Optimal. Leaf size=13 \[ \frac{1}{12} d \log \left (3 x^4+2\right ) \]
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Rubi [A] time = 0.0037983, antiderivative size = 13, 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, 260} \[ \frac{1}{12} d \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 260
Rubi steps
\begin{align*} \int \frac{d x^3}{2+3 x^4} \, dx &=d \int \frac{x^3}{2+3 x^4} \, dx\\ &=\frac{1}{12} d \log \left (2+3 x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0028887, size = 13, normalized size = 1. \[ \frac{1}{12} d \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 12, normalized size = 0.9 \begin{align*}{\frac{d\ln \left ( 3\,{x}^{4}+2 \right ) }{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943257, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{12} \, d \log \left (3 \, x^{4} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.39175, size = 31, normalized size = 2.38 \begin{align*} \frac{1}{12} \, d \log \left (3 \, x^{4} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.076402, size = 10, normalized size = 0.77 \begin{align*} \frac{d \log{\left (3 x^{4} + 2 \right )}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07502, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{12} \, d \log \left (3 \, x^{4} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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