Optimal. Leaf size=12 \[ \frac {3 x}{\sqrt [3]{b x^2}} \]
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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} \[ \frac {3 x}{\sqrt [3]{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [3]{b x^2}} \, dx &=\frac {x^{2/3} \int \frac {1}{x^{2/3}} \, dx}{\sqrt [3]{b x^2}}\\ &=\frac {3 x}{\sqrt [3]{b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {3 x}{\sqrt [3]{b x^2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 15, normalized size = 1.25 \[ \frac {3 \, \left (b x^{2}\right )^{\frac {2}{3}}}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 9, normalized size = 0.75 \[ \frac {3}{\left (\frac {b}{x}\right )^{\frac {1}{3}}} \]
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 \[ \frac {3 x}{\left (b \,x^{2}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 10, normalized size = 0.83 \[ \frac {3 \, x}{\left (b x^{2}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 13, normalized size = 1.08 \[ \frac {3\,{\left (x^4\right )}^{1/3}}{b^{1/3}\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.83, size = 14, normalized size = 1.17 \[ \frac {3 x}{\sqrt [3]{b} \sqrt [3]{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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