3.2146 \(\int \frac{\left (a+b x+c x^2\right )^4}{(d+e x)^7} \, dx\)
Optimal. Leaf size=426 \[ -\frac{6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{2 e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)}+\frac{4 (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{3 e^9 (d+e x)^3}-\frac{\left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{2 e^9 (d+e x)^4}+\frac{2 c^2 \log (d+e x) \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9}+\frac{4 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{5 e^9 (d+e x)^5}-\frac{\left (a e^2-b d e+c d^2\right )^4}{6 e^9 (d+e x)^6}-\frac{c^3 x (7 c d-4 b e)}{e^8}+\frac{c^4 x^2}{2 e^7} \]
[Out]
-((c^3*(7*c*d - 4*b*e)*x)/e^8) + (c^4*x^2)/(2*e^7) - (c*d^2 - b*d*e + a*e^2)^4/(
6*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x
)^5) - ((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))
)/(2*e^9*(d + e*x)^4) + (4*(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)))/(3*e^9*(d + e*x)^3) - (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))/(2*e^9*(d + e*x)^2) + (4*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*c^2*(14*c^2*d^2 + 3*b^2*e^2 -
2*c*e*(7*b*d - a*e))*Log[d + e*x])/e^9
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Rubi [A] time = 1.7543, antiderivative size = 426, 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
\[ -\frac{6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{2 e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)}+\frac{4 (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{3 e^9 (d+e x)^3}-\frac{\left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{2 e^9 (d+e x)^4}+\frac{2 c^2 \log (d+e x) \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9}+\frac{4 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{5 e^9 (d+e x)^5}-\frac{\left (a e^2-b d e+c d^2\right )^4}{6 e^9 (d+e x)^6}-\frac{c^3 x (7 c d-4 b e)}{e^8}+\frac{c^4 x^2}{2 e^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x + c*x^2)^4/(d + e*x)^7,x]
[Out]
-((c^3*(7*c*d - 4*b*e)*x)/e^8) + (c^4*x^2)/(2*e^7) - (c*d^2 - b*d*e + a*e^2)^4/(
6*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x
)^5) - ((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))
)/(2*e^9*(d + e*x)^4) + (4*(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)))/(3*e^9*(d + e*x)^3) - (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))/(2*e^9*(d + e*x)^2) + (4*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*c^2*(14*c^2*d^2 + 3*b^2*e^2 -
2*c*e*(7*b*d - a*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)**7,x)
[Out]
Timed out
