Optimal. Leaf size=13 \[ -\frac {3 b}{\sqrt [3]{x}}+a \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14}
\begin {gather*} a \log (x)-\frac {3 b}{\sqrt [3]{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x} \, dx &=\int \left (\frac {b}{x^{4/3}}+\frac {a}{x}\right ) \, dx\\ &=-\frac {3 b}{\sqrt [3]{x}}+a \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} -\frac {3 b}{\sqrt [3]{x}}+a \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 12, normalized size = 0.92
method | result | size |
derivativedivides | \(-\frac {3 b}{x^{\frac {1}{3}}}+a \ln \left (x \right )\) | \(12\) |
default | \(-\frac {3 b}{x^{\frac {1}{3}}}+a \ln \left (x \right )\) | \(12\) |
trager | \(-\frac {3 b}{x^{\frac {1}{3}}}+a \ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 11, normalized size = 0.85 \begin {gather*} a \log \left (x\right ) - \frac {3 \, b}{x^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 1.46 \begin {gather*} \frac {3 \, {\left (a x \log \left (x^{\frac {1}{3}}\right ) - b x^{\frac {2}{3}}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 12, normalized size = 0.92 \begin {gather*} a \log {\left (x \right )} - \frac {3 b}{\sqrt [3]{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 12, normalized size = 0.92 \begin {gather*} a \log \left ({\left | x \right |}\right ) - \frac {3 \, b}{x^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 14, normalized size = 1.08 \begin {gather*} 3\,a\,\ln \left (x^{1/3}\right )-\frac {3\,b}{x^{1/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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