Optimal. Leaf size=27 \[ e^{4/x}-x-\log (3)+(2-\log (3)) \log (x)+\log (\log (3)) \]
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Rubi [A]
time = 0.03, antiderivative size = 20, normalized size of antiderivative = 0.74, number of steps
used = 6, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {6, 14, 2240, 45}
\begin {gather*} -x+e^{4/x}+(2-\log (3)) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rule 45
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 e^{4/x}-x^2+x (2-\log (3))}{x^2} \, dx\\ &=\int \left (-\frac {4 e^{4/x}}{x^2}+\frac {2-x-\log (3)}{x}\right ) \, dx\\ &=-\left (4 \int \frac {e^{4/x}}{x^2} \, dx\right )+\int \frac {2-x-\log (3)}{x} \, dx\\ &=e^{4/x}+\int \left (-1+\frac {2-\log (3)}{x}\right ) \, dx\\ &=e^{4/x}-x+(2-\log (3)) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 0.78 \begin {gather*} e^{4/x}-x+2 \log (x)-\log (3) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 24, normalized size = 0.89
method | result | size |
risch | \(-x -\ln \left (3\right ) \ln \left (x \right )+2 \ln \left (x \right )+{\mathrm e}^{\frac {4}{x}}\) | \(21\) |
derivativedivides | \(-x +\ln \left (3\right ) \ln \left (\frac {1}{x}\right )-2 \ln \left (\frac {1}{x}\right )+{\mathrm e}^{\frac {4}{x}}\) | \(24\) |
default | \(-x +\ln \left (3\right ) \ln \left (\frac {1}{x}\right )-2 \ln \left (\frac {1}{x}\right )+{\mathrm e}^{\frac {4}{x}}\) | \(24\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {4}{x}}-x^{2}}{x}+\left (2-\ln \left (3\right )\right ) \ln \left (x \right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 20, normalized size = 0.74 \begin {gather*} -\log \left (3\right ) \log \left (x\right ) - x + e^{\frac {4}{x}} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 18, normalized size = 0.67 \begin {gather*} -{\left (\log \left (3\right ) - 2\right )} \log \left (x\right ) - x + e^{\frac {4}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 0.52 \begin {gather*} - x + e^{\frac {4}{x}} - \left (-2 + \log {\left (3 \right )}\right ) \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 37, normalized size = 1.37 \begin {gather*} x {\left (\frac {\log \left (3\right ) \log \left (\frac {4}{x}\right )}{x} + \frac {e^{\frac {4}{x}}}{x} - \frac {2 \, \log \left (\frac {4}{x}\right )}{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.78, size = 29, normalized size = 1.07 \begin {gather*} \frac {x^2\,{\mathrm {e}}^{4/x}-x^3}{x^2}-\ln \left (x\right )\,\left (\ln \left (3\right )-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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