Optimal. Leaf size=34 \[ -\frac {x^2 f^a \Gamma \left (\frac {2}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{2/3}} \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2218} \[ -\frac {x^2 f^a \text {Gamma}\left (\frac {2}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+b x^3} x \, dx &=-\frac {f^a x^2 \Gamma \left (\frac {2}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{2/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ -\frac {x^2 f^a \Gamma \left (\frac {2}{3},-b x^3 \log (f)\right )}{3 \left (-b x^3 \log (f)\right )^{2/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 29, normalized size = 0.85 \[ \frac {\left (-b \log \relax (f)\right )^{\frac {1}{3}} f^{a} \Gamma \left (\frac {2}{3}, -b x^{3} \log \relax (f)\right )}{3 \, b \log \relax (f)} \]
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 \[ \int f^{b x^{3} + a} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.03, size = 75, normalized size = 2.21 \[ \frac {\left (-\frac {\left (-b \right )^{\frac {2}{3}} x^{2} \Gamma \left (\frac {2}{3}, -b \,x^{3} \ln \relax (f )\right ) \ln \relax (f )^{\frac {2}{3}}}{\left (-b \,x^{3} \ln \relax (f )\right )^{\frac {2}{3}}}+\frac {\left (-b \right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right ) x^{2} \ln \relax (f )^{\frac {2}{3}}}{\left (-b \,x^{3} \ln \relax (f )\right )^{\frac {2}{3}}}\right ) f^{a}}{3 \left (-b \right )^{\frac {2}{3}} \ln \relax (f )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 28, normalized size = 0.82 \[ -\frac {f^{a} x^{2} \Gamma \left (\frac {2}{3}, -b x^{3} \log \relax (f)\right )}{3 \, \left (-b x^{3} \log \relax (f)\right )^{\frac {2}{3}}} \]
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 \[ \int f^{b\,x^3+a}\,x \,d x \]
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 \[ \int f^{a + b x^{3}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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