Optimal. Leaf size=23 \[ \frac{3}{7} (z-1)^{7/3}+\frac{3}{4} (z-1)^{4/3} \]
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Rubi [A] time = 0.0037208, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{3}{7} (z-1)^{7/3}+\frac{3}{4} (z-1)^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \sqrt [3]{-1+z} z \, dz &=\int \left (\sqrt [3]{-1+z}+(-1+z)^{4/3}\right ) \, dz\\ &=\frac{3}{4} (-1+z)^{4/3}+\frac{3}{7} (-1+z)^{7/3}\\ \end{align*}
Mathematica [A] time = 0.0047318, size = 16, normalized size = 0.7 \[ \frac{3}{28} (z-1)^{4/3} (4 z+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.6 \begin{align*}{\frac{12\,z+9}{28} \left ( -1+z \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.932029, size = 20, normalized size = 0.87 \begin{align*} \frac{3}{7} \,{\left (z - 1\right )}^{\frac{7}{3}} + \frac{3}{4} \,{\left (z - 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.415033, size = 49, normalized size = 2.13 \begin{align*} \frac{3}{28} \,{\left (4 \, z^{2} - z - 3\right )}{\left (z - 1\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.85472, size = 92, normalized size = 4. \begin{align*} \begin{cases} \frac{3 z^{2} \sqrt [3]{z - 1}}{7} - \frac{3 z \sqrt [3]{z - 1}}{28} - \frac{9 \sqrt [3]{z - 1}}{28} & \text{for}\: \left |{z}\right | > 1 \\\frac{3 z^{2} \sqrt [3]{1 - z} e^{\frac{i \pi }{3}}}{7} - \frac{3 z \sqrt [3]{1 - z} e^{\frac{i \pi }{3}}}{28} - \frac{9 \sqrt [3]{1 - z} e^{\frac{i \pi }{3}}}{28} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14098, size = 20, normalized size = 0.87 \begin{align*} \frac{3}{7} \,{\left (z - 1\right )}^{\frac{7}{3}} + \frac{3}{4} \,{\left (z - 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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