Optimal. Leaf size=2 \[ \text{LogIntegral}(x) \]
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Rubi [A] time = 0.001793, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2298} \[ \text{LogIntegral}(x) \]
Antiderivative was successfully verified.
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Rule 2298
Rubi steps
\begin{align*} \int \frac{1}{\log (x)} \, dx &=\text{li}(x)\\ \end{align*}
Mathematica [F] time = 0.0021106, size = 0, normalized size = 0. \[ \int \frac{1}{\log (x)} \, dx \]
Verification is Not applicable to the result.
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Maple [B] time = 0., size = 9, normalized size = 4.5 \begin{align*} -{\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0224, size = 4, normalized size = 2. \begin{align*}{\rm Ei}\left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.80083, size = 23, normalized size = 11.5 \begin{align*} \logintegral \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.439018, size = 2, normalized size = 1. \begin{align*} \operatorname{li}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12029, size = 4, normalized size = 2. \begin{align*}{\rm Ei}\left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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