Optimal. Leaf size=17 \[ -\frac{c^2}{3 e (d+e x)^3} \]
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Rubi [A] time = 0.0165511, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{c^2}{3 e (d+e x)^3} \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^8,x]
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Rubi in Sympy [A] time = 18.247, size = 14, normalized size = 0.82 \[ - \frac{c^{2}}{3 e \left (d + e x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**8,x)
[Out]
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Mathematica [A] time = 0.00419946, size = 17, normalized size = 1. \[ -\frac{c^2}{3 e (d+e x)^3} \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^8,x]
[Out]
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Maple [A] time = 0.001, size = 16, normalized size = 0.9 \[ -{\frac{{c}^{2}}{3\,e \left ( ex+d \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^8,x)
[Out]
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Maxima [A] time = 0.697802, size = 51, normalized size = 3. \[ -\frac{c^{2}}{3 \,{\left (e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^2/(e*x + d)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204313, size = 51, normalized size = 3. \[ -\frac{c^{2}}{3 \,{\left (e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^2/(e*x + d)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.55844, size = 39, normalized size = 2.29 \[ - \frac{c^{2}}{3 d^{3} e + 9 d^{2} e^{2} x + 9 d e^{3} x^{2} + 3 e^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.210462, size = 89, normalized size = 5.24 \[ -\frac{{\left (c^{2} x^{4} e^{8} + 4 \, c^{2} d x^{3} e^{7} + 6 \, c^{2} d^{2} x^{2} e^{6} + 4 \, c^{2} d^{3} x e^{5} + c^{2} d^{4} e^{4}\right )} e^{\left (-5\right )}}{3 \,{\left (x e + d\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^2/(e*x + d)^8,x, algorithm="giac")
[Out]