Optimal. Leaf size=15 \[ \frac {3 e \log (i \pi +\log (6))}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 30}
\begin {gather*} \frac {3 e \log (\log (6)+i \pi )}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((3 e \log (i \pi +\log (6))) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 e \log (i \pi +\log (6))}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {3 e \log (i \pi +\log (6))}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.07, size = 16, normalized size = 1.07
method | result | size |
gosper | \(\frac {3 \,{\mathrm e} \ln \left (\ln \left (6\right )+i \pi \right )}{x}\) | \(16\) |
default | \(\frac {3 \,{\mathrm e} \ln \left (\ln \left (6\right )+i \pi \right )}{x}\) | \(16\) |
norman | \(\frac {3 \,{\mathrm e} \ln \left (\ln \left (6\right )+i \pi \right )}{x}\) | \(16\) |
risch | \(\frac {3 \,{\mathrm e} \ln \left (i \pi +\ln \left (2\right )+\ln \left (3\right )\right )}{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \left (6\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \left (6\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 e \log {\left (\log {\left (6 \right )} + i \pi \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \left (6\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.82, size = 15, normalized size = 1.00 \begin {gather*} \frac {3\,\mathrm {e}\,\ln \left (\ln \left (6\right )+\Pi \,1{}\mathrm {i}\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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