Optimal. Leaf size=20 \[ -\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)} \]
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Rubi [A] time = 0.0214927, antiderivative size = 20, 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} \[ -\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int \frac{f^{a+\frac{b}{x^2}}}{x^3} \, dx &=-\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)}\\ \end{align*}
Mathematica [A] time = 0.0037513, size = 20, normalized size = 1. \[ -\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 19, normalized size = 1. \begin{align*} -{\frac{1}{2\,b\ln \left ( f \right ) }{f}^{a+{\frac{b}{{x}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00888, size = 24, normalized size = 1.2 \begin{align*} -\frac{f^{a + \frac{b}{x^{2}}}}{2 \, b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.76488, size = 50, normalized size = 2.5 \begin{align*} -\frac{f^{\frac{a x^{2} + b}{x^{2}}}}{2 \, b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.11768, size = 29, normalized size = 1.45 \begin{align*} \begin{cases} - \frac{f^{a + \frac{b}{x^{2}}}}{2 b \log{\left (f \right )}} & \text{for}\: 2 b \log{\left (f \right )} \neq 0 \\- \frac{1}{2 x^{2}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.73057, size = 24, normalized size = 1.2 \begin{align*} -\frac{f^{a + \frac{b}{x^{2}}}}{2 \, b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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