Optimal. Leaf size=24 \[ \frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^3 \log (f)\right ) \]
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Rubi [A] time = 0.0209877, 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} \[ \frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^3}}{x^{16}} \, dx &=\frac{1}{3} b^5 f^a \Gamma \left (-5,-b x^3 \log (f)\right ) \log ^5(f)\\ \end{align*}
Mathematica [A] time = 0.0023457, size = 24, normalized size = 1. \[ \frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.06, size = 249, normalized size = 10.4 \begin{align*} -{\frac{{f}^{a}{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}{3} \left ({\frac{1}{5\,{b}^{5}{x}^{15} \left ( \ln \left ( f \right ) \right ) ^{5}}}+{\frac{1}{4\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}}}+{\frac{1}{6\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}}}+{\frac{1}{12\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}}}+{\frac{1}{24\,b{x}^{3}\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{137\,{b}^{5}{x}^{15} \left ( \ln \left ( f \right ) \right ) ^{5}+300\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}+600\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}+1200\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}+1800\,b{x}^{3}\ln \left ( f \right ) +1440}{7200\,{b}^{5}{x}^{15} \left ( \ln \left ( f \right ) \right ) ^{5}}}+{\frac{ \left ( 6\,{b}^{4}{x}^{12} \left ( \ln \left ( f \right ) \right ) ^{4}+6\,{b}^{3}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{3}+12\,{b}^{2}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{2}+36\,b{x}^{3}\ln \left ( f \right ) +144 \right ){{\rm e}^{b{x}^{3}\ln \left ( f \right ) }}}{720\,{b}^{5}{x}^{15} \left ( \ln \left ( f \right ) \right ) ^{5}}}+{\frac{\ln \left ( -b{x}^{3}\ln \left ( f \right ) \right ) }{120}}+{\frac{{\it Ei} \left ( 1,-b{x}^{3}\ln \left ( f \right ) \right ) }{120}} \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^{16}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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