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Mathematica [A] time = 0.80966, size = 764, normalized size = 1.79 \[ \frac{-3 c^2 e^2 \left (2 a^2 e^2 \left (d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right )+20 a b e \left (d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right )+b^2 (-d) \left (147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right )\right )-2 c e^3 \left (a^3 e^3 \left (d^2+6 d e x+15 e^2 x^2\right )+3 a^2 b e^2 \left (d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right )+6 a b^2 e \left (d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right )+10 b^3 \left (d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right )\right )-e^4 \left (5 a^4 e^4+4 a^3 b e^3 (d+6 e x)+3 a^2 b^2 e^2 \left (d^2+6 d e x+15 e^2 x^2\right )+2 a b^3 e \left (d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right )+b^4 \left (d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right )\right )+60 c^2 (d+e x)^6 \log (d+e x) \left (2 c e (a e-7 b d)+3 b^2 e^2+14 c^2 d^2\right )+2 c^3 e \left (a d e \left (147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right )-b \left (669 d^7+3594 d^6 e x+7725 d^5 e^2 x^2+8200 d^4 e^3 x^3+4050 d^3 e^4 x^4+360 d^2 e^5 x^5-360 d e^6 x^6-60 e^7 x^7\right )\right )+c^4 \left (1023 d^8+5298 d^7 e x+10725 d^6 e^2 x^2+10100 d^5 e^3 x^3+3375 d^4 e^4 x^4-1170 d^3 e^5 x^5-1035 d^2 e^6 x^6-120 d e^7 x^7+15 e^8 x^8\right )}{30 e^9 (d+e x)^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x + c*x^2)^4/(d + e*x)^7,x]
[Out]
(c^4*(1023*d^8 + 5298*d^7*e*x + 10725*d^6*e^2*x^2 + 10100*d^5*e^3*x^3 + 3375*d^4
*e^4*x^4 - 1170*d^3*e^5*x^5 - 1035*d^2*e^6*x^6 - 120*d*e^7*x^7 + 15*e^8*x^8) - e
^4*(5*a^4*e^4 + 4*a^3*b*e^3*(d + 6*e*x) + 3*a^2*b^2*e^2*(d^2 + 6*d*e*x + 15*e^2*
x^2) + 2*a*b^3*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + b^4*(d^4 + 6*d^
3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) - 2*c*e^3*(a^3*e^3*(d^2 + 6
*d*e*x + 15*e^2*x^2) + 3*a^2*b*e^2*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)
+ 6*a*b^2*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 10
*b^3*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x
^5)) - 3*c^2*e^2*(2*a^2*e^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 1
5*e^4*x^4) + 20*a*b*e*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*
e^4*x^4 + 6*e^5*x^5) - b^2*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^
2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) + 2*c^3*e*(a*d*e*(147*d^5 + 822*d^4*e
*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5) - b*(66
9*d^7 + 3594*d^6*e*x + 7725*d^5*e^2*x^2 + 8200*d^4*e^3*x^3 + 4050*d^3*e^4*x^4 +
360*d^2*e^5*x^5 - 360*d*e^6*x^6 - 60*e^7*x^7)) + 60*c^2*(14*c^2*d^2 + 3*b^2*e^2
+ 2*c*e*(-7*b*d + a*e))*(d + e*x)^6*Log[d + e*x])/(30*e^9*(d + e*x)^6)
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Maple [B] time = 0.024, size = 1364, 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)^7,x)
[Out]
