Optimal. Leaf size=232 \[ \frac{1}{2} x F_1\left (\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^3,-\frac{x^3}{8}\right )+\sqrt [3]{1-x^3}-\frac{\log \left (x^3+8\right )}{\sqrt [3]{3}}+\frac{1}{2} 3^{2/3} \log \left (3^{2/3}-\sqrt [3]{1-x^3}\right )-\log \left (-\sqrt [3]{1-x^3}-x\right )+\frac{1}{2} 3^{2/3} \log \left (-\sqrt [3]{1-x^3}-\frac{1}{2} 3^{2/3} x\right )-\frac{2 \tan ^{-1}\left (\frac{1-\frac{2 x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )}{\sqrt{3}}+\sqrt [6]{3} \tan ^{-1}\left (\frac{1-\frac{3^{2/3} x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )-\sqrt [6]{3} \tan ^{-1}\left (\frac{2 \sqrt [3]{1-x^3}}{3 \sqrt [6]{3}}+\frac{1}{\sqrt{3}}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.0499624, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sqrt [3]{1-x^3}}{2+x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\sqrt [3]{1-x^3}}{2+x} \, dx &=\int \frac{\sqrt [3]{1-x^3}}{2+x} \, dx\\ \end{align*}
Mathematica [F] time = 0.343464, size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{1-x^3}}{2+x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.048, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{2+x}\sqrt [3]{-{x}^{3}+1}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x + 2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt [3]{- \left (x - 1\right ) \left (x^{2} + x + 1\right )}}{x + 2}\, dx \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 \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x + 2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]