Optimal. Leaf size=15 \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0030703, antiderivative size = 15, normalized size of antiderivative = 1., 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} \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{\left (1+x^{2/3}\right )^{3/2}}{\sqrt [3]{x}} \, dx &=\frac{3}{5} \left (1+x^{2/3}\right )^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0050031, size = 15, normalized size = 1. \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 10, normalized size = 0.7 \begin{align*}{\frac{3}{5} \left ( 1+{x}^{{\frac{2}{3}}} \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.94605, size = 12, normalized size = 0.8 \begin{align*} \frac{3}{5} \,{\left (x^{\frac{2}{3}} + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 6.50195, size = 66, normalized size = 4.4 \begin{align*} \frac{3}{5} \,{\left (x^{\frac{4}{3}} + 2 \, x^{\frac{2}{3}} + 1\right )} \sqrt{x^{\frac{2}{3}} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 1.18405, size = 49, normalized size = 3.27 \begin{align*} \frac{3 x^{\frac{4}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{6 x^{\frac{2}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{3 \sqrt{x^{\frac{2}{3}} + 1}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14004, size = 12, normalized size = 0.8 \begin{align*} \frac{3}{5} \,{\left (x^{\frac{2}{3}} + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]