Optimal. Leaf size=14 \[ \frac{3 x}{5 \left (\frac{b}{x}\right )^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.001393, 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} \[ \frac{3 x}{5 \left (\frac{b}{x}\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x}\right )^{2/3}} \, dx &=\frac{\int x^{2/3} \, dx}{\left (\frac{b}{x}\right )^{2/3} x^{2/3}}\\ &=\frac{3 x}{5 \left (\frac{b}{x}\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0017159, size = 14, normalized size = 1. \[ \frac{3 x}{5 \left (\frac{b}{x}\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{5} \left ({\frac{b}{x}} \right ) ^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.973182, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{5 \, \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 = 1.63053, size = 31, normalized size = 2.21 \begin{align*} \frac{3 \, x^{2} \left (\frac{b}{x}\right )^{\frac{1}{3}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.572401, size = 15, normalized size = 1.07 \begin{align*} \frac{3 x}{5 b^{\frac{2}{3}} \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 = 1.14345, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{5 \, \left (\frac{b}{x}\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]