Optimal. Leaf size=435 \[ \frac{x \sqrt [3]{a+b x^3} F_1\left (\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right )}{c \sqrt [3]{\frac{b x^3}{a}+1}}+\frac{\sqrt [3]{b c^3-a d^3} \log \left (c^3+d^3 x^3\right )}{3 d^2}-\frac{\sqrt [3]{b c^3-a d^3} \log \left (\frac{x \sqrt [3]{b c^3-a d^3}}{c}-\sqrt [3]{a+b x^3}\right )}{2 d^2}-\frac{\sqrt [3]{b c^3-a d^3} \log \left (\sqrt [3]{b c^3-a d^3}+d \sqrt [3]{a+b x^3}\right )}{2 d^2}-\frac{\sqrt [3]{b c^3-a d^3} \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c^3-a d^3}}{c \sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{\sqrt{3} d^2}+\frac{\sqrt [3]{b c^3-a d^3} \tan ^{-1}\left (\frac{1-\frac{2 d \sqrt [3]{a+b x^3}}{\sqrt [3]{b c^3-a d^3}}}{\sqrt{3}}\right )}{\sqrt{3} d^2}+\frac{\sqrt [3]{b} c \log \left (\sqrt [3]{b} x-\sqrt [3]{a+b x^3}\right )}{2 d^2}+\frac{\sqrt [3]{b} c \tan ^{-1}\left (\frac{\frac{2 \sqrt [3]{b} x}{\sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{\sqrt{3} d^2}+\frac{\sqrt [3]{a+b x^3}}{d} \]
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Rubi [F] time = 0.0815726, 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 = {} \[ \int \frac{\sqrt [3]{a+b x^3}}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt [3]{a+b x^3}}{c+d x} \, dx &=\int \frac{\sqrt [3]{a+b x^3}}{c+d x} \, dx\\ \end{align*}
Mathematica [F] time = 0.332267, size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{a+b x^3}}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Maple [F] time = 0.048, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c}\sqrt [3]{b{x}^{3}+a}}\, 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 (b x^{3} + a\right )}^{\frac{1}{3}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{\sqrt [3]{a + b x^{3}}}{c + d x}\, 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 (b x^{3} + a\right )}^{\frac{1}{3}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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