Optimal. Leaf size=32 \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
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Rubi [A] time = 0.0199567, antiderivative size = 32, 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, 44} \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
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Rule 266
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x \left (2+3 x^4\right )^2} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{1}{x (2+3 x)^2} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (\frac{1}{4 x}-\frac{3}{2 (2+3 x)^2}-\frac{3}{4 (2+3 x)}\right ) \, dx,x,x^4\right )\\ &=\frac{1}{8 \left (2+3 x^4\right )}+\frac{\log (x)}{4}-\frac{1}{16} \log \left (2+3 x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0081473, size = 32, normalized size = 1. \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 27, normalized size = 0.8 \begin{align*}{\frac{1}{24\,{x}^{4}+16}}+{\frac{\ln \left ( x \right ) }{4}}-{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.982029, size = 38, normalized size = 1.19 \begin{align*} \frac{1}{8 \,{\left (3 \, x^{4} + 2\right )}} - \frac{1}{16} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{16} \, \log \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66831, size = 101, normalized size = 3.16 \begin{align*} -\frac{{\left (3 \, x^{4} + 2\right )} \log \left (3 \, x^{4} + 2\right ) - 4 \,{\left (3 \, x^{4} + 2\right )} \log \left (x\right ) - 2}{16 \,{\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 = 0.160597, size = 22, normalized size = 0.69 \begin{align*} \frac{\log{\left (x \right )}}{4} - \frac{\log{\left (3 x^{4} + 2 \right )}}{16} + \frac{1}{24 x^{4} + 16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11793, size = 47, normalized size = 1.47 \begin{align*} \frac{3 \, x^{4} + 4}{16 \,{\left (3 \, x^{4} + 2\right )}} - \frac{1}{16} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{16} \, \log \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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