Optimal. Leaf size=14 \[ \frac{3}{2} x \sqrt [3]{\frac{b}{x}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0016445, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{3}{2} x \sqrt [3]{\frac{b}{x}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt [3]{\frac{b}{x}} \, dx &=\left (\sqrt [3]{\frac{b}{x}} \sqrt [3]{x}\right ) \int \frac{1}{\sqrt [3]{x}} \, dx\\ &=\frac{3}{2} \sqrt [3]{\frac{b}{x}} x\\ \end{align*}
Mathematica [A] time = 0.0009351, size = 14, normalized size = 1. \[ \frac{3}{2} x \sqrt [3]{\frac{b}{x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{2}\sqrt [3]{{\frac{b}{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.995227, size = 14, normalized size = 1. \begin{align*} \frac{3}{2} \, x \left (\frac{b}{x}\right )^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.6553, size = 26, normalized size = 1.86 \begin{align*} \frac{3}{2} \, x \left (\frac{b}{x}\right )^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.222572, size = 15, normalized size = 1.07 \begin{align*} \frac{3 \sqrt [3]{b} x \sqrt [3]{\frac{1}{x}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1913, size = 14, normalized size = 1. \begin{align*} \frac{3 \, b}{2 \, \left (\frac{b}{x}\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]