Optimal. Leaf size=18 \[ \frac{x \left (a+\frac{b}{x^{3/5}}\right )^{5/3}}{a} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0025717, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {191} \[ \frac{x \left (a+\frac{b}{x^{3/5}}\right )^{5/3}}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 191
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x^{3/5}}\right )^{2/3} \, dx &=\frac{\left (a+\frac{b}{x^{3/5}}\right )^{5/3} x}{a}\\ \end{align*}
Mathematica [A] time = 0.0172939, size = 18, normalized size = 1. \[ \frac{x \left (a+\frac{b}{x^{3/5}}\right )^{5/3}}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.018, size = 0, normalized size = 0. \begin{align*} \int \left ( a+{b{x}^{-{\frac{3}{5}}}} \right ) ^{{\frac{2}{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.982942, size = 19, normalized size = 1.06 \begin{align*} \frac{{\left (a + \frac{b}{x^{\frac{3}{5}}}\right )}^{\frac{5}{3}} x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 59.8269, size = 78, normalized size = 4.33 \begin{align*} - \frac{5 b^{\frac{2}{3}} x^{\frac{3}{5}} \left (\frac{a x^{\frac{3}{5}}}{b} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{5}{3}\right )}{3 \Gamma \left (- \frac{2}{3}\right )} - \frac{5 b^{\frac{5}{3}} \left (\frac{a x^{\frac{3}{5}}}{b} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{5}{3}\right )}{3 a \Gamma \left (- \frac{2}{3}\right )} \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{\left (a + \frac{b}{x^{\frac{3}{5}}}\right )}^{\frac{2}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]