Optimal. Leaf size=5 \[ c^2 x \]
[Out]
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Rubi [A] time = 0.00948238, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ c^2 x \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 18.086, size = 3, normalized size = 0.6 \[ c^{2} x \]
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)**4,x)
[Out]
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Mathematica [A] time = 0.000591329, size = 5, normalized size = 1. \[ c^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^4,x]
[Out]
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Maple [A] time = 0.001, size = 6, normalized size = 1.2 \[{c}^{2}x \]
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)^4,x)
[Out]
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Maxima [A] time = 0.694996, size = 7, normalized size = 1.4 \[ c^{2} x \]
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)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204663, size = 7, normalized size = 1.4 \[ c^{2} x \]
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)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.178734, size = 3, normalized size = 0.6 \[ c^{2} x \]
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)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.210789, size = 7, normalized size = 1.4 \[ c^{2} x \]
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)^4,x, algorithm="giac")
[Out]