Optimal. Leaf size=6 \[ \text {Ei}\left (e^x+x\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6839, 2209}
\begin {gather*} \text {ExpIntegralEi}\left (x+e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 6839
Rubi steps
\begin {align*} \int \frac {e^{e^x+x} \left (1+e^x\right )}{e^x+x} \, dx &=\text {Subst}\left (\int \frac {e^x}{x} \, dx,x,e^x+x\right )\\ &=\text {Ei}\left (e^x+x\right )\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 6, normalized size = 1.00 \begin {gather*} \text {Ei}\left (e^x+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. \(12\) vs.
\(2(5)=10\).
time = 0.02, size = 13, normalized size = 2.17
method | result | size |
derivativedivides | \(-\expIntegral \left (1, -{\mathrm e}^{x}-x \right )\) | \(13\) |
default | \(-\expIntegral \left (1, -{\mathrm e}^{x}-x \right )\) | \(13\) |
risch | \(-\expIntegral \left (1, -{\mathrm e}^{x}-x \right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.75, size = 5, normalized size = 0.83 \begin {gather*} {\rm Ei}\left (x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.04, size = 5, normalized size = 0.83 \begin {gather*} \operatorname {Ei}{\left (x + e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 5, normalized size = 0.83 \begin {gather*} {\rm Ei}\left (x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 5, normalized size = 0.83 \begin {gather*} \mathrm {ei}\left (x+{\mathrm {e}}^x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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