Optimal. Leaf size=12 \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
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Rubi [A] time = 0.0014454, antiderivative size = 12, 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, 30} \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{b x^4}} \, dx &=\frac{x^{4/3} \int \frac{1}{x^{4/3}} \, dx}{\sqrt [3]{b x^4}}\\ &=-\frac{3 x}{\sqrt [3]{b x^4}}\\ \end{align*}
Mathematica [A] time = 0.0018404, size = 12, normalized size = 1. \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -3\,{\frac{x}{\sqrt [3]{b{x}^{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.978753, size = 14, normalized size = 1.17 \begin{align*} -\frac{3 \, x}{\left (b x^{4}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6545, size = 35, normalized size = 2.92 \begin{align*} -\frac{3 \, \left (b x^{4}\right )^{\frac{2}{3}}}{b x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.364231, size = 15, normalized size = 1.25 \begin{align*} - \frac{3 x}{\sqrt [3]{b} \sqrt [3]{x^{4}}} \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^{4}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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