Optimal. Leaf size=4 \[ \text{ExpIntegralEi}(a t) \]
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Rubi [A] time = 0.0120414, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {2178} \[ \text{ExpIntegralEi}(a t) \]
Antiderivative was successfully verified.
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Rule 2178
Rubi steps
\begin{align*} \int \frac{e^{a t}}{t} \, dt &=\text{Ei}(a t)\\ \end{align*}
Mathematica [A] time = 0.005839, size = 4, normalized size = 1. \[ \text{ExpIntegralEi}(a t) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 2.3 \begin{align*} -{\it Ei} \left ( 1,-at \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03016, size = 5, normalized size = 1.25 \begin{align*}{\rm Ei}\left (a t\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.997875, size = 12, normalized size = 3. \begin{align*}{\rm Ei}\left (a t\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.78138, size = 3, normalized size = 0.75 \begin{align*} \operatorname{Ei}{\left (a t \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07686, size = 5, normalized size = 1.25 \begin{align*}{\rm Ei}\left (a t\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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