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 = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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 29
Rule 31
Rule 36
Rule 266
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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {\log (x)}{2}-\frac {1}{8} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 15, normalized size = 0.79 \[ -\frac {1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 17, normalized size = 0.89 \[ -\frac {1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac {1}{8} \, \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.84 \[ \frac {\ln \relax (x )}{2}-\frac {\ln \left (3 x^{4}+2\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 17, normalized size = 0.89 \[ -\frac {1}{8} \, \log \left (3 \, x^{4} + 2\right ) + \frac {1}{8} \, \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 13, normalized size = 0.68 \[ \frac {\ln \relax (x)}{2}-\frac {\ln \left (x^4+\frac {2}{3}\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 14, normalized size = 0.74 \[ \frac {\log {\relax (x )}}{2} - \frac {\log {\left (3 x^{4} + 2 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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