Optimal. Leaf size=16 \[ \frac {1}{5 \log (2) \log \left (4 x^2\right )} \]
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Rubi [A]
time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2339, 30}
\begin {gather*} \frac {1}{5 \log (2) \log \left (4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2339
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {2 \int \frac {1}{x \log ^2\left (4 x^2\right )} \, dx}{5 \log (2)}\\ &=-\frac {\text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left (4 x^2\right )\right )}{5 \log (2)}\\ &=\frac {1}{5 \log (2) \log \left (4 x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {1}{5 \log (2) \log \left (4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 15, normalized size = 0.94
method | result | size |
derivativedivides | \(\frac {1}{5 \ln \left (4 x^{2}\right ) \ln \left (2\right )}\) | \(15\) |
default | \(\frac {1}{5 \ln \left (4 x^{2}\right ) \ln \left (2\right )}\) | \(15\) |
norman | \(\frac {1}{5 \ln \left (4 x^{2}\right ) \ln \left (2\right )}\) | \(15\) |
risch | \(\frac {1}{5 \ln \left (4 x^{2}\right ) \ln \left (2\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.88 \begin {gather*} \frac {1}{5 \, \log \left (2\right ) \log \left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 14, normalized size = 0.88 \begin {gather*} \frac {1}{5 \, \log \left (2\right ) \log \left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{5 \log {\left (2 \right )} \log {\left (4 x^{2} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 14, normalized size = 0.88 \begin {gather*} \frac {1}{5 \, \log \left (2\right ) \log \left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.96, size = 14, normalized size = 0.88 \begin {gather*} \frac {1}{5\,\ln \left (2\right )\,\ln \left (4\,x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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