Optimal. Leaf size=23 \[ \frac {3}{7} (z-1)^{7/3}+\frac {3}{4} (z-1)^{4/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, 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.
[In]
[Out]
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 = 0.01, size = 16, normalized size = 0.70 \[ \frac {3}{28} (z-1)^{4/3} (4 z+3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 17, normalized size = 0.74 \[ \frac {3}{28} \, {\left (4 \, z^{2} - z - 3\right )} {\left (z - 1\right )}^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.01, size = 15, normalized size = 0.65 \[ \frac {3}{7} \, {\left (z - 1\right )}^{\frac {7}{3}} + \frac {3}{4} \, {\left (z - 1\right )}^{\frac {4}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.57 \[ \frac {3 \left (z -1\right )^{\frac {4}{3}} \left (4 z +3\right )}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.71, size = 15, normalized size = 0.65 \[ \frac {3}{7} \, {\left (z - 1\right )}^{\frac {7}{3}} + \frac {3}{4} \, {\left (z - 1\right )}^{\frac {4}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 12, normalized size = 0.52 \[ \frac {3\,\left (4\,z+3\right )\,{\left (z-1\right )}^{4/3}}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.99, size = 92, normalized size = 4.00 \[ \begin {cases} \frac {3 z^{2} \sqrt [3]{z - 1}}{7} - \frac {3 z \sqrt [3]{z - 1}}{28} - \frac {9 \sqrt [3]{z - 1}}{28} & \text {for}\: \left |{z}\right | > 1 \\\frac {3 z^{2} \sqrt [3]{1 - z} e^{\frac {i \pi }{3}}}{7} - \frac {3 z \sqrt [3]{1 - z} e^{\frac {i \pi }{3}}}{28} - \frac {9 \sqrt [3]{1 - z} e^{\frac {i \pi }{3}}}{28} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________