Optimal. Leaf size=19 \[ \frac {1}{9} \left (-\frac {1}{4}-e^x-\log (x)\right )^2 \]
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Rubi [B] time = 0.07, antiderivative size = 39, normalized size of antiderivative = 2.05, number of steps used = 6, number of rules used = 5, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14, 2194, 2301, 2288} \begin {gather*} \frac {e^{2 x}}{9}+\frac {1}{144} (4 \log (x)+1)^2+\frac {e^x (x+4 x \log (x))}{18 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2194
Rule 2288
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{18} \int \frac {1+4 e^{2 x} x+e^x (4+x)+\left (4+4 e^x x\right ) \log (x)}{x} \, dx\\ &=\frac {1}{18} \int \left (4 e^{2 x}+\frac {1+4 \log (x)}{x}+\frac {e^x (4+x+4 x \log (x))}{x}\right ) \, dx\\ &=\frac {1}{18} \int \frac {1+4 \log (x)}{x} \, dx+\frac {1}{18} \int \frac {e^x (4+x+4 x \log (x))}{x} \, dx+\frac {2}{9} \int e^{2 x} \, dx\\ &=\frac {e^{2 x}}{9}+\frac {1}{144} (1+4 \log (x))^2+\frac {e^x (x+4 x \log (x))}{18 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 17, normalized size = 0.89 \begin {gather*} \frac {1}{144} \left (1+4 e^x+4 \log (x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 27, normalized size = 1.42 \begin {gather*} \frac {1}{18} \, {\left (4 \, e^{x} + 1\right )} \log \relax (x) + \frac {1}{9} \, \log \relax (x)^{2} + \frac {1}{9} \, e^{\left (2 \, x\right )} + \frac {1}{18} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 27, normalized size = 1.42 \begin {gather*} \frac {2}{9} \, e^{x} \log \relax (x) + \frac {1}{9} \, \log \relax (x)^{2} + \frac {1}{9} \, e^{\left (2 \, x\right )} + \frac {1}{18} \, e^{x} + \frac {1}{18} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 1.47
method | result | size |
default | \(\frac {\ln \relax (x )}{18}+\frac {2 \,{\mathrm e}^{x} \ln \relax (x )}{9}+\frac {{\mathrm e}^{x}}{18}+\frac {{\mathrm e}^{2 x}}{9}+\frac {\ln \relax (x )^{2}}{9}\) | \(28\) |
norman | \(\frac {\ln \relax (x )}{18}+\frac {2 \,{\mathrm e}^{x} \ln \relax (x )}{9}+\frac {{\mathrm e}^{x}}{18}+\frac {{\mathrm e}^{2 x}}{9}+\frac {\ln \relax (x )^{2}}{9}\) | \(28\) |
risch | \(\frac {\ln \relax (x )}{18}+\frac {2 \,{\mathrm e}^{x} \ln \relax (x )}{9}+\frac {{\mathrm e}^{x}}{18}+\frac {{\mathrm e}^{2 x}}{9}+\frac {\ln \relax (x )^{2}}{9}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 27, normalized size = 1.42 \begin {gather*} \frac {2}{9} \, e^{x} \log \relax (x) + \frac {1}{9} \, \log \relax (x)^{2} + \frac {1}{9} \, e^{\left (2 \, x\right )} + \frac {1}{18} \, e^{x} + \frac {1}{18} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 27, normalized size = 1.42 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}}{9}+\frac {{\mathrm {e}}^x}{18}+\frac {\ln \relax (x)}{18}+\frac {2\,{\mathrm {e}}^x\,\ln \relax (x)}{9}+\frac {{\ln \relax (x)}^2}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 29, normalized size = 1.53 \begin {gather*} \frac {\left (36 \log {\relax (x )} + 9\right ) e^{x}}{162} + \frac {e^{2 x}}{9} + \frac {\log {\relax (x )}^{2}}{9} + \frac {\log {\relax (x )}}{18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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