Optimal. Leaf size=12 \[ -\frac {x}{\left (b x^3\right )^{2/3}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, 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, 30} \[ -\frac {x}{\left (b x^3\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (b x^3\right )^{2/3}} \, dx &=\frac {x^2 \int \frac {1}{x^2} \, dx}{\left (b x^3\right )^{2/3}}\\ &=-\frac {x}{\left (b x^3\right )^{2/3}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ -\frac {x}{\left (b x^3\right )^{2/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 15, normalized size = 1.25 \[ -\frac {\left (b x^{3}\right )^{\frac {1}{3}}}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.67 \[ -\frac {1}{b^{\frac {2}{3}} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \[ -\frac {x}{\left (b \,x^{3}\right )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 10, normalized size = 0.83 \[ -\frac {x}{\left (b x^{3}\right )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 15, normalized size = 1.25 \[ -\frac {{\left (b\,x^3\right )}^{1/3}}{b\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.54, size = 14, normalized size = 1.17 \[ - \frac {x}{b^{\frac {2}{3}} \left (x^{3}\right )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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