Optimal. Leaf size=19 \[ \log \left (\frac {1}{4} e^{\frac {2}{e^3}+e^x} x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.42, 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+2 \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 {2}{x}\right ) \, dx\\ &=2 \log (x)+\int e^x \, dx\\ &=e^x+2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.42 \begin {gather*} e^x+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 7, normalized size = 0.37 \begin {gather*} e^{x} + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 7, normalized size = 0.37 \begin {gather*} e^{x} + 2 \, \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 = 0.42
method | result | size |
default | \(2 \ln \relax (x )+{\mathrm e}^{x}\) | \(8\) |
norman | \(2 \ln \relax (x )+{\mathrm e}^{x}\) | \(8\) |
risch | \(2 \ln \relax (x )+{\mathrm e}^{x}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 7, normalized size = 0.37 \begin {gather*} e^{x} + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 7, normalized size = 0.37 \begin {gather*} {\mathrm {e}}^x+2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.37 \begin {gather*} e^{x} + 2 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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