56*c^4/e^9/(e*x+d)*d^3-1/e^3/(e*x+d)^4*a^3*c-3/2/e^3/(e*x+d)^4*a^2*b^2-3/2/e^5/(
e*x+d)^4*b^4*d^2-7/e^9/(e*x+d)^4*c^4*d^6+4*c^3/e^7*b*x-7*c^4/e^8*d*x-3/e^5/(e*x+
d)^2*a^2*c^2-35/e^9/(e*x+d)^2*c^4*d^4-4/3/e^4/(e*x+d)^3*a*b^3+4/3/e^5/(e*x+d)^3*
b^4*d+56/3/e^9/(e*x+d)^3*c^4*d^5+4*c^3/e^7*ln(e*x+d)*a+6*c^2/e^7*ln(e*x+d)*b^2+2
8*c^4/e^9*ln(e*x+d)*d^2-1/2*b^4/e^5/(e*x+d)^2-1/6/e/(e*x+d)^6*a^4-4/5/e^2/(e*x+d
)^5*a^3*b+4/5/e^5/(e*x+d)^5*b^4*d^3+8/5/e^9/(e*x+d)^5*c^4*d^7-1/6/e^5/(e*x+d)^6*
d^4*b^4-1/6/e^9/(e*x+d)^6*c^4*d^8-4*c/e^6/(e*x+d)*b^3+2/e^4/(e*x+d)^6*d^3*a^2*b*
c+30/e^6/(e*x+d)^2*a*b*c^2*d+16/e^5/(e*x+d)^3*a*b^2*c*d-2/e^5/(e*x+d)^6*d^4*a*b^
2*c+2/e^6/(e*x+d)^6*d^5*a*b*c^2+9/e^4/(e*x+d)^4*a^2*b*c*d-18/e^5/(e*x+d)^4*a*b^2
*c*d^2+30/e^6/(e*x+d)^4*a*b*c^2*d^3-40/e^6/(e*x+d)^3*a*b*c^2*d^2-36/5/e^4/(e*x+d
)^5*a^2*b*c*d^2+48/5/e^5/(e*x+d)^5*a*b^2*c*d^3-12/e^6/(e*x+d)^5*a*b*c^2*d^4-6/e^
5/(e*x+d)^2*a*b^2*c-30/e^7/(e*x+d)^2*a*c^3*d^2+8/5/e^3/(e*x+d)^5*a^3*c*d+12/5/e^
3/(e*x+d)^5*a^2*b^2*d+24/5/e^5/(e*x+d)^5*a^2*c^2*d^3-12/5/e^4/(e*x+d)^5*a*b^3*d^
2+24/5/e^7/(e*x+d)^5*a*c^3*d^5-4/e^6/(e*x+d)^5*b^3*c*d^4+36/5/e^7/(e*x+d)^5*b^2*
c^2*d^5-28/5/e^8/(e*x+d)^5*b*c^3*d^6+2/3/e^2/(e*x+d)^6*d*a^3*b-2/3/e^3/(e*x+d)^6
*a^3*c*d^2-1/e^3/(e*x+d)^6*d^2*a^2*b^2-1/e^5/(e*x+d)^6*a^2*c^2*d^4+2/3/e^4/(e*x+
d)^6*d^3*a*b^3-2/3/e^7/(e*x+d)^6*a*c^3*d^6+2/3/e^6/(e*x+d)^6*d^5*b^3*c-1/e^7/(e*
x+d)^6*d^6*b^2*c^2+2/3/e^8/(e*x+d)^6*b*c^3*d^7-12*c^2/e^6/(e*x+d)*a*b+24*c^3/e^7
/(e*x+d)*a*d+36*c^2/e^7/(e*x+d)*b^2*d-84*c^3/e^8/(e*x+d)*b*d^2-9/e^5/(e*x+d)^4*a
^2*c^2*d^2+3/e^4/(e*x+d)^4*a*b^3*d-15/e^7/(e*x+d)^4*a*c^3*d^4+10/e^6/(e*x+d)^4*b
^3*c*d^3-45/2/e^7/(e*x+d)^4*b^2*c^2*d^4+21/e^8/(e*x+d)^4*b*c^3*d^5-28*c^3/e^8*ln
(e*x+d)*b*d+1/2*c^4*x^2/e^7+10/e^6/(e*x+d)^2*b^3*c*d-45/e^7/(e*x+d)^2*b^2*c^2*d^
2+70/e^8/(e*x+d)^2*b*c^3*d^3-4/e^4/(e*x+d)^3*a^2*b*c+8/e^5/(e*x+d)^3*a^2*d*c^2+8
0/3/e^7/(e*x+d)^3*c^3*d^3*a-40/3/e^6/(e*x+d)^3*b^3*c*d^2+40/e^7/(e*x+d)^3*b^2*c^
2*d^3-140/3/e^8/(e*x+d)^3*b*c^3*d^4
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Maxima [A] time = 0.835364, size = 1169, normalized size = 2.74 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^4/(e*x + d)^7,x, algorithm="maxima")
[Out]
1/30*(1023*c^4*d^8 - 1338*b*c^3*d^7*e - 4*a^3*b*d*e^7 - 5*a^4*e^8 + 147*(3*b^2*c
^2 + 2*a*c^3)*d^6*e^2 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^6
+ 120*(14*c^4*d^3*e^5 - 21*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 + 15*(490*c^4*d^4*e^4 - 700*b*c^3*d^3*e^5 + 90*(3*b^2*c^
2 + 2*a*c^3)*d^2*e^6 - 20*(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 + 20*(658*c^4*d^5*e^3 - 910*b*c^3*d^4*e^4 + 110*(3*b^2*c^2 + 2*a*c
^3)*d^3*e^5 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 15*(798*c^4*d^6*e^2 - 1078*b*c^3*d^5*e^3
