Optimal. Leaf size=34 \[ -\frac {x^4 f^a \Gamma \left (\frac {4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}} \]
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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} \[ -\frac {x^4 f^a \text {Gamma}\left (\frac {4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+b x^3} x^3 \, dx &=-\frac {f^a x^4 \Gamma \left (\frac {4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ -\frac {x^4 f^a \Gamma \left (\frac {4}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{4/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 47, normalized size = 1.38 \[ \frac {3 \, b f^{b x^{3} + a} x \log \relax (f) - \left (-b \log \relax (f)\right )^{\frac {2}{3}} f^{a} \Gamma \left (\frac {1}{3}, -b x^{3} \log \relax (f)\right )}{9 \, b^{2} \log \relax (f)^{2}} \]
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 \[ \int f^{b x^{3} + a} x^{3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 109, normalized size = 3.21 \[ -\frac {\left (\frac {\left (-b \right )^{\frac {4}{3}} x \Gamma \left (\frac {1}{3}, -b \,x^{3} \ln \relax (f )\right ) \ln \relax (f )^{\frac {1}{3}}}{3 \left (-b \,x^{3} \ln \relax (f )\right )^{\frac {1}{3}} b}+\frac {\left (-b \right )^{\frac {4}{3}} x \,{\mathrm e}^{b \,x^{3} \ln \relax (f )} \ln \relax (f )^{\frac {1}{3}}}{b}-\frac {2 \left (-b \right )^{\frac {4}{3}} \pi \sqrt {3}\, x \ln \relax (f )^{\frac {1}{3}}}{9 \Gamma \left (\frac {2}{3}\right ) \left (-b \,x^{3} \ln \relax (f )\right )^{\frac {1}{3}} b}\right ) f^{a}}{3 \left (-b \right )^{\frac {1}{3}} b \ln \relax (f )^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 28, normalized size = 0.82 \[ -\frac {f^{a} x^{4} \Gamma \left (\frac {4}{3}, -b x^{3} \log \relax (f)\right )}{3 \, \left (-b x^{3} \log \relax (f)\right )^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.18, size = 75, normalized size = 2.21 \[ \frac {f^a\,f^{b\,x^3}\,x}{3\,b\,\ln \relax (f)}-\frac {f^a\,x^4\,\Gamma \left (\frac {1}{3},-b\,x^3\,\ln \relax (f)\right )}{9\,{\left (-b\,x^3\,\ln \relax (f)\right )}^{4/3}}+\frac {2\,\pi \,\sqrt {3}\,f^a\,x^4}{27\,\Gamma \left (\frac {2}{3}\right )\,{\left (-b\,x^3\,\ln \relax (f)\right )}^{4/3}} \]
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 \[ \int f^{a + b x^{3}} x^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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