Optimal. Leaf size=22 \[ 5-3 \left (e^4+\frac {e^9 x}{\log (144)}+\log (\log (4 x))\right ) \]
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Rubi [A] time = 0.28, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 7, number of rules used = 5, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.172, Rules used = {12, 6741, 6742, 2302, 29} \begin {gather*} -\frac {3 e^9 x}{\log (144)}-3 \log (\log (4 x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2302
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-3 \log (144)-3 e^9 x \log (4 x)}{x \log (4 x)} \, dx}{\log (144)}\\ &=\frac {\int \frac {3 \left (-\log (144)-e^9 x \log (4 x)\right )}{x \log (4 x)} \, dx}{\log (144)}\\ &=\frac {3 \int \frac {-\log (144)-e^9 x \log (4 x)}{x \log (4 x)} \, dx}{\log (144)}\\ &=\frac {3 \int \left (-e^9-\frac {\log (144)}{x \log (4 x)}\right ) \, dx}{\log (144)}\\ &=-\frac {3 e^9 x}{\log (144)}-3 \int \frac {1}{x \log (4 x)} \, dx\\ &=-\frac {3 e^9 x}{\log (144)}-3 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (4 x)\right )\\ &=-\frac {3 e^9 x}{\log (144)}-3 \log (\log (4 x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.82 \begin {gather*} -\frac {3 e^9 x}{\log (144)}-3 \log (\log (4 x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 20, normalized size = 0.91 \begin {gather*} -\frac {3 \, {\left (x e^{9} + 2 \, \log \left (12\right ) \log \left (\log \left (4 \, x\right )\right )\right )}}{2 \, \log \left (12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 35, normalized size = 1.59 \begin {gather*} -\frac {3 \, {\left (x e^{9} + 2 \, \log \relax (3) \log \left (2 \, \log \relax (2) + \log \relax (x)\right ) + 4 \, \log \relax (2) \log \left (2 \, \log \relax (2) + \log \relax (x)\right )\right )}}{2 \, \log \left (12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.82
method | result | size |
norman | \(-\frac {3 \,{\mathrm e}^{9} x}{2 \ln \left (12\right )}-3 \ln \left (\ln \left (4 x \right )\right )\) | \(18\) |
derivativedivides | \(\frac {-\frac {3 x \,{\mathrm e}^{9}}{2}-3 \ln \left (12\right ) \ln \left (\ln \left (4 x \right )\right )}{\ln \left (12\right )}\) | \(22\) |
default | \(\frac {-\frac {3 x \,{\mathrm e}^{9}}{2}-3 \ln \left (12\right ) \ln \left (\ln \left (4 x \right )\right )}{\ln \left (12\right )}\) | \(22\) |
risch | \(-\frac {3 x \,{\mathrm e}^{9}}{2 \left (\ln \relax (3)+2 \ln \relax (2)\right )}-\frac {6 \ln \left (\ln \left (4 x \right )\right ) \ln \relax (2)}{\ln \relax (3)+2 \ln \relax (2)}-\frac {3 \ln \left (\ln \left (4 x \right )\right ) \ln \relax (3)}{\ln \relax (3)+2 \ln \relax (2)}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 20, normalized size = 0.91 \begin {gather*} -\frac {3 \, {\left (x e^{9} + 2 \, \log \left (12\right ) \log \left (\log \left (4 \, x\right )\right )\right )}}{2 \, \log \left (12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.07, size = 17, normalized size = 0.77 \begin {gather*} -3\,\ln \left (\ln \left (4\,x\right )\right )-\frac {3\,x\,{\mathrm {e}}^9}{2\,\ln \left (12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.91 \begin {gather*} - \frac {3 x e^{9}}{2 \log {\left (12 \right )}} - 3 \log {\left (\log {\left (4 x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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