Optimal. Leaf size=24 \[ -\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x^3}\right ) \]
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Rubi [A] time = 0.0279187, 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} \[ -\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int f^{a+\frac{b}{x^3}} x^{14} \, dx &=-\frac{1}{3} b^5 f^a \Gamma \left (-5,-\frac{b \log (f)}{x^3}\right ) \log ^5(f)\\ \end{align*}
Mathematica [A] time = 0.0023997, size = 24, normalized size = 1. \[ -\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.056, size = 249, normalized size = 10.4 \begin{align*}{\frac{{f}^{a}{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}{3} \left ({\frac{{x}^{15}}{5\,{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}}+{\frac{{x}^{12}}{4\,{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}}+{\frac{{x}^{9}}{6\, \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}}+{\frac{{x}^{6}}{12\, \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}}+{\frac{{x}^{3}}{24\,b\ln \left ( f \right ) }}+{\frac{137}{7200}}+{\frac{\ln \left ( x \right ) }{40}}-{\frac{\ln \left ( -b \right ) }{120}}-{\frac{\ln \left ( \ln \left ( f \right ) \right ) }{120}}-{\frac{{x}^{15}}{7200\,{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}} \left ( 137\,{\frac{{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}{{x}^{15}}}+300\,{\frac{{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{{x}^{12}}}+600\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{x}^{9}}}+1200\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{x}^{6}}}+1800\,{\frac{b\ln \left ( f \right ) }{{x}^{3}}}+1440 \right ) }+{\frac{{x}^{15}}{720\,{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}} \left ( 6\,{\frac{{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{{x}^{12}}}+6\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{x}^{9}}}+12\,{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{x}^{6}}}+36\,{\frac{b\ln \left ( f \right ) }{{x}^{3}}}+144 \right ){{\rm e}^{{\frac{b\ln \left ( f \right ) }{{x}^{3}}}}}}+{\frac{1}{120}\ln \left ( -{\frac{b\ln \left ( f \right ) }{{x}^{3}}} \right ) }+{\frac{1}{120}{\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^{14}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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