Optimal. Leaf size=15 \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
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Rubi [A] time = 0.0059596, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {263, 260} \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
Antiderivative was successfully verified.
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Rule 263
Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{\sqrt [3]{x}}\right ) x} \, dx &=\int \frac{1}{\left (b+a \sqrt [3]{x}\right ) x^{2/3}} \, dx\\ &=\frac{3 \log \left (b+a \sqrt [3]{x}\right )}{a}\\ \end{align*}
Mathematica [A] time = 0.0030245, size = 15, normalized size = 1. \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \begin{align*} 3\,{\frac{\ln \left ( b+a\sqrt [3]{x} \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959822, size = 27, normalized size = 1.8 \begin{align*} \frac{3 \, \log \left (a + \frac{b}{x^{\frac{1}{3}}}\right )}{a} + \frac{\log \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48365, size = 32, normalized size = 2.13 \begin{align*} \frac{3 \, \log \left (a x^{\frac{1}{3}} + b\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.864197, size = 20, normalized size = 1.33 \begin{align*} \begin{cases} \frac{3 \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a} & \text{for}\: a \neq 0 \\\frac{3 \sqrt [3]{x}}{b} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18845, size = 19, normalized size = 1.27 \begin{align*} \frac{3 \, \log \left ({\left | a x^{\frac{1}{3}} + b \right |}\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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