Optimal. Leaf size=177 \[ \frac{1}{2} x^2 \, _2F_1\left (\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right )+\frac{1}{2} \left (1-x^3\right )^{2/3}-\frac{1}{2} \log \left (\sqrt [3]{1-x^3}+x\right )+\frac{3 \log \left (2^{2/3} \sqrt [3]{1-x^3}+x-1\right )}{2 \sqrt [3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left (\frac{\frac{\sqrt [3]{2} (1-x)}{\sqrt [3]{1-x^3}}+1}{\sqrt{3}}\right )}{\sqrt [3]{2}}+\frac{\tan ^{-1}\left (\frac{1-\frac{2 x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )}{\sqrt{3}}-\frac{\log \left ((1-x) (x+1)^2\right )}{2 \sqrt [3]{2}} \]
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Rubi [F] time = 0.0599141, 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 = {} \[ \int \frac{\left (1-x^3\right )^{2/3}}{1+x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (1-x^3\right )^{2/3}}{1+x} \, dx &=\int \frac{\left (1-x^3\right )^{2/3}}{1+x} \, dx\\ \end{align*}
Mathematica [F] time = 0.389881, size = 0, normalized size = 0. \[ \int \frac{\left (1-x^3\right )^{2/3}}{1+x} \, dx \]
Verification is Not applicable to the result.
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Maple [F] time = 0.041, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{1+x} \left ( -{x}^{3}+1 \right ) ^{{\frac{2}{3}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}{x + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}{x + 1}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (- \left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac{2}{3}}}{x + 1}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}{x + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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