Optimal. Leaf size=30 \[ 1+\log (5)-\log \left (e^{8-2 e^3-2 x}\right )+\frac {1}{5} e^{-3+x} \log (x) \]
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Rubi [A] time = 0.05, antiderivative size = 15, normalized size of antiderivative = 0.50, number of steps used = 4, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 14, 2288} \begin {gather*} 2 x+\frac {1}{5} e^{x-3} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {e^{-3+x}+10 x+e^{-3+x} x \log (x)}{x} \, dx\\ &=\frac {1}{5} \int \left (10+\frac {e^{-3+x} (1+x \log (x))}{x}\right ) \, dx\\ &=2 x+\frac {1}{5} \int \frac {e^{-3+x} (1+x \log (x))}{x} \, dx\\ &=2 x+\frac {1}{5} e^{-3+x} \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.53 \begin {gather*} \frac {1}{5} \left (10 x+e^{-3+x} \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 12, normalized size = 0.40 \begin {gather*} \frac {1}{5} \, e^{\left (x - 3\right )} \log \relax (x) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.50 \begin {gather*} \frac {1}{5} \, {\left (10 \, x e^{3} + e^{x} \log \relax (x)\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 0.43
method | result | size |
default | \(2 x +\frac {\ln \relax (x ) {\mathrm e}^{x -3}}{5}\) | \(13\) |
norman | \(2 x +\frac {\ln \relax (x ) {\mathrm e}^{x -3}}{5}\) | \(13\) |
risch | \(2 x +\frac {\ln \relax (x ) {\mathrm e}^{x -3}}{5}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 12, normalized size = 0.40 \begin {gather*} \frac {1}{5} \, e^{\left (x - 3\right )} \log \relax (x) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.79, size = 12, normalized size = 0.40 \begin {gather*} 2\,x+\frac {{\mathrm {e}}^{-3}\,{\mathrm {e}}^x\,\ln \relax (x)}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 12, normalized size = 0.40 \begin {gather*} 2 x + \frac {e^{x - 3} \log {\relax (x )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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