Optimal. Leaf size=21 \[ -5-\frac {3}{4} \left (e+\frac {x}{5}+\frac {4}{\log (4 x)}\right ) \]
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Rubi [A]
time = 0.10, antiderivative size = 14, normalized size of antiderivative = 0.67, number of steps
used = 5, number of rules used = 4, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 6820, 2339,
30} \begin {gather*} -\frac {3 x}{20}-\frac {3}{\log (4 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2339
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{20} \int \frac {60-3 x \log ^2(4 x)}{x \log ^2(4 x)} \, dx\\ &=\frac {1}{20} \int \left (-3+\frac {60}{x \log ^2(4 x)}\right ) \, dx\\ &=-\frac {3 x}{20}+3 \int \frac {1}{x \log ^2(4 x)} \, dx\\ &=-\frac {3 x}{20}+3 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (4 x)\right )\\ &=-\frac {3 x}{20}-\frac {3}{\log (4 x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.67 \begin {gather*} -\frac {3 x}{20}-\frac {3}{\log (4 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.51, size = 13, normalized size = 0.62
method | result | size |
derivativedivides | \(-\frac {3 x}{20}-\frac {3}{\ln \left (4 x \right )}\) | \(13\) |
default | \(-\frac {3 x}{20}-\frac {3}{\ln \left (4 x \right )}\) | \(13\) |
risch | \(-\frac {3 x}{20}-\frac {3}{\ln \left (4 x \right )}\) | \(13\) |
norman | \(\frac {-3-\frac {3 x \ln \left (4 x \right )}{20}}{\ln \left (4 x \right )}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 12, normalized size = 0.57 \begin {gather*} -\frac {3}{20} \, x - \frac {3}{\log \left (4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 16, normalized size = 0.76 \begin {gather*} -\frac {3 \, {\left (x \log \left (4 \, x\right ) + 20\right )}}{20 \, \log \left (4 \, x\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 = 0.57 \begin {gather*} - \frac {3 x}{20} - \frac {3}{\log {\left (4 x \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 {3}{20} \, x - \frac {3}{\log \left (4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.37, size = 12, normalized size = 0.57 \begin {gather*} -\frac {3\,x}{20}-\frac {3}{\ln \left (4\,x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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