Optimal. Leaf size=234 \[ \frac {1}{3} x^2 \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {5}{3};x^3\right )+\frac {\left (1-x^3\right )^{2/3} x}{3 \left (x^3+1\right )}-\frac {\left (1-x^3\right )^{2/3}}{3 \left (x^3+1\right )}-\frac {\log \left (\sqrt [3]{2}-\sqrt [3]{1-x^3}\right )}{3 \sqrt [3]{2}}+\frac {\log \left (-\sqrt [3]{1-x^3}-\sqrt [3]{2} x\right )}{3 \sqrt [3]{2}}-\frac {2^{2/3} \tan ^{-1}\left (\frac {1-\frac {2 \sqrt [3]{2} x}{\sqrt [3]{1-x^3}}}{\sqrt {3}}\right )}{3 \sqrt {3}}-\frac {2^{2/3} \tan ^{-1}\left (\frac {2^{2/3} \sqrt [3]{1-x^3}+1}{\sqrt {3}}\right )}{3 \sqrt {3}}+\frac {2 \left (1-x^3\right )^{2/3} x^2}{3 \left (x^3+1\right )} \]
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Rubi [F] time = 0.41, 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 = {} \[ \int \frac {\left (1-x^3\right )^{2/3}}{\left (1-x+x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (1-x^3\right )^{2/3}}{\left (1-x+x^2\right )^2} \, dx &=\int \left (-\frac {4 \left (1-x^3\right )^{2/3}}{3 \left (1+i \sqrt {3}-2 x\right )^2}+\frac {4 i \left (1-x^3\right )^{2/3}}{3 \sqrt {3} \left (1+i \sqrt {3}-2 x\right )}-\frac {4 \left (1-x^3\right )^{2/3}}{3 \left (-1+i \sqrt {3}+2 x\right )^2}+\frac {4 i \left (1-x^3\right )^{2/3}}{3 \sqrt {3} \left (-1+i \sqrt {3}+2 x\right )}\right ) \, dx\\ &=-\left (\frac {4}{3} \int \frac {\left (1-x^3\right )^{2/3}}{\left (1+i \sqrt {3}-2 x\right )^2} \, dx\right )-\frac {4}{3} \int \frac {\left (1-x^3\right )^{2/3}}{\left (-1+i \sqrt {3}+2 x\right )^2} \, dx+\frac {(4 i) \int \frac {\left (1-x^3\right )^{2/3}}{1+i \sqrt {3}-2 x} \, dx}{3 \sqrt {3}}+\frac {(4 i) \int \frac {\left (1-x^3\right )^{2/3}}{-1+i \sqrt {3}+2 x} \, dx}{3 \sqrt {3}}\\ \end {align*}
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Mathematica [F] time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {\left (1-x^3\right )^{2/3}}{\left (1-x+x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [F] time = 4.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (-x^{3} + 1\right )}^{\frac {2}{3}}}{x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, x + 1}, x\right ) \]
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 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {2}{3}}}{{\left (x^{2} - x + 1\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.19, size = 0, normalized size = 0.00 \[ \int \frac {\left (-x^{3}+1\right )^{\frac {2}{3}}}{\left (x^{2}-x +1\right )^{2}}\, dx \]
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 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {2}{3}}}{{\left (x^{2} - x + 1\right )}^{2}}\,{d x} \]
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 \[ \int \frac {{\left (1-x^3\right )}^{2/3}}{{\left (x^2-x+1\right )}^2} \,d x \]
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 \[ \int \frac {\left (- \left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac {2}{3}}}{\left (x^{2} - x + 1\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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