Optimal. Leaf size=18 \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014808, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {32} \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{-a+b x}} \, dx &=\frac{3 (-a+b x)^{2/3}}{2 b}\\ \end{align*}
Mathematica [A] time = 0.0078637, size = 18, normalized size = 1. \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 0.8 \begin{align*}{\frac{3}{2\,b} \left ( bx-a \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.986556, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.43817, size = 31, normalized size = 1.72 \begin{align*} \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.068408, size = 12, normalized size = 0.67 \begin{align*} \frac{3 \left (- a + b x\right )^{\frac{2}{3}}}{2 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19638, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]