Optimal. Leaf size=23 \[ \frac {3 \left (1+e-\log \left (x^2 (6-\log (3))^2\right )\right )}{x} \]
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Rubi [A]
time = 0.04, antiderivative size = 29, normalized size of antiderivative = 1.26, number of steps
used = 2, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {2511, 2341}
\begin {gather*} \frac {3 \left (-\log \left (x^2 (6-\log (3))^2\right )+e+3\right )}{x}-\frac {6}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rule 2511
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9-3 e+3 \log \left (x^2 (6-\log (3))^2\right )}{x^2} \, dx\\ &=-\frac {6}{x}+\frac {3 \left (3+e-\log \left (x^2 (6-\log (3))^2\right )\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 28, normalized size = 1.22 \begin {gather*} \frac {3}{x}+\frac {3 e}{x}-\frac {3 \log \left (x^2 (-6+\log (3))^2\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 45, normalized size = 1.96
method | result | size |
norman | \(\frac {3-3 \ln \left (x^{2} \ln \left (3\right )^{2}-12 x^{2} \ln \left (3\right )+36 x^{2}\right )+3 \,{\mathrm e}}{x}\) | \(35\) |
risch | \(-\frac {3 \ln \left (x^{2} \ln \left (3\right )^{2}-12 x^{2} \ln \left (3\right )+36 x^{2}\right )}{x}+\frac {3 \,{\mathrm e}}{x}+\frac {3}{x}\) | \(41\) |
default | \(-\frac {3 \ln \left (x^{2} \ln \left (3\right )^{2}-12 x^{2} \ln \left (3\right )+36 x^{2}\right )}{x}-\frac {6}{x}-\frac {3 \left (-3-{\mathrm e}\right )}{x}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 40, normalized size = 1.74 \begin {gather*} \frac {3 \, e}{x} - \frac {3 \, \log \left (x^{2} \log \left (3\right )^{2} - 12 \, x^{2} \log \left (3\right ) + 36 \, x^{2}\right )}{x} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 33, normalized size = 1.43 \begin {gather*} \frac {3 \, {\left (e - \log \left (x^{2} \log \left (3\right )^{2} - 12 \, x^{2} \log \left (3\right ) + 36 \, x^{2}\right ) + 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 37, normalized size = 1.61 \begin {gather*} - \frac {3 \log {\left (- 12 x^{2} \log {\left (3 \right )} + x^{2} \log {\left (3 \right )}^{2} + 36 x^{2} \right )}}{x} - \frac {- 3 e - 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 33, normalized size = 1.43 \begin {gather*} \frac {3 \, {\left (e - \log \left (x^{2} \log \left (3\right )^{2} - 12 \, x^{2} \log \left (3\right ) + 36 \, x^{2}\right ) + 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.24, size = 38, normalized size = 1.65 \begin {gather*} \frac {3\,\mathrm {e}+3}{x}-\frac {3\,\ln \left (x^2\,{\ln \left (3\right )}^2-12\,x^2\,\ln \left (3\right )+36\,x^2\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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