Optimal. Leaf size=23 \[ 2 \left (3+\frac {x+4 \left (x+e^x x\right ) (x+\log (x))}{x^2}\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 33, normalized size of antiderivative = 1.43, number of steps
used = 4, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {14, 2341, 2326}
\begin {gather*} \frac {8 e^x \left (x^2+x \log (x)\right )}{x^2}+\frac {8}{x}-\frac {2 (3-4 \log (x))}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2326
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (-3+4 \log (x))}{x^2}+\frac {8 e^x \left (1+x^2-\log (x)+x \log (x)\right )}{x^2}\right ) \, dx\\ &=-\left (2 \int \frac {-3+4 \log (x)}{x^2} \, dx\right )+8 \int \frac {e^x \left (1+x^2-\log (x)+x \log (x)\right )}{x^2} \, dx\\ &=\frac {8}{x}-\frac {2 (3-4 \log (x))}{x}+\frac {8 e^x \left (x^2+x \log (x)\right )}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 21, normalized size = 0.91 \begin {gather*} \frac {2+8 e^x x+8 \left (1+e^x\right ) \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 30, normalized size = 1.30
method | result | size |
norman | \(\frac {2+8 \,{\mathrm e}^{x} x +8 \,{\mathrm e}^{x} \ln \left (x \right )+8 \ln \left (x \right )}{x}\) | \(22\) |
risch | \(\frac {8 \left ({\mathrm e}^{x}+1\right ) \ln \left (x \right )}{x}+\frac {8 \,{\mathrm e}^{x} x +2}{x}\) | \(25\) |
default | \(\frac {8 \,{\mathrm e}^{x} x +8 \,{\mathrm e}^{x} \ln \left (x \right )}{x}+\frac {2}{x}+\frac {8 \ln \left (x \right )}{x}\) | \(30\) |
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 = 0.41, size = 20, normalized size = 0.87 \begin {gather*} \frac {2 \, {\left (4 \, x e^{x} + 4 \, {\left (e^{x} + 1\right )} \log \left (x\right ) + 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 22, normalized size = 0.96 \begin {gather*} \frac {\left (8 x + 8 \log {\left (x \right )}\right ) e^{x}}{x} + \frac {8 \log {\left (x \right )}}{x} + \frac {2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 22, normalized size = 0.96 \begin {gather*} \frac {2 \, {\left (4 \, x e^{x} + 4 \, e^{x} \log \left (x\right ) + 4 \, \log \left (x\right ) + 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.37, size = 21, normalized size = 0.91 \begin {gather*} 8\,{\mathrm {e}}^x+\frac {8\,\ln \left (x\right )+8\,{\mathrm {e}}^x\,\ln \left (x\right )+2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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