Optimal. Leaf size=21 \[ b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x}\right ) \]
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Rubi [A] time = 0.0198408, antiderivative size = 21, 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} \[ b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int f^{a+\frac{b}{x}} x^3 \, dx &=b^4 f^a \Gamma \left (-4,-\frac{b \log (f)}{x}\right ) \log ^4(f)\\ \end{align*}
Mathematica [A] time = 0.0022257, size = 21, normalized size = 1. \[ b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.064, size = 99, normalized size = 4.7 \begin{align*}{\frac{{f}^{a}{x}^{4}}{4}{f}^{{\frac{b}{x}}}}+{\frac{b\ln \left ( f \right ){f}^{a}{x}^{3}}{12}{f}^{{\frac{b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{f}^{a}{x}^{2}}{24}{f}^{{\frac{b}{x}}}}+{\frac{ \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{f}^{a}x}{24}{f}^{{\frac{b}{x}}}}+{\frac{{b}^{4} \left ( \ln \left ( f \right ) \right ) ^{4}{f}^{a}}{24}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{x}} \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] time = 0., size = 0, normalized size = 0. \begin{align*} \int f^{a + \frac{b}{x}} x^{3}\, dx \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}} x^{3}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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