Optimal. Leaf size=21 \[ -\frac {9 x^{4/3}}{16}+\frac {3}{4} x^{4/3} \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2341}
\begin {gather*} \frac {3}{4} x^{4/3} \log (x)-\frac {9 x^{4/3}}{16} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2341
Rubi steps
\begin {align*} \int \sqrt [3]{x} \log (x) \, dx &=-\frac {9 x^{4/3}}{16}+\frac {3}{4} x^{4/3} \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 15, normalized size = 0.71 \begin {gather*} \frac {3}{16} x^{4/3} (-3+4 \log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 14, normalized size = 0.67
method | result | size |
derivativedivides | \(-\frac {9 x^{\frac {4}{3}}}{16}+\frac {3 x^{\frac {4}{3}} \ln \left (x \right )}{4}\) | \(14\) |
default | \(-\frac {9 x^{\frac {4}{3}}}{16}+\frac {3 x^{\frac {4}{3}} \ln \left (x \right )}{4}\) | \(14\) |
risch | \(-\frac {9 x^{\frac {4}{3}}}{16}+\frac {3 x^{\frac {4}{3}} \ln \left (x \right )}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{4} \, x^{\frac {4}{3}} \log \left (x\right ) - \frac {9}{16} \, x^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 14, normalized size = 0.67 \begin {gather*} \frac {3}{16} \, {\left (4 \, x \log \left (x\right ) - 3 \, x\right )} x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 105 vs.
\(2 (19) = 38\).
time = 1.96, size = 105, normalized size = 5.00 \begin {gather*} \begin {cases} - \frac {3 x^{\frac {4}{3}} \log {\left (\frac {1}{x} \right )}}{4} + \frac {3 x^{\frac {4}{3}} \log {\left (x \right )}}{4} - \frac {9 x^{\frac {4}{3}}}{8} & \text {for}\: \frac {1}{\left |{x}\right |} < 1 \wedge \left |{x}\right | < 1 \\\frac {3 x^{\frac {4}{3}} \log {\left (x \right )}}{4} - \frac {9 x^{\frac {4}{3}}}{16} & \text {for}\: \left |{x}\right | < 1 \\- \frac {3 x^{\frac {4}{3}} \log {\left (\frac {1}{x} \right )}}{4} - \frac {9 x^{\frac {4}{3}}}{16} & \text {for}\: \frac {1}{\left |{x}\right |} < 1 \\- {G_{3, 3}^{2, 1}\left (\begin {matrix} 1 & \frac {7}{3}, \frac {7}{3} \\\frac {4}{3}, \frac {4}{3} & 0 \end {matrix} \middle | {x} \right )} + {G_{3, 3}^{0, 3}\left (\begin {matrix} \frac {7}{3}, \frac {7}{3}, 1 & \\ & \frac {4}{3}, \frac {4}{3}, 0 \end {matrix} \middle | {x} \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.64, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{4} \, x^{\frac {4}{3}} \log \left (x\right ) - \frac {9}{16} \, x^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.34, size = 9, normalized size = 0.43 \begin {gather*} \frac {3\,x^{4/3}\,\left (\ln \left (x\right )-\frac {3}{4}\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________