Optimal. Leaf size=12 \[ 3 x \left (\frac{b}{x}\right )^{2/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014171, antiderivative size = 12, 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} \[ 3 x \left (\frac{b}{x}\right )^{2/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x}\right )^{2/3} \, dx &=\left (\left (\frac{b}{x}\right )^{2/3} x^{2/3}\right ) \int \frac{1}{x^{2/3}} \, dx\\ &=3 \left (\frac{b}{x}\right )^{2/3} x\\ \end{align*}
Mathematica [A] time = 0.0011418, size = 12, normalized size = 1. \[ 3 x \left (\frac{b}{x}\right )^{2/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 11, normalized size = 0.9 \begin{align*} 3\, \left ({\frac{b}{x}} \right ) ^{2/3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.979768, size = 14, normalized size = 1.17 \begin{align*} 3 \, x \left (\frac{b}{x}\right )^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.72077, size = 23, normalized size = 1.92 \begin{align*} 3 \, x \left (\frac{b}{x}\right )^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.286561, size = 14, normalized size = 1.17 \begin{align*} 3 b^{\frac{2}{3}} x \left (\frac{1}{x}\right )^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17897, size = 14, normalized size = 1.17 \begin{align*} \frac{3 \, b}{\left (\frac{b}{x}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]