Optimal. Leaf size=20 \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
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Rubi [A] time = 0.0129456, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2209} \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int f^{a+b x^2} x \, dx &=\frac{f^{a+b x^2}}{2 b \log (f)}\\ \end{align*}
Mathematica [A] time = 0.0023447, size = 20, normalized size = 1. \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 19, normalized size = 1. \begin{align*}{\frac{{f}^{b{x}^{2}+a}}{2\,b\ln \left ( f \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04665, size = 24, normalized size = 1.2 \begin{align*} \frac{f^{b x^{2} + a}}{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 = 1.52332, size = 41, normalized size = 2.05 \begin{align*} \frac{f^{b x^{2} + a}}{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 = 0.121413, size = 24, normalized size = 1.2 \begin{align*} \begin{cases} \frac{f^{a + b x^{2}}}{2 b \log{\left (f \right )}} & \text{for}\: 2 b \log{\left (f \right )} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17054, size = 24, normalized size = 1.2 \begin{align*} \frac{f^{b x^{2} + a}}{2 \, b \log \left (f\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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