Optimal. Leaf size=20 \[ \frac{x^4}{12}-\frac{1}{18} \log \left (3 x^4+2\right ) \]
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Rubi [A] time = 0.0127968, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{x^4}{12}-\frac{1}{18} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^7}{2+3 x^4} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{x}{2+3 x} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (\frac{1}{3}-\frac{2}{3 (2+3 x)}\right ) \, dx,x,x^4\right )\\ &=\frac{x^4}{12}-\frac{1}{18} \log \left (2+3 x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0049126, size = 21, normalized size = 1.05 \[ \frac{1}{36} \left (3 x^4-2 \log \left (3 x^4+2\right )+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 17, normalized size = 0.9 \begin{align*}{\frac{{x}^{4}}{12}}-{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989227, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{12} \, x^{4} - \frac{1}{18} \, \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 = 1.63523, size = 43, normalized size = 2.15 \begin{align*} \frac{1}{12} \, x^{4} - \frac{1}{18} \, \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 = 0.10083, size = 14, normalized size = 0.7 \begin{align*} \frac{x^{4}}{12} - \frac{\log{\left (3 x^{4} + 2 \right )}}{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11947, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{12} \, x^{4} - \frac{1}{18} \, \log \left (3 \, x^{4} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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