Optimal. Leaf size=15 \[ \frac{1}{2} f^a \text{Ei}\left (b x^2 \log (f)\right ) \]
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Rubi [A] time = 0.0212704, 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} \[ \frac{1}{2} f^a \text{Ei}\left (b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{f^{a+b x^2}}{x} \, dx &=\frac{1}{2} f^a \text{Ei}\left (b x^2 \log (f)\right )\\ \end{align*}
Mathematica [A] time = 0.0019738, size = 15, normalized size = 1. \[ \frac{1}{2} f^a \text{Ei}\left (b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 16, normalized size = 1.1 \begin{align*} -{\frac{{f}^{a}{\it Ei} \left ( 1,-b{x}^{2}\ln \left ( f \right ) \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28702, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, f^{a}{\rm Ei}\left (b x^{2} \log \left (f\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73133, size = 35, normalized size = 2.33 \begin{align*} \frac{1}{2} \, f^{a}{\rm Ei}\left (b x^{2} \log \left (f\right )\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 + b x^{2}}}{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^{b x^{2} + a}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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