Optimal. Leaf size=17 \[ -\frac{1}{4 c e (d+e x)^4} \]
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Rubi [A] time = 0.0164961, 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 \[ -\frac{1}{4 c e (d+e x)^4} \]
Antiderivative was successfully verified.
[In] Int[1/((d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 17.9969, size = 14, normalized size = 0.82 \[ - \frac{1}{4 c e \left (d + e x\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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Mathematica [A] time = 0.0108509, size = 17, normalized size = 1. \[ -\frac{1}{4 c e (d+e x)^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/((d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)),x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.9 \[ -{\frac{1}{4\,ce \left ( ex+d \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)
[Out]
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Maxima [A] time = 0.702447, size = 69, normalized size = 4.06 \[ -\frac{1}{4 \,{\left (c e^{5} x^{4} + 4 \, c d e^{4} x^{3} + 6 \, c d^{2} e^{3} x^{2} + 4 \, c d^{3} e^{2} x + c d^{4} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206751, size = 69, normalized size = 4.06 \[ -\frac{1}{4 \,{\left (c e^{5} x^{4} + 4 \, c d e^{4} x^{3} + 6 \, c d^{2} e^{3} x^{2} + 4 \, c d^{3} e^{2} x + c d^{4} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.79058, size = 58, normalized size = 3.41 \[ - \frac{1}{4 c d^{4} e + 16 c d^{3} e^{2} x + 24 c d^{2} e^{3} x^{2} + 16 c d e^{4} x^{3} + 4 c e^{5} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^3),x, algorithm="giac")
[Out]