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 = 0.02, antiderivative size = 32, normalized size of antiderivative = 1.00, 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 44
Rule 266
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*}
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Mathematica [A] time = 0.01, size = 32, normalized size = 1.00 \[ \frac {1}{8 \left (3 x^4+2\right )}-\frac {1}{16} \log \left (3 x^4+2\right )+\frac {\log (x)}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 40, normalized size = 1.25 \[ -\frac {{\left (3 \, x^{4} + 2\right )} \log \left (3 \, x^{4} + 2\right ) - 4 \, {\left (3 \, x^{4} + 2\right )} \log \relax (x) - 2}{16 \, {\left (3 \, x^{4} + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 35, normalized size = 1.09 \[ \frac {3 \, x^{4} + 4}{16 \, {\left (3 \, x^{4} + 2\right )}} - \frac {1}{16} \, \log \left (3 \, x^{4} + 2\right ) + \frac {1}{16} \, \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ \frac {\ln \relax (x )}{4}-\frac {\ln \left (3 x^{4}+2\right )}{16}+\frac {1}{24 x^{4}+16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 28, normalized size = 0.88 \[ \frac {1}{8 \, {\left (3 \, x^{4} + 2\right )}} - \frac {1}{16} \, \log \left (3 \, x^{4} + 2\right ) + \frac {1}{16} \, \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 22, normalized size = 0.69 \[ \frac {\ln \relax (x)}{4}-\frac {\ln \left (x^4+\frac {2}{3}\right )}{16}+\frac {1}{24\,\left (x^4+\frac {2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 22, normalized size = 0.69 \[ \frac {\log {\relax (x )}}{4} - \frac {\log {\left (3 x^{4} + 2 \right )}}{16} + \frac {1}{24 x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
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