Optimal. Leaf size=24 \[ -\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-b x^3 \log (f)\right ) \]
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Rubi [A] time = 0.0209979, 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} \[ -\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^3}}{x^{13}} \, dx &=-\frac{1}{3} b^4 f^a \Gamma \left (-4,-b x^3 \log (f)\right ) \log ^4(f)\\ \end{align*}
Mathematica [A] time = 0.0023959, size = 24, normalized size = 1. \[ -\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.054, size = 213, normalized size = 8.9 \begin{align*}{\frac{{f}^{a}{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{3} \left ( -{\frac{1}{4\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}}}-{\frac{1}{3\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}}}-{\frac{1}{4\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}}}-{\frac{1}{6\,b{x}^{3}\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{125\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}+240\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}+360\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}+480\,b{x}^{3}\ln \left ( f \right ) +360}{1440\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}}}-{\frac{ \left ( 5\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}+5\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}+10\,b{x}^{3}\ln \left ( f \right ) +30 \right ){{\rm e}^{b{x}^{3}\ln \left ( f \right ) }}}{120\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}}}-{\frac{\ln \left ( -b{x}^{3}\ln \left ( f \right ) \right ) }{24}}-{\frac{{\it Ei} \left ( 1,-b{x}^{3}\ln \left ( f \right ) \right ) }{24}} \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 \frac{f^{b x^{3} + a}}{x^{13}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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