(e*x+d)^5*a^2*c^2*d^2+12/5/e^4/(e*x+d)^5*a*b^3*d-12/e^7/(e*x+d
)^5*a*c^3*d^4+8/e^6/(e*x+d)^5*b^3*c*d^3-10/e^6/(e*x+d)^4*b^3*c*d^2+30/e^7/(e*x+d
)^4*b^2*c^2*d^3-35/e^8/(e*x+d)^4*b*c^3*d^4-18/e^7/(e*x+d)^5*b^2*c^2*d^4+84/5/e^8
/(e*x+d)^5*b*c^3*d^5+4/3/e^3/(e*x+d)^6*a^3*c*d+2/e^3/(e*x+d)^6*a^2*b^2*d+4/e^5/(
e*x+d)^6*a^2*c^2*d^3+12/e^5/(e*x+d)^4*a*b^2*c*d-30/e^6/(e*x+d)^4*a*b*c^2*d^2+12/
7/e^4/(e*x+d)^7*d^3*a^2*b*c-12/7/e^5/(e*x+d)^7*d^4*a*b^2*c+12/7/e^6/(e*x+d)^7*d^
5*a*b*c^2+20/e^6/(e*x+d)^3*a*b*c^2*d+36/5/e^4/(e*x+d)^5*a^2*b*c*d-1/e^4/(e*x+d)^
4*a*b^3+1/e^5/(e*x+d)^4*b^4*d+14/e^9/(e*x+d)^4*c^4*d^5+28*c^4/e^9/(e*x+d)^2*d^3-
2/e^5/(e*x+d)^3*a^2*c^2-70/3/e^9/(e*x+d)^3*c^4*d^4+4*c^3/e^8*ln(e*x+d)*b-8*c^4/e
^9*ln(e*x+d)*d-4/5/e^3/(e*x+d)^5*a^3*c-6/5/e^3/(e*x+d)^5*a^2*b^2-6/5/e^5/(e*x+d)
^5*b^4*d^2-28/5/e^9/(e*x+d)^5*c^4*d^6-2/3/e^2/(e*x+d)^6*a^3*b+2/3/e^5/(e*x+d)^6*
b^4*d^3+4/3/e^9/(e*x+d)^6*c^4*d^7-4*c^3/e^7/(e*x+d)*a-6*c^2/e^7/(e*x+d)*b^2-28*c
^4/e^9/(e*x+d)*d^2-1/7/e^5/(e*x+d)^7*d^4*b^4-1/7/e^9/(e*x+d)^7*c^4*d^8-2*c/e^6/(
e*x+d)^2*b^3-2/e^4/(e*x+d)^6*a*b^3*d^2+4/e^7/(e*x+d)^6*a*c^3*d^5+20/e^7/(e*x+d)^
4*c^3*d^3*a+4/7/e^2/(e*x+d)^7*d*a^3*b-72/5/e^5/(e*x+d)^5*a*b^2*c*d^2+24/e^6/(e*x
+d)^5*a*b*c^2*d^3-6/e^4/(e*x+d)^6*a^2*b*c*d^2+8/e^5/(e*x+d)^6*a*b^2*c*d^3-10/e^6
/(e*x+d)^6*a*b*c^2*d^4-4/7/e^3/(e*x+d)^7*a^3*c*d^2-6/7/e^3/(e*x+d)^7*d^2*a^2*b^2
-6/7/e^5/(e*x+d)^7*a^2*c^2*d^4+4/7/e^4/(e*x+d)^7*d^3*a*b^3-4/7/e^7/(e*x+d)^7*a*c
^3*d^6+4/7/e^6/(e*x+d)^7*d^5*b^3*c-6/7/e^7/(e*x+d)^7*d^6*b^2*c^2+4/7/e^8/(e*x+d)
^7*d^7*b*c^3-6*c^2/e^6/(e*x+d)^2*a*b-14/3/e^8/(e*x+d)^6*b*c^3*d^6+28*c^3/e^8/(e*
x+d)*b*d-4/e^5/(e*x+d)^3*a*b^2*c-20/e^7/(e*x+d)^3*a*c^3*d^2+20/3/e^6/(e*x+d)^3*b
^3*c*d+c^4*x/e^8+12*c^3/e^7/(e*x+d)^2*a*d+18*c^2/e^7/(e*x+d)^2*b^2*d-42*c^3/e^8/
(e*x+d)^2*b*d^2-3/e^4/(e*x+d)^4*a^2*b*c+6/e^5/(e*x+d)^4*a^2*d*c^2+6/e^7/(e*x+d)^
6*b^2*c^2*d^5-1/7/e/(e*x+d)^7*a^4-1/3*b^4/e^5/(e*x+d)^3

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Maxima [A]  time = 0.855127, size = 1177, normalized size = 2.78 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + b*x + a)^4/(e*x + d)^8,x, algorithm="maxima")

[Out]

