Optimal. Leaf size=18 \[ -\frac {f^{a+\frac {b}{x}}}{b \log (f)} \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ -\frac {f^{a+\frac {b}{x}}}{b \log (f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 20, normalized size = 1.11 \[ -\frac {f^{\frac {a x + b}{x}}}{b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 20, normalized size = 1.11 \[ -\frac {f^{\frac {a x + b}{x}}}{b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.06 \[ -\frac {f^{a +\frac {b}{x}}}{b \ln \relax (f )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.06, size = 18, normalized size = 1.00 \[ -\frac {f^{a + \frac {b}{x}}}{b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.52, size = 18, normalized size = 1.00 \[ -\frac {f^{a+\frac {b}{x}}}{b\,\ln \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 1.11 \[ \begin {cases} - \frac {f^{a + \frac {b}{x}}}{b \log {\relax (f )}} & \text {for}\: b \log {\relax (f )} \neq 0 \\- \frac {1}{x} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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