Optimal. Leaf size=15 \[ -\frac{1}{3} f^a \text{Ei}\left (\frac{b \log (f)}{x^3}\right ) \]
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Rubi [A] time = 0.0223782, antiderivative size = 15, 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 = {2210} \[ -\frac{1}{3} f^a \text{Ei}\left (\frac{b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{f^{a+\frac{b}{x^3}}}{x} \, dx &=-\frac{1}{3} f^a \text{Ei}\left (\frac{b \log (f)}{x^3}\right )\\ \end{align*}
Mathematica [A] time = 0.0020762, size = 15, normalized size = 1. \[ -\frac{1}{3} f^a \text{Ei}\left (\frac{b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.029, size = 41, normalized size = 2.7 \begin{align*} -{\frac{{f}^{a}}{3} \left ( -3\,\ln \left ( x \right ) +\ln \left ( -b \right ) +\ln \left ( \ln \left ( f \right ) \right ) -\ln \left ( -{\frac{b\ln \left ( f \right ) }{{x}^{3}}} \right ) -{\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 [A] time = 1.27502, size = 18, normalized size = 1.2 \begin{align*} -\frac{1}{3} \, f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{3}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70802, size = 36, normalized size = 2.4 \begin{align*} -\frac{1}{3} \, f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{3}}\right ) \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 \frac{f^{a + \frac{b}{x^{3}}}}{x}\, 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 \frac{f^{a + \frac{b}{x^{3}}}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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