Optimal. Leaf size=15 \[ \frac{3}{4} \sqrt [3]{x^4-4 x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0093661, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {1588} \[ \frac{3}{4} \sqrt [3]{x^4-4 x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1588
Rubi steps
\begin{align*} \int \frac{-1+x^3}{\left (-4 x+x^4\right )^{2/3}} \, dx &=\frac{3}{4} \sqrt [3]{-4 x+x^4}\\ \end{align*}
Mathematica [A] time = 0.0256064, size = 15, normalized size = 1. \[ \frac{3}{4} \sqrt [3]{x \left (x^3-4\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 18, normalized size = 1.2 \begin{align*}{\frac{3\,x \left ({x}^{3}-4 \right ) }{4} \left ({x}^{4}-4\,x \right ) ^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10455, size = 15, normalized size = 1. \begin{align*} \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.36459, size = 31, normalized size = 2.07 \begin{align*} \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.185364, size = 12, normalized size = 0.8 \begin{align*} \frac{3 \sqrt [3]{x^{4} - 4 x}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10566, size = 15, normalized size = 1. \begin{align*} \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]