Optimal. Leaf size=19 \[ -\frac {1}{3}+\log (4)+\frac {2}{\log \left (2 x+\log ^2(2)\right )} \]
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Rubi [A] time = 0.04, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 4, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {12, 2390, 2302, 30} \begin {gather*} \frac {2}{\log \left (2 x+\log ^2(2)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2302
Rule 2390
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (4 \int \frac {1}{\left (2 x+\log ^2(2)\right ) \log ^2\left (2 x+\log ^2(2)\right )} \, dx\right )\\ &=-\left (2 \operatorname {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,2 x+\log ^2(2)\right )\right )\\ &=-\left (2 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left (2 x+\log ^2(2)\right )\right )\right )\\ &=\frac {2}{\log \left (2 x+\log ^2(2)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{\log \left (2 x+\log ^2(2)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{\log \left (\log \relax (2)^{2} + 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{\log \left (\log \relax (2)^{2} + 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.31, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(\frac {2}{\ln \left (\ln \relax (2)^{2}+2 x \right )}\) | \(14\) |
default | \(\frac {2}{\ln \left (\ln \relax (2)^{2}+2 x \right )}\) | \(14\) |
norman | \(\frac {2}{\ln \left (\ln \relax (2)^{2}+2 x \right )}\) | \(14\) |
risch | \(\frac {2}{\ln \left (\ln \relax (2)^{2}+2 x \right )}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{\log \left (\log \relax (2)^{2} + 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{\ln \left (2\,x+{\ln \relax (2)}^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.53 \begin {gather*} \frac {2}{\log {\left (2 x + \log {\relax (2 )}^{2} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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