Optimal. Leaf size=17 \[ \frac{d \left (e+f x^4\right )^3}{12 f} \]
[Out]
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Rubi [A] time = 0.0180704, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{d \left (e+f x^4\right )^3}{12 f} \]
Antiderivative was successfully verified.
[In] Int[d*x^3*(e + f*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 2.56475, size = 12, normalized size = 0.71 \[ \frac{d \left (e + f x^{4}\right )^{3}}{12 f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(d*x**3*(f*x**4+e)**2,x)
[Out]
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Mathematica [A] time = 0.00149336, size = 33, normalized size = 1.94 \[ \frac{1}{4} d e^2 x^4+\frac{1}{4} d e f x^8+\frac{1}{12} d f^2 x^{12} \]
Antiderivative was successfully verified.
[In] Integrate[d*x^3*(e + f*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 27, normalized size = 1.6 \[ d \left ({\frac{{f}^{2}{x}^{12}}{12}}+{\frac{ef{x}^{8}}{4}}+{\frac{{e}^{2}{x}^{4}}{4}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(d*x^3*(f*x^4+e)^2,x)
[Out]
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Maxima [A] time = 1.41036, size = 20, normalized size = 1.18 \[ \frac{{\left (f x^{4} + e\right )}^{3} d}{12 \, f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*d*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203853, size = 1, normalized size = 0.06 \[ \frac{1}{12} x^{12} f^{2} d + \frac{1}{4} x^{8} f e d + \frac{1}{4} x^{4} e^{2} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*d*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.049223, size = 29, normalized size = 1.71 \[ \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(d*x**3*(f*x**4+e)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209642, size = 22, normalized size = 1.29 \[ \frac{{\left (f x^{4} + e\right )}^{3} d}{12 \, f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*d*x^3,x, algorithm="giac")
[Out]