Optimal. Leaf size=21 \[ \frac{3}{4} x^{4/3} \log (x)-\frac{9 x^{4/3}}{16} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0067835, antiderivative size = 21, normalized size of antiderivative = 1., 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 = {2304} \[ \frac{3}{4} x^{4/3} \log (x)-\frac{9 x^{4/3}}{16} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2304
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 = 0.0023618, size = 15, normalized size = 0.71 \[ \frac{3}{16} x^{4/3} (4 \log (x)-3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 14, normalized size = 0.7 \begin{align*} -{\frac{9}{16}{x}^{{\frac{4}{3}}}}+{\frac{3\,\ln \left ( x \right ) }{4}{x}^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.06314, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{4} \, x^{\frac{4}{3}} \log \left (x\right ) - \frac{9}{16} \, x^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.93388, size = 45, normalized size = 2.14 \begin{align*} \frac{3}{16} \,{\left (4 \, x \log \left (x\right ) - 3 \, x\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 3.09549, size = 66, normalized size = 3.14 \begin{align*} \begin{cases} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.31856, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{4} \, x^{\frac{4}{3}} \log \left (x\right ) - \frac{9}{16} \, x^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]