Optimal. Leaf size=32 \[ -\frac {x f^a \Gamma \left (\frac {1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
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Rubi [A] time = 0.00, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2208} \[ -\frac {x f^a \text {Gamma}\left (\frac {1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
Antiderivative was successfully verified.
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Rule 2208
Rubi steps
\begin {align*} \int f^{a+b x^3} \, dx &=-\frac {f^a x \Gamma \left (\frac {1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ -\frac {x f^a \Gamma \left (\frac {1}{3},-b x^3 \log (f)\right )}{3 \sqrt [3]{-b x^3 \log (f)}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 29, normalized size = 0.91 \[ \frac {\left (-b \log \relax (f)\right )^{\frac {2}{3}} f^{a} \Gamma \left (\frac {1}{3}, -b x^{3} \log \relax (f)\right )}{3 \, b \log \relax (f)} \]
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 \[ \int f^{b x^{3} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.03, size = 78, normalized size = 2.44 \[ \frac {\left (-\frac {\left (-b \right )^{\frac {1}{3}} x \Gamma \left (\frac {1}{3}, -b \,x^{3} \ln \relax (f )\right ) \ln \relax (f )^{\frac {1}{3}}}{\left (-b \,x^{3} \ln \relax (f )\right )^{\frac {1}{3}}}+\frac {2 \left (-b \right )^{\frac {1}{3}} \pi \sqrt {3}\, x \ln \relax (f )^{\frac {1}{3}}}{3 \Gamma \left (\frac {2}{3}\right ) \left (-b \,x^{3} \ln \relax (f )\right )^{\frac {1}{3}}}\right ) f^{a}}{3 \left (-b \right )^{\frac {1}{3}} \ln \relax (f )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 26, normalized size = 0.81 \[ -\frac {f^{a} x \Gamma \left (\frac {1}{3}, -b x^{3} \log \relax (f)\right )}{3 \, \left (-b x^{3} \log \relax (f)\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int f^{b\,x^3+a} \,d x \]
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 \[ \int f^{a + b x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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