Optimal. Leaf size=30 \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0170899, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176, Rules used = {374, 376, 77} \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 374
Rule 376
Rule 77
Rubi steps
\begin{align*} \int \frac{1+\frac{1}{\sqrt [3]{x}}}{-1+\frac{1}{\sqrt [3]{x}}} \, dx &=\int \frac{1+\sqrt [3]{x}}{1-\sqrt [3]{x}} \, dx\\ &=3 \operatorname{Subst}\left (\int \frac{x^2 (1+x)}{1-x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (-2-\frac{2}{-1+x}-2 x-x^2\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-6 \sqrt [3]{x}-3 x^{2/3}-x-6 \log \left (1-\sqrt [3]{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0128185, size = 30, normalized size = 1. \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 23, normalized size = 0.8 \begin{align*} -x-3\,{x}^{2/3}-6\,\sqrt [3]{x}-6\,\ln \left ( -1+\sqrt [3]{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.944397, size = 30, normalized size = 1. \begin{align*} -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.12879, size = 66, normalized size = 2.2 \begin{align*} -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.150008, size = 26, normalized size = 0.87 \begin{align*} - 3 x^{\frac{2}{3}} - 6 \sqrt [3]{x} - x - 6 \log{\left (\sqrt [3]{x} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05281, size = 31, normalized size = 1.03 \begin{align*} -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log \left ({\left | x^{\frac{1}{3}} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]