Optimal. Leaf size=19 \[ \frac{\log (x)}{2}-\frac{1}{8} \log \left (3 x^4+2\right ) \]
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Rubi [A] time = 0.0081227, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308, Rules used = {266, 36, 29, 31} \[ \frac{\log (x)}{2}-\frac{1}{8} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 36
Rule 29
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x \left (2+3 x^4\right )} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{1}{x (2+3 x)} \, dx,x,x^4\right )\\ &=\frac{1}{8} \operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,x^4\right )-\frac{3}{8} \operatorname{Subst}\left (\int \frac{1}{2+3 x} \, dx,x,x^4\right )\\ &=\frac{\log (x)}{2}-\frac{1}{8} \log \left (2+3 x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0034749, size = 19, normalized size = 1. \[ \frac{\log (x)}{2}-\frac{1}{8} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( x \right ) }{2}}-{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02881, size = 23, normalized size = 1.21 \begin{align*} -\frac{1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{8} \, \log \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.62523, size = 46, normalized size = 2.42 \begin{align*} -\frac{1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.128638, size = 14, normalized size = 0.74 \begin{align*} \frac{\log{\left (x \right )}}{2} - \frac{\log{\left (3 x^{4} + 2 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12402, size = 23, normalized size = 1.21 \begin{align*} -\frac{1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{8} \, \log \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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