Optimal. Leaf size=384 \[ -\frac {\left (a^3+b^3\right )^{2/3} \log \left (a^3+b^3 x^3\right )}{3 b^3}+\frac {\left (a^3+b^3\right )^{2/3} \log \left (-\frac {x \sqrt [3]{a^3+b^3}}{a}-\sqrt [3]{1-x^3}\right )}{2 b^3}+\frac {\left (a^3+b^3\right )^{2/3} \log \left (\sqrt [3]{a^3+b^3}-b \sqrt [3]{1-x^3}\right )}{2 b^3}-\frac {\left (a^3+b^3\right )^{2/3} \tan ^{-1}\left (\frac {1-\frac {2 x \sqrt [3]{a^3+b^3}}{a \sqrt [3]{1-x^3}}}{\sqrt {3}}\right )}{\sqrt {3} b^3}+\frac {\left (a^3+b^3\right )^{2/3} \tan ^{-1}\left (\frac {\frac {2 b \sqrt [3]{1-x^3}}{\sqrt [3]{a^3+b^3}}+1}{\sqrt {3}}\right )}{\sqrt {3} b^3}-\frac {a^2 \log \left (\sqrt [3]{1-x^3}+x\right )}{2 b^3}+\frac {a^2 \tan ^{-1}\left (\frac {1-\frac {2 x}{\sqrt [3]{1-x^3}}}{\sqrt {3}}\right )}{\sqrt {3} b^3}-\frac {x^2 \left (a^3+b^3\right ) F_1\left (\frac {2}{3};\frac {1}{3},1;\frac {5}{3};x^3,-\frac {b^3 x^3}{a^3}\right )}{2 a^2 b^2}+\frac {a x^2 \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {5}{3};x^3\right )}{2 b^2}+\frac {\left (1-x^3\right )^{2/3}}{2 b} \]
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Rubi [F] time = 0.07, 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 = {} \[ \int \frac {\left (1-x^3\right )^{2/3}}{a+b x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (1-x^3\right )^{2/3}}{a+b x} \, dx &=\int \frac {\left (1-x^3\right )^{2/3}}{a+b x} \, dx\\ \end {align*}
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Mathematica [F] time = 0.28, size = 0, normalized size = 0.00 \[ \int \frac {\left (1-x^3\right )^{2/3}}{a+b x} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
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 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {2}{3}}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\left (-x^{3}+1\right )^{\frac {2}{3}}}{b x +a}\, dx \]
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 \[ \int \frac {{\left (-x^{3} + 1\right )}^{\frac {2}{3}}}{b x + a}\,{d x} \]
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 \[ \int \frac {{\left (1-x^3\right )}^{2/3}}{a+b\,x} \,d x \]
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 \[ \int \frac {\left (- \left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac {2}{3}}}{a + b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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