-1/105*(1443*c^4*d^8 - 1089*b*c^3*d^7*e + 10*a^3*b*d*e^7 + 15*a^4*e^8 + 30*(3*b^
2*c^2 + 2*a*c^3)*d^6*e^2 + 10*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c +
6*a^2*c^2)*d^4*e^4 + 3*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2
*e^6 + 210*(14*c^4*d^2*e^6 - 14*b*c^3*d*e^7 + (3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 2
10*(70*c^4*d^3*e^5 - 63*b*c^3*d^2*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + (b^3*c +
3*a*b*c^2)*e^8)*x^5 + 35*(910*c^4*d^4*e^4 - 770*b*c^3*d^3*e^5 + 30*(3*b^2*c^2 +
2*a*c^3)*d^2*e^6 + 10*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2
)*e^8)*x^4 + 35*(1078*c^4*d^5*e^3 - 875*b*c^3*d^4*e^4 + 30*(3*b^2*c^2 + 2*a*c^3)
*d^3*e^5 + 10*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7
+ 3*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 21*(1218*c^4*d^6*e^2 - 959*b*c^3*d^5*e^3 + 3
0*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 10*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b
^2*c + 6*a^2*c^2)*d^2*e^6 + 3*(a*b^3 + 3*a^2*b*c)*d*e^7 + 2*(3*a^2*b^2 + 2*a^3*c
)*e^8)*x^2 + 7*(1338*c^4*d^7*e - 1029*b*c^3*d^6*e^2 + 10*a^3*b*e^8 + 30*(3*b^2*c
^2 + 2*a*c^3)*d^5*e^3 + 10*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a
^2*c^2)*d^3*e^5 + 3*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)
*x)/(e^16*x^7 + 7*d*e^15*x^6 + 21*d^2*e^14*x^5 + 35*d^3*e^13*x^4 + 35*d^4*e^12*x
^3 + 21*d^5*e^11*x^2 + 7*d^6*e^10*x + d^7*e^9) + c^4*x/e^8 - 4*(2*c^4*d - b*c^3*
e)*log(e*x + d)/e^9

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Fricas [A]  time = 0.211184, size = 1461, normalized size = 3.45 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + b*x + a)^4/(e*x + d)^8,x, algorithm="fricas")

[Out]

1/105*(105*c^4*e^8*x^8 + 735*c^4*d*e^7*x^7 - 1443*c^4*d^8 + 1089*b*c^3*d^7*e - 1
0*a^3*b*d*e^7 - 15*a^4*e^8 - 30*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 10*(b^3*c + 3*a*
b*c^2)*d^5*e^3 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 3*(a*b^3 + 3*a^2*b*c)*
d^3*e^5 - 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 105*(7*c^4*d^2*e^6 - 28*b*c^3*d*e^7
+ 2*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 105*(105*c^4*d^3*e^5 - 126*b*c^3*d^2*e^6 +
6*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 2*(b^3*c + 3*a*b*c^2)*e^8)*x^5 - 35*(805*c^4*d^4
*e^4 - 770*b*c^3*d^3*e^5 + 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 10*(b^3*c + 3*a*b*
c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 35*(1015*c^4*d^5*e^3 - 87
5*b*c^3*d^4*e^4 + 30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 10*(b^3*c + 3*a*b*c^2)*d^2*
e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 3*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 - 21
*(1183*c^4*d^6*e^2 - 959*b*c^3*d^5*e^3 + 30*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 10*(
b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 3*(a*b^3 +
3*a^2*b*c)*d*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 - 7*(1323*c^4*d^7*e - 1029*
b*c^3*d^6*e^2 + 10*a^3*b*e^8 + 30*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 10*(b^3*c + 3*
a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 3*(a*b^3 + 3*a^2*b*c
)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x - 420*(2*c^4*d^8 - b*c^3*d^7*e + (2
*c^4*d*e^7 - b*c^3*e^8)*x^7 + 7*(2*c^4*d^2*e^6 - b*c^3*d*e^7)*x^6 + 21*(2*c^4*d^
3*e^5 - b*c^3*d^2*e^6)*x^5 + 35*(2*c^4*d^4*e^4 - b*c^3*d^3*e^5)*x^4 + 35*(2*c^4*
d^5*e^3 - b*c^3*d^4*e^4)*x^3 + 21*(2*c^4*d^6*e^2 - b*c^3*d^5*e^3)*x^2 + 7*(2*c^4
*d^7*e - b*c^3*d^6*e^2)*x)*log(e*x + d))/(e^16*x^7 + 7*d*e^15*x^6 + 21*d^2*e^14*
x^5 + 35*d^3*e^13*x^4 + 35*d^4*e^12*x^3 + 21*d^5*e^11*x^2 + 7*d^6*e^10*x + d^7*e
^9)

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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((c*x**2+b*x+a)**4/(e*x+d)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.203909, 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)^4/(e*x + d)^8,x, algorithm="giac")

[Out]

Done