Optimal. Leaf size=26 \[ \frac {1}{2} x \left (3+\frac {1}{3} \left (-4+e^x+\frac {7}{2 x}\right )+x\right ) \log (x) \]
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Rubi [A]
time = 0.04, antiderivative size = 33, normalized size of antiderivative = 1.27, number of steps
used = 10, number of rules used = 4, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14, 2326,
2350} \begin {gather*} \frac {1}{2} x^2 \log (x)+\frac {1}{6} e^x x \log (x)+\frac {5}{6} x \log (x)+\frac {7 \log (x)}{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rule 2350
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{12} \int \frac {7+10 x+2 e^x x+6 x^2+\left (10 x+12 x^2+e^x \left (2 x+2 x^2\right )\right ) \log (x)}{x} \, dx\\ &=\frac {1}{12} \int \left (2 e^x (1+\log (x)+x \log (x))+\frac {7+10 x+6 x^2+10 x \log (x)+12 x^2 \log (x)}{x}\right ) \, dx\\ &=\frac {1}{12} \int \frac {7+10 x+6 x^2+10 x \log (x)+12 x^2 \log (x)}{x} \, dx+\frac {1}{6} \int e^x (1+\log (x)+x \log (x)) \, dx\\ &=\frac {1}{6} e^x x \log (x)+\frac {1}{12} \int \left (\frac {7+10 x+6 x^2}{x}+2 (5+6 x) \log (x)\right ) \, dx\\ &=\frac {1}{6} e^x x \log (x)+\frac {1}{12} \int \frac {7+10 x+6 x^2}{x} \, dx+\frac {1}{6} \int (5+6 x) \log (x) \, dx\\ &=\frac {1}{6} e^x x \log (x)+\frac {1}{6} \left (5 x+3 x^2\right ) \log (x)+\frac {1}{12} \int \left (10+\frac {7}{x}+6 x\right ) \, dx-\frac {1}{6} \int (5+3 x) \, dx\\ &=\frac {7 \log (x)}{12}+\frac {1}{6} e^x x \log (x)+\frac {1}{6} \left (5 x+3 x^2\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 21, normalized size = 0.81 \begin {gather*} \frac {1}{12} \left (7+2 \left (5+e^x\right ) x+6 x^2\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 25, normalized size = 0.96
method | result | size |
risch | \(\frac {\left (6 x^{2}+2 \,{\mathrm e}^{x} x +10 x \right ) \ln \left (x \right )}{12}+\frac {7 \ln \left (x \right )}{12}\) | \(24\) |
default | \(\frac {x \,{\mathrm e}^{x} \ln \left (x \right )}{6}+\frac {x^{2} \ln \left (x \right )}{2}+\frac {5 x \ln \left (x \right )}{6}+\frac {7 \ln \left (x \right )}{12}\) | \(25\) |
norman | \(\frac {x \,{\mathrm e}^{x} \ln \left (x \right )}{6}+\frac {x^{2} \ln \left (x \right )}{2}+\frac {5 x \ln \left (x \right )}{6}+\frac {7 \ln \left (x \right )}{12}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 19, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, {\left (6 \, x^{2} + 2 \, x e^{x} + 10 \, x + 7\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 29, normalized size = 1.12 \begin {gather*} \frac {x e^{x} \log {\left (x \right )}}{6} + \left (\frac {x^{2}}{2} + \frac {5 x}{6}\right ) \log {\left (x \right )} + \frac {7 \log {\left (x \right )}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 24, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) + \frac {1}{6} \, x e^{x} \log \left (x\right ) + \frac {5}{6} \, x \log \left (x\right ) + \frac {7}{12} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.35, size = 19, normalized size = 0.73 \begin {gather*} \frac {\ln \left (x\right )\,\left (10\,x+2\,x\,{\mathrm {e}}^x+6\,x^2+7\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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