Optimal. Leaf size=24 \[ \frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x^3}\right ) \]
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Rubi [A] time = 0.0330287, antiderivative size = 24, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0023848, size = 24, normalized size = 1. \[ \frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.052, size = 213, normalized size = 8.9 \begin{align*} -{\frac{{f}^{a}{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{3} \left ( -{\frac{{x}^{12}}{4\,{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}}-{\frac{{x}^{9}}{3\, \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}}-{\frac{{x}^{6}}{4\, \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}}-{\frac{{x}^{3}}{6\,b\ln \left ( f \right ) }}-{\frac{25}{288}}-{\frac{\ln \left ( x \right ) }{8}}+{\frac{\ln \left ( -b \right ) }{24}}+{\frac{\ln \left ( \ln \left ( f \right ) \right ) }{24}}+{\frac{{x}^{12}}{1440\,{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}} \left ( 125\,{\frac{{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{{x}^{12}}}+240\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{x}^{9}}}+360\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{x}^{6}}}+480\,{\frac{b\ln \left ( f \right ) }{{x}^{3}}}+360 \right ) }-{\frac{{x}^{12}}{120\,{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}} \left ( 5\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{x}^{9}}}+5\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{x}^{6}}}+10\,{\frac{b\ln \left ( f \right ) }{{x}^{3}}}+30 \right ){{\rm e}^{{\frac{b\ln \left ( f \right ) }{{x}^{3}}}}}}-{\frac{1}{24}\ln \left ( -{\frac{b\ln \left ( f \right ) }{{x}^{3}}} \right ) }-{\frac{1}{24}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{{x}^{3}}} \right ) } \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int f^{a + \frac{b}{x^{3}}} x^{11}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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