Optimal. Leaf size=25 \[ \frac {1}{10}+x+\frac {1}{4} e^x \left (-4+3 \left (\log (x)+x^2 \log (x)\right )\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 28, normalized size of antiderivative = 1.12, number of steps used = 4, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 14, 2288} \begin {gather*} x-\frac {e^x \left (-3 x^3 \log (x)+4 x-3 x \log (x)\right )}{4 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}{4} \int \frac {4 x+e^x \left (3-4 x+3 x^2\right )+e^x \left (3 x+6 x^2+3 x^3\right ) \log (x)}{x} \, dx\\ &=\frac {1}{4} \int \left (4+\frac {e^x \left (3-4 x+3 x^2+3 x \log (x)+6 x^2 \log (x)+3 x^3 \log (x)\right )}{x}\right ) \, dx\\ &=x+\frac {1}{4} \int \frac {e^x \left (3-4 x+3 x^2+3 x \log (x)+6 x^2 \log (x)+3 x^3 \log (x)\right )}{x} \, dx\\ &=x-\frac {e^x \left (4 x-3 x \log (x)-3 x^3 \log (x)\right )}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 25, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (-4 e^x+4 x+3 e^x \left (1+x^2\right ) \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 17, normalized size = 0.68 \begin {gather*} \frac {3}{4} \, {\left (x^{2} + 1\right )} e^{x} \log \relax (x) + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 21, normalized size = 0.84 \begin {gather*} \frac {3}{4} \, x^{2} e^{x} \log \relax (x) + \frac {3}{4} \, e^{x} \log \relax (x) + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 18, normalized size = 0.72
method | result | size |
risch | \(\frac {3 \left (x^{2}+1\right ) {\mathrm e}^{x} \ln \relax (x )}{4}+x -{\mathrm e}^{x}\) | \(18\) |
default | \(x +\frac {3 \,{\mathrm e}^{x} \ln \relax (x )}{4}+\frac {3 x^{2} {\mathrm e}^{x} \ln \relax (x )}{4}-{\mathrm e}^{x}\) | \(22\) |
norman | \(x +\frac {3 \,{\mathrm e}^{x} \ln \relax (x )}{4}+\frac {3 x^{2} {\mathrm e}^{x} \ln \relax (x )}{4}-{\mathrm e}^{x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 34, normalized size = 1.36 \begin {gather*} \frac {3}{4} \, {\left (x^{2} \log \relax (x) - x + 1\right )} e^{x} + \frac {3}{4} \, {\left (x - 1\right )} e^{x} + \frac {3}{4} \, e^{x} \log \relax (x) + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.46, size = 21, normalized size = 0.84 \begin {gather*} x-{\mathrm {e}}^x+\frac {3\,{\mathrm {e}}^x\,\ln \relax (x)}{4}+\frac {3\,x^2\,{\mathrm {e}}^x\,\ln \relax (x)}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 20, normalized size = 0.80 \begin {gather*} x + \frac {\left (3 x^{2} \log {\relax (x )} + 3 \log {\relax (x )} - 4\right ) e^{x}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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