Optimal. Leaf size=232 \[ \frac {1}{2} x F_1\left (\frac {1}{3};-\frac {1}{3},1;\frac {4}{3};x^3,-\frac {x^3}{8}\right )+\sqrt [3]{1-x^3}-\frac {\log \left (x^3+8\right )}{\sqrt [3]{3}}+\frac {1}{2} 3^{2/3} \log \left (3^{2/3}-\sqrt [3]{1-x^3}\right )-\log \left (-\sqrt [3]{1-x^3}-x\right )+\frac {1}{2} 3^{2/3} \log \left (-\sqrt [3]{1-x^3}-\frac {1}{2} 3^{2/3} x\right )-\frac {2 \tan ^{-1}\left (\frac {1-\frac {2 x}{\sqrt [3]{1-x^3}}}{\sqrt {3}}\right )}{\sqrt {3}}+\sqrt [6]{3} \tan ^{-1}\left (\frac {1-\frac {3^{2/3} x}{\sqrt [3]{1-x^3}}}{\sqrt {3}}\right )-\sqrt [6]{3} \tan ^{-1}\left (\frac {2 \sqrt [3]{1-x^3}}{3 \sqrt [6]{3}}+\frac {1}{\sqrt {3}}\right ) \]
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Rubi [F] time = 0.05, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\sqrt [3]{1-x^3}}{2+x} \, dx \]
Verification is Not applicable to the result.
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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*}
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Mathematica [F] time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt [3]{1-x^3}}{2+x} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {1}{3}}}{x + 2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.85, size = 0, normalized size = 0.00 \[ \int \frac {\left (-x^{3}+1\right )^{\frac {1}{3}}}{x +2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {1}{3}}}{x + 2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {{\left (1-x^3\right )}^{1/3}}{x+2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt [3]{- \left (x - 1\right ) \left (x^{2} + x + 1\right )}}{x + 2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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