Optimal. Leaf size=24 \[ \frac {1}{3} b^4 f^a \log ^4(f) \Gamma \left (-4,-\frac {b \log (f)}{x^3}\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 24, 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} \[ \frac {1}{3} b^4 f^a \log ^4(f) \text {Gamma}\left (-4,-\frac {b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+\frac {b}{x^3}} x^{11} \, dx &=\frac {1}{3} b^4 f^a \Gamma \left (-4,-\frac {b \log (f)}{x^3}\right ) \log ^4(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ \frac {1}{3} b^4 f^a \log ^4(f) \Gamma \left (-4,-\frac {b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 72, normalized size = 3.00 \[ -\frac {1}{72} \, b^{4} f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{3}}\right ) \log \relax (f)^{4} + \frac {1}{72} \, {\left (6 \, x^{12} + 2 \, b x^{9} \log \relax (f) + b^{2} x^{6} \log \relax (f)^{2} + b^{3} x^{3} \log \relax (f)^{3}\right )} f^{\frac {a x^{3} + b}{x^{3}}} \]
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 \[ \int f^{a + \frac {b}{x^{3}}} x^{11}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 213, normalized size = 8.88 \[ -\frac {\left (-\frac {\left (\frac {10 b \ln \relax (f )}{x^{3}}+\frac {5 b^{2} \ln \relax (f )^{2}}{x^{6}}+\frac {5 b^{3} \ln \relax (f )^{3}}{x^{9}}+30\right ) x^{12} {\mathrm e}^{\frac {b \ln \relax (f )}{x^{3}}}}{120 b^{4} \ln \relax (f )^{4}}+\frac {\left (\frac {480 b \ln \relax (f )}{x^{3}}+\frac {360 b^{2} \ln \relax (f )^{2}}{x^{6}}+\frac {240 b^{3} \ln \relax (f )^{3}}{x^{9}}+\frac {125 b^{4} \ln \relax (f )^{4}}{x^{12}}+360\right ) x^{12}}{1440 b^{4} \ln \relax (f )^{4}}-\frac {x^{12}}{4 b^{4} \ln \relax (f )^{4}}-\frac {x^{9}}{3 b^{3} \ln \relax (f )^{3}}-\frac {x^{6}}{4 b^{2} \ln \relax (f )^{2}}-\frac {x^{3}}{6 b \ln \relax (f )}-\frac {\Ei \left (1, -\frac {b \ln \relax (f )}{x^{3}}\right )}{24}-\frac {\ln \relax (x )}{8}+\frac {\ln \left (-b \right )}{24}-\frac {\ln \left (-\frac {b \ln \relax (f )}{x^{3}}\right )}{24}+\frac {\ln \left (\ln \relax (f )\right )}{24}-\frac {25}{288}\right ) b^{4} f^{a} \ln \relax (f )^{4}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.29, size = 22, normalized size = 0.92 \[ \frac {1}{3} \, b^{4} f^{a} \Gamma \left (-4, -\frac {b \log \relax (f)}{x^{3}}\right ) \log \relax (f)^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.78, size = 90, normalized size = 3.75 \[ \frac {b^4\,f^a\,{\ln \relax (f)}^4\,\mathrm {expint}\left (-\frac {b\,\ln \relax (f)}{x^3}\right )}{72}+\frac {b^4\,f^a\,f^{\frac {b}{x^3}}\,{\ln \relax (f)}^4\,\left (\frac {x^3}{24\,b\,\ln \relax (f)}+\frac {x^6}{24\,b^2\,{\ln \relax (f)}^2}+\frac {x^9}{12\,b^3\,{\ln \relax (f)}^3}+\frac {x^{12}}{4\,b^4\,{\ln \relax (f)}^4}\right )}{3} \]
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 \[ \int f^{a + \frac {b}{x^{3}}} x^{11}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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