Optimal. Leaf size=21 \[ 3-\log \left (\frac {2+\log \left (x^2\right )}{16-e^3}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.43, number of steps
used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 31}
\begin {gather*} -\log \left (\log \left (x^2\right )+2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int \frac {1}{2 x+x \log \left (x^2\right )} \, dx\right )\\ &=-\text {Subst}\left (\int \frac {1}{2+x} \, dx,x,\log \left (x^2\right )\right )\\ &=-\log \left (2+\log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 0.43 \begin {gather*} -\log \left (2+\log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 10, normalized size = 0.48
method | result | size |
default | \(-\ln \left (2+\ln \left (x^{2}\right )\right )\) | \(10\) |
norman | \(-\ln \left (2+\ln \left (x^{2}\right )\right )\) | \(10\) |
risch | \(-\ln \left (2+\ln \left (x^{2}\right )\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 7, normalized size = 0.33 \begin {gather*} -\log \left (\log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.43 \begin {gather*} -\log \left (\log \left (x^{2}\right ) + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.38 \begin {gather*} - \log {\left (\log {\left (x^{2} \right )} + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 12, normalized size = 0.57 \begin {gather*} -\frac {1}{2} \, \log \left (4 \, {\left (\log \left ({\left | x \right |}\right ) + 1\right )}^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.42, size = 9, normalized size = 0.43 \begin {gather*} -\ln \left (\ln \left (x^2\right )+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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