Optimal. Leaf size=234 \[ \frac{1}{3} x^2 \, _2F_1\left (\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right )+\frac{2 \left (1-x^3\right )^{2/3} x^2}{3 \left (x^3+1\right )}+\frac{\left (1-x^3\right )^{2/3} x}{3 \left (x^3+1\right )}-\frac{\left (1-x^3\right )^{2/3}}{3 \left (x^3+1\right )}-\frac{\log \left (\sqrt [3]{2}-\sqrt [3]{1-x^3}\right )}{3 \sqrt [3]{2}}+\frac{\log \left (-\sqrt [3]{1-x^3}-\sqrt [3]{2} x\right )}{3 \sqrt [3]{2}}-\frac{2^{2/3} \tan ^{-1}\left (\frac{1-\frac{2 \sqrt [3]{2} x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )}{3 \sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left (\frac{2^{2/3} \sqrt [3]{1-x^3}+1}{\sqrt{3}}\right )}{3 \sqrt{3}} \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.414851, 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 = {} \[ \int \frac{\left (1-x^3\right )^{2/3}}{\left (1-x+x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
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*}
Mathematica [F] time = 0.45237, size = 0, normalized size = 0. \[ \int \frac{\left (1-x^3\right )^{2/3}}{\left (1-x+x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.091, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ({x}^{2}-x+1 \right ) ^{2}} \left ( -{x}^{3}+1 \right ) ^{{\frac{2}{3}}}}\, 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{2}{3}}}{{\left (x^{2} - x + 1\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\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 ) \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{\left (- \left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac{2}{3}}}{\left (x^{2} - x + 1\right )^{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{2}{3}}}{{\left (x^{2} - x + 1\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]