Optimal. Leaf size=69 \[ -\frac{f^{a+\frac{b}{x^3}} \left (12 b^2 x^6 \log ^2(f)-4 b^3 x^3 \log ^3(f)+b^4 \log ^4(f)-24 b x^9 \log (f)+24 x^{12}\right )}{3 b^5 x^{12} \log ^5(f)} \]
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Rubi [C] time = 0.0226648, antiderivative size = 24, normalized size of antiderivative = 0.35, 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} \[ -\frac{f^a \text{Gamma}\left (5,-\frac{b \log (f)}{x^3}\right )}{3 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+\frac{b}{x^3}}}{x^{16}} \, dx &=-\frac{f^a \Gamma \left (5,-\frac{b \log (f)}{x^3}\right )}{3 b^5 \log ^5(f)}\\ \end{align*}
Mathematica [C] time = 0.0027375, size = 24, normalized size = 0.35 \[ -\frac{f^a \text{Gamma}\left (5,-\frac{b \log (f)}{x^3}\right )}{3 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.028, size = 121, normalized size = 1.8 \begin{align*}{\frac{1}{{x}^{15}} \left ( -8\,{\frac{{x}^{15}}{{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}+8\,{\frac{{x}^{12}}{{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}-4\,{\frac{{x}^{9}}{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}+{\frac{4\,{x}^{6}}{3\, \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}-{\frac{{x}^{3}}{3\,b\ln \left ( f \right ) }{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.30783, size = 30, normalized size = 0.43 \begin{align*} -\frac{f^{a} \Gamma \left (5, -\frac{b \log \left (f\right )}{x^{3}}\right )}{3 \, b^{5} \log \left (f\right )^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65528, size = 178, normalized size = 2.58 \begin{align*} -\frac{{\left (24 \, x^{12} - 24 \, b x^{9} \log \left (f\right ) + 12 \, b^{2} x^{6} \log \left (f\right )^{2} - 4 \, b^{3} x^{3} \log \left (f\right )^{3} + b^{4} \log \left (f\right )^{4}\right )} f^{\frac{a x^{3} + b}{x^{3}}}}{3 \, b^{5} x^{12} \log \left (f\right )^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.152325, size = 71, normalized size = 1.03 \begin{align*} \frac{f^{a + \frac{b}{x^{3}}} \left (- b^{4} \log{\left (f \right )}^{4} + 4 b^{3} x^{3} \log{\left (f \right )}^{3} - 12 b^{2} x^{6} \log{\left (f \right )}^{2} + 24 b x^{9} \log{\left (f \right )} - 24 x^{12}\right )}{3 b^{5} x^{12} \log{\left (f \right )}^{5}} \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^{a + \frac{b}{x^{3}}}}{x^{16}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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