Optimal. Leaf size=17 \[ \frac{d \left (e+f x^4\right )^3}{12 f} \]
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Rubi [A] time = 0.0050034, 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, Rules used = {12, 261} \[ \frac{d \left (e+f x^4\right )^3}{12 f} \]
Antiderivative was successfully verified.
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Rule 12
Rule 261
Rubi steps
\begin{align*} \int d x^3 \left (e+f x^4\right )^2 \, dx &=d \int x^3 \left (e+f x^4\right )^2 \, dx\\ &=\frac{d \left (e+f x^4\right )^3}{12 f}\\ \end{align*}
Mathematica [A] time = 0.0008476, 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.
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Maple [A] time = 0.039, size = 27, normalized size = 1.6 \begin{align*} d \left ({\frac{{f}^{2}{x}^{12}}{12}}+{\frac{ef{x}^{8}}{4}}+{\frac{{e}^{2}{x}^{4}}{4}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01359, size = 20, normalized size = 1.18 \begin{align*} \frac{{\left (f x^{4} + e\right )}^{3} d}{12 \, f} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.05472, size = 66, normalized size = 3.88 \begin{align*} \frac{1}{12} x^{12} f^{2} d + \frac{1}{4} x^{8} f e d + \frac{1}{4} x^{4} e^{2} d \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.059406, size = 29, normalized size = 1.71 \begin{align*} \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06087, size = 22, normalized size = 1.29 \begin{align*} \frac{{\left (f x^{4} + e\right )}^{3} d}{12 \, f} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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