Optimal. Leaf size=34 \[ \frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2218} \[ \frac {f^a \text {Gamma}\left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^3}}}{x^3} \, dx &=\frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ \frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 29, normalized size = 0.85 \[ -\frac {\left (-b \log \relax (f)\right )^{\frac {1}{3}} f^{a} \Gamma \left (\frac {2}{3}, -\frac {b \log \relax (f)}{x^{3}}\right )}{3 \, b \log \relax (f)} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{3}}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 78, normalized size = 2.29 \[ \frac {\left (-b \right )^{\frac {1}{3}} \left (-\frac {\left (-b \right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {b \ln \relax (f )}{x^{3}}\right ) \ln \relax (f )^{\frac {2}{3}}}{\left (-\frac {b \ln \relax (f )}{x^{3}}\right )^{\frac {2}{3}} x^{2}}+\frac {\left (-b \right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right ) \ln \relax (f )^{\frac {2}{3}}}{\left (-\frac {b \ln \relax (f )}{x^{3}}\right )^{\frac {2}{3}} x^{2}}\right ) f^{a}}{3 b \ln \relax (f )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.40, size = 28, normalized size = 0.82 \[ \frac {f^{a} \Gamma \left (\frac {2}{3}, -\frac {b \log \relax (f)}{x^{3}}\right )}{3 \, x^{2} \left (-\frac {b \log \relax (f)}{x^{3}}\right )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 33, normalized size = 0.97 \[ -\frac {f^a\,\left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3},-\frac {b\,\ln \relax (f)}{x^3}\right )\right )}{3\,x^2\,{\left (-\frac {b\,\ln \relax (f)}{x^3}\right )}^{2/3}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{3}}}}{x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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