Optimal. Leaf size=14 \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014599, 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} \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{\frac{b}{x^2}}} \, dx &=\frac{\int x^{2/3} \, dx}{\sqrt [3]{\frac{b}{x^2}} x^{2/3}}\\ &=\frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}}\\ \end{align*}
Mathematica [A] time = 0.0016263, size = 14, normalized size = 1. \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{5}{\frac{1}{\sqrt [3]{{\frac{b}{{x}^{2}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.971083, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{5 \, \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.67953, size = 34, normalized size = 2.43 \begin{align*} \frac{3 \, x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.378672, size = 17, normalized size = 1.21 \begin{align*} \frac{3 x}{5 \sqrt [3]{b} \sqrt [3]{\frac{1}{x^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]