Optimal. Leaf size=4 \[ \operatorname {ExpIntegralEi}(a x) \]
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Rubi [A] time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, 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} \[ \text {ExpIntegralEi}(a x) \]
Antiderivative was successfully verified.
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Rule 2178
Rubi steps
\begin {align*} \int \frac {e^{a x}}{x} \, dx &=\text {Ei}(a x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 4, normalized size = 1.00 \[ \operatorname {ExpIntegralEi}(a x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 4, normalized size = 1.00 \[ {\rm Ei}\left (a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 4, normalized size = 1.00 \[ {\rm Ei}\left (a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 9, normalized size = 2.25 \[ -\Ei \left (1, -a x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 4, normalized size = 1.00 \[ {\rm Ei}\left (a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 4, normalized size = 1.00 \[ \mathrm {ei}\left (a\,x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.78, size = 3, normalized size = 0.75 \[ \operatorname {Ei}{\left (a x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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