Optimal. Leaf size=22 \[ 16-\frac {1}{4} \log \left (\log \left (2+e^5-\log \left (\log \left (\frac {7}{x}\right )\right )\right )\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 6, number of rules used = 4, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {12, 2390, 2302, 29} \begin {gather*} -\frac {1}{4} \log \left (\log \left (-\log \left (\log \left (\frac {7}{x}\right )\right )+e^5+2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2302
Rule 2390
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\operatorname {Subst}\left (\int -\frac {1}{4 x \left (2+e^5-\log (x)\right ) \log \left (2+e^5-\log (x)\right )} \, dx,x,\log \left (\frac {7}{x}\right )\right )\\ &=\frac {1}{4} \operatorname {Subst}\left (\int \frac {1}{x \left (2+e^5-\log (x)\right ) \log \left (2+e^5-\log (x)\right )} \, dx,x,\log \left (\frac {7}{x}\right )\right )\\ &=\frac {1}{4} \operatorname {Subst}\left (\int \frac {1}{\left (2+e^5-x\right ) \log \left (2+e^5-x\right )} \, dx,x,\log \left (\log \left (\frac {7}{x}\right )\right )\right )\\ &=-\left (\frac {1}{4} \operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,2+e^5-\log \left (\log \left (\frac {7}{x}\right )\right )\right )\right )\\ &=-\left (\frac {1}{4} \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (2+e^5-\log \left (\log \left (\frac {7}{x}\right )\right )\right )\right )\right )\\ &=-\frac {1}{4} \log \left (\log \left (2+e^5-\log \left (\log \left (\frac {7}{x}\right )\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 20, normalized size = 0.91 \begin {gather*} -\frac {1}{4} \log \left (\log \left (2+e^5-\log \left (\log \left (\frac {7}{x}\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 17, normalized size = 0.77 \begin {gather*} -\frac {1}{4} \, \log \left (\log \left (e^{5} - \log \left (\log \left (\frac {7}{x}\right )\right ) + 2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 18, normalized size = 0.82 \begin {gather*} -\frac {1}{4} \, \log \left ({\left | \log \left (e^{5} - \log \left (\log \left (\frac {7}{x}\right )\right ) + 2\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (4 x \ln \left (\frac {7}{x}\right ) \ln \left (\ln \left (\frac {7}{x}\right )\right )+\left (-4 x \,{\mathrm e}^{5}-8 x \right ) \ln \left (\frac {7}{x}\right )\right ) \ln \left (-\ln \left (\ln \left (\frac {7}{x}\right )\right )+{\mathrm e}^{5}+2\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 18, normalized size = 0.82 \begin {gather*} -\frac {1}{4} \, \log \left (\log \left (e^{5} - \log \left (\log \relax (7) - \log \relax (x)\right ) + 2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.20, size = 17, normalized size = 0.77 \begin {gather*} -\frac {\ln \left (\ln \left ({\mathrm {e}}^5-\ln \left (\ln \left (\frac {7}{x}\right )\right )+2\right )\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 17, normalized size = 0.77 \begin {gather*} - \frac {\log {\left (\log {\left (- \log {\left (\log {\left (\frac {7}{x} \right )} \right )} + 2 + e^{5} \right )} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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