Optimal. Leaf size=2 \[ \text {Ei}(x) \]
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Rubi [A]
time = 0.01, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2209}
\begin {gather*} \text {Ei}(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int \frac {e^x}{x} \, dx &=\text {Ei}(x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \text {Ei}(x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.78, size = 2, normalized size = 1.00 \begin {gather*} \text {ExpIntegralEi}\left [x\right ] \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(7\) vs.
\(2(2)=4\).
time = 0.01, size = 8, normalized size = 4.00
method | result | size |
default | \(-\expIntegral \left (1, -x \right )\) | \(8\) |
risch | \(-\expIntegral \left (1, -x \right )\) | \(8\) |
meijerg | \(\ln \left (x \right )+i \pi -\ln \left (-x \right )-\expIntegral \left (1, -x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 2, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 2, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {Ei}{\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {Ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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