Optimal. Leaf size=17 \[ \log \left (e^{-\frac {e^4 \log ^2(3)}{x}} x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {45}
\begin {gather*} \log (x)-\frac {e^4 \log ^2(3)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x}+\frac {e^4 \log ^2(3)}{x^2}\right ) \, dx\\ &=-\frac {e^4 \log ^2(3)}{x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^4 \log ^2(3)}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 15, normalized size = 0.88
method | result | size |
default | \(-\frac {{\mathrm e}^{4} \ln \left (3\right )^{2}}{x}+\ln \left (x \right )\) | \(15\) |
norman | \(-\frac {{\mathrm e}^{4} \ln \left (3\right )^{2}}{x}+\ln \left (x \right )\) | \(15\) |
risch | \(-\frac {{\mathrm e}^{4} \ln \left (3\right )^{2}}{x}+\ln \left (x \right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{2}}{x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 18, normalized size = 1.06 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{2} - x \log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \log {\left (x \right )} - \frac {e^{4} \log {\left (3 \right )}^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{2}}{x} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.77, size = 14, normalized size = 0.82 \begin {gather*} \ln \left (x\right )-\frac {{\mathrm {e}}^4\,{\ln \left (3\right )}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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