Optimal. Leaf size=17 \[ 3+e^x+x-\log \left (e^x x\right )+\log (\log (5)) \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 0.47, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {14, 2194} \begin {gather*} e^x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x-\frac {1}{x}\right ) \, dx\\ &=-\log (x)+\int e^x \, dx\\ &=e^x-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.47 \begin {gather*} e^x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 7, normalized size = 0.41 \begin {gather*} e^{x} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 7, normalized size = 0.41 \begin {gather*} e^{x} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.47
method | result | size |
default | \({\mathrm e}^{x}-\ln \relax (x )\) | \(8\) |
norman | \({\mathrm e}^{x}-\ln \relax (x )\) | \(8\) |
risch | \({\mathrm e}^{x}-\ln \relax (x )\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 7, normalized size = 0.41 \begin {gather*} e^{x} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 7, normalized size = 0.41 \begin {gather*} {\mathrm {e}}^x-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 5, normalized size = 0.29 \begin {gather*} e^{x} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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