Optimal. Leaf size=18 \[ -\frac{f^{a+\frac{b}{x}}}{b \log (f)} \]
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Rubi [A] time = 0.018051, antiderivative size = 18, 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 = {2209} \[ -\frac{f^{a+\frac{b}{x}}}{b \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int \frac{f^{a+\frac{b}{x}}}{x^2} \, dx &=-\frac{f^{a+\frac{b}{x}}}{b \log (f)}\\ \end{align*}
Mathematica [A] time = 0.0033678, size = 18, normalized size = 1. \[ -\frac{f^{a+\frac{b}{x}}}{b \log (f)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 19, normalized size = 1.1 \begin{align*} -{\frac{1}{b\ln \left ( f \right ) }{f}^{a+{\frac{b}{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12925, size = 24, normalized size = 1.33 \begin{align*} -\frac{f^{a + \frac{b}{x}}}{b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69438, size = 39, normalized size = 2.17 \begin{align*} -\frac{f^{\frac{a x + b}{x}}}{b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.113452, size = 20, normalized size = 1.11 \begin{align*} \begin{cases} - \frac{f^{a + \frac{b}{x}}}{b \log{\left (f \right )}} & \text{for}\: b \log{\left (f \right )} \neq 0 \\- \frac{1}{x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.29895, size = 24, normalized size = 1.33 \begin{align*} -\frac{f^{a + \frac{b}{x}}}{b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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