Optimal. Leaf size=11 \[ \left (x^{2/3}-1\right )^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {261} \[ \left (x^{2/3}-1\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {\sqrt {-1+x^{2/3}}}{\sqrt [3]{x}} \, dx &=\left (-1+x^{2/3}\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \left (x^{2/3}-1\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.91, size = 7, normalized size = 0.64 \[ {\left (x^{\frac {2}{3}} - 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 7, normalized size = 0.64 \[ {\left (x^{\frac {2}{3}} - 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 8, normalized size = 0.73 \[ \left (x^{\frac {2}{3}}-1\right )^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 7, normalized size = 0.64 \[ {\left (x^{\frac {2}{3}} - 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.19, size = 7, normalized size = 0.64 \[ {\left (x^{2/3}-1\right )}^{3/2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.24, size = 24, normalized size = 2.18 \[ x^{\frac {2}{3}} \sqrt {x^{\frac {2}{3}} - 1} - \sqrt {x^{\frac {2}{3}} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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