+ 125*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d*e^7 - (3*a^2*b^2 + 2*a^3
*c)*e^8)*x^2 + 6*(918*c^4*d^7*e - 1218*b*c^3*d^6*e^2 - 4*a^3*b*e^8 + 137*(3*b^2*
c^2 + 2*a*c^3)*d^5*e^3 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - (3*a^2*b^2 + 2*a^3*c)*d*e^7)*
x)/(e^15*x^6 + 6*d*e^14*x^5 + 15*d^2*e^13*x^4 + 20*d^3*e^12*x^3 + 15*d^4*e^11*x^
2 + 6*d^5*e^10*x + d^6*e^9) + 1/2*(c^4*e*x^2 - 2*(7*c^4*d - 4*b*c^3*e)*x)/e^8 +
2*(14*c^4*d^2 - 14*b*c^3*d*e + (3*b^2*c^2 + 2*a*c^3)*e^2)*log(e*x + d)/e^9
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Fricas [A] time = 0.211477, size = 1608, normalized size = 3.77 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^4/(e*x + d)^7,x, algorithm="fricas")
[Out]
1/30*(15*c^4*e^8*x^8 + 1023*c^4*d^8 - 1338*b*c^3*d^7*e - 4*a^3*b*d*e^7 - 5*a^4*e
^8 + 147*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - (3*a^2*b^2 +
2*a^3*c)*d^2*e^6 - 120*(c^4*d*e^7 - b*c^3*e^8)*x^7 - 45*(23*c^4*d^2*e^6 - 16*b*c
^3*d*e^7)*x^6 - 30*(39*c^4*d^3*e^5 + 24*b*c^3*d^2*e^6 - 12*(3*b^2*c^2 + 2*a*c^3)
*d*e^7 + 4*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 15*(225*c^4*d^4*e^4 - 540*b*c^3*d^3*e^
5 + 90*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 20*(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 + 20*(505*c^4*d^5*e^3 - 820*b*c^3*d^4*e^4 + 110*(3
*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 15*(715*c^4*d^6*e^2 - 103
0*b*c^3*d^5*e^3 + 125*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d*e^7 - (3
*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 6*(883*c^4*d^7*e - 1198*b*c^3*d^6*e^2 - 4*a^3*b*e
^8 + 137*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 20*(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 - 2*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - (3*a^2*b^2 +
2*a^3*c)*d*e^7)*x + 60*(14*c^4*d^8 - 14*b*c^3*d^7*e + (3*b^2*c^2 + 2*a*c^3)*d^6*
e^2 + (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 + 6*(14*
c^4*d^3*e^5 - 14*b*c^3*d^2*e^6 + (3*b^2*c^2 + 2*a*c^3)*d*e^7)*x^5 + 15*(14*c^4*d
^4*e^4 - 14*b*c^3*d^3*e^5 + (3*b^2*c^2 + 2*a*c^3)*d^2*e^6)*x^4 + 20*(14*c^4*d^5*
e^3 - 14*b*c^3*d^4*e^4 + (3*b^2*c^2 + 2*a*c^3)*d^3*e^5)*x^3 + 15*(14*c^4*d^6*e^2
- 14*b*c^3*d^5*e^3 + (3*b^2*c^2 + 2*a*c^3)*d^4*e^4)*x^2 + 6*(14*c^4*d^7*e - 14*
b*c^3*d^6*e^2 + (3*b^2*c^2 + 2*a*c^3)*d^5*e^3)*x)*log(e*x + d))/(e^15*x^6 + 6*d*
e^14*x^5 + 15*d^2*e^13*x^4 + 20*d^3*e^12*x^3 + 15*d^4*e^11*x^2 + 6*d^5*e^10*x +
d^6*e^9)
_______________________________________________________________________________________
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)**7,x)
[Out]
Timed out
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GIAC/XCAS [A] time = 0.205767, 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)^7,x, algorithm="giac")
[Out]
Done