Optimal. Leaf size=13 \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
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Rubi [A] time = 0.0013001, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 29} \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{b x^3}} \, dx &=\frac{x \int \frac{1}{x} \, dx}{\sqrt [3]{b x^3}}\\ &=\frac{x \log (x)}{\sqrt [3]{b x^3}}\\ \end{align*}
Mathematica [A] time = 0.0013723, size = 13, normalized size = 1. \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 12, normalized size = 0.9 \begin{align*}{x\ln \left ( x \right ){\frac{1}{\sqrt [3]{b{x}^{3}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.95983, size = 15, normalized size = 1.15 \begin{align*} \frac{x \log \left (x\right )}{\left (b x^{3}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74394, size = 41, normalized size = 3.15 \begin{align*} \frac{\left (b x^{3}\right )^{\frac{2}{3}} \log \left (x\right )}{b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt [3]{b x^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (b x^{3}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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