Optimal. Leaf size=30 \[ \frac {i \pi -x+e^2 \log (3)+\log \left (-4 \left (-e^2+\log (4)\right )\right )}{x} \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 0.90, number of steps
used = 2, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 30}
\begin {gather*} \frac {i \pi +e^2 \log (3)+\log \left (4 \left (e^2-\log (4)\right )\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (-i \pi -e^2 \log (3)-\log \left (4 \left (e^2-\log (4)\right )\right )\right ) \int \frac {1}{x^2} \, dx\\ &=\frac {i \pi +e^2 \log (3)+\log \left (4 \left (e^2-\log (4)\right )\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 27, normalized size = 0.90 \begin {gather*} \frac {i \pi +e^2 \log (3)+\log \left (4 \left (e^2-\log (4)\right )\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {{\mathrm e}^{2} \ln \left (3\right )+\ln \left (8 \ln \left (2\right )-4 \,{\mathrm e}^{2}\right )}{x}\) | \(21\) |
default | \(-\frac {-\ln \left (8 \ln \left (2\right )-4 \,{\mathrm e}^{2}\right )-{\mathrm e}^{2} \ln \left (3\right )}{x}\) | \(25\) |
norman | \(\frac {{\mathrm e}^{2} \ln \left (3\right )+2 \ln \left (2\right )+\ln \left (2 \ln \left (2\right )-{\mathrm e}^{2}\right )}{x}\) | \(25\) |
risch | \(\frac {{\mathrm e}^{2} \ln \left (3\right )}{x}+\frac {2 \ln \left (2\right )}{x}+\frac {\ln \left (2 \ln \left (2\right )-{\mathrm e}^{2}\right )}{x}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 20, normalized size = 0.67 \begin {gather*} \frac {e^{2} \log \left (3\right ) + \log \left (-4 \, e^{2} + 8 \, \log \left (2\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 20, normalized size = 0.67 \begin {gather*} \frac {e^{2} \log \left (3\right ) + \log \left (-4 \, e^{2} + 8 \, \log \left (2\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 29, normalized size = 0.97 \begin {gather*} - \frac {- e^{2} \log {\left (3 \right )} - \log {\left (- 2 \log {\left (2 \right )} + e^{2} \right )} - 2 \log {\left (2 \right )} - i \pi }{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.67 \begin {gather*} \frac {e^{2} \log \left (3\right ) + \log \left (-4 \, e^{2} + 8 \, \log \left (2\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 20, normalized size = 0.67 \begin {gather*} \frac {\ln \left (8\,\ln \left (2\right )-4\,{\mathrm {e}}^2\right )+{\mathrm {e}}^2\,\ln \left (3\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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