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 = 0.08, 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 = {} \[ \int \frac {\sqrt [3]{a+b x^3}}{c+d x} \, dx \]
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*}
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Mathematica [F] time = 0.33, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt [3]{a+b x^3}}{c+d x} \, dx \]
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 \[ \int \frac {{\left (b x^{3} + a\right )}^{\frac {1}{3}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \,x^{3}+a \right )^{\frac {1}{3}}}{d x +c}\, dx \]
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 \[ \int \frac {{\left (b x^{3} + a\right )}^{\frac {1}{3}}}{d x + c}\,{d x} \]
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 \[ \int \frac {{\left (b\,x^3+a\right )}^{1/3}}{c+d\,x} \,d x \]
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 \[ \int \frac {\sqrt [3]{a + b x^{3}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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