Optimal. Leaf size=13 \[ \frac {x \log (x)}{\sqrt [3]{b x^3}} \]
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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 = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 29}
\begin {gather*} \frac {x \log (x)}{\sqrt [3]{b x^3}} \end {gather*}
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*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {x \log (x)}{\sqrt [3]{b x^3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 12, normalized size = 0.92
method | result | size |
risch | \(\frac {x \ln \left (x \right )}{\left (b \,x^{3}\right )^{\frac {1}{3}}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 11, normalized size = 0.85 \begin {gather*} \frac {x \log \left (x\right )}{\left (b x^{3}\right )^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 1.23 \begin {gather*} \frac {\left (b x^{3}\right )^{\frac {2}{3}} \log \left (x\right )}{b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt [3]{b x^{3}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.13, size = 1, normalized size = 0.08 \begin {gather*} +\infty \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {1}{{\left (b\,x^3\right )}^{1/3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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