Optimal. Leaf size=23 \[ \frac {x^2+\frac {1}{4} x (-5+\log (5)) \log \left (4 x^2\right )}{x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2303} \begin {gather*} -\frac {(5-\log (5)) \log \left (4 x^2\right )}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2303
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-10+2 \log (5)+(5-\log (5)) \log \left (4 x^2\right )}{x^2} \, dx\\ &=-\frac {(5-\log (5)) \log \left (4 x^2\right )}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.74 \begin {gather*} \frac {(-5+\log (5)) \log \left (4 x^2\right )}{4 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 15, normalized size = 0.65 \begin {gather*} \frac {{\left (\log \relax (5) - 5\right )} \log \left (4 \, x^{2}\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 15, normalized size = 0.65 \begin {gather*} \frac {{\left (\log \relax (5) - 5\right )} \log \left (4 \, x^{2}\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.70
method | result | size |
risch | \(\frac {\left (\ln \relax (5)-5\right ) \ln \left (4 x^{2}\right )}{4 x}\) | \(16\) |
norman | \(\frac {\left (\frac {\ln \relax (5)}{4}-\frac {5}{4}\right ) \ln \left (4 x^{2}\right )}{x}\) | \(17\) |
default | \(-\frac {5 \ln \relax (2)}{2 x}+\frac {\ln \relax (2) \ln \relax (5)}{2 x}+\frac {\ln \relax (5) \ln \left (x^{2}\right )}{4 x}-\frac {5 \ln \left (x^{2}\right )}{4 x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 39, normalized size = 1.70 \begin {gather*} \frac {1}{4} \, {\left (\frac {\log \left (4 \, x^{2}\right )}{x} + \frac {2}{x}\right )} \log \relax (5) - \frac {\log \relax (5)}{2 \, x} - \frac {5 \, \log \left (4 \, x^{2}\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.73, size = 15, normalized size = 0.65 \begin {gather*} \frac {\ln \left (4\,x^2\right )\,\left (\ln \relax (5)-5\right )}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 0.61 \begin {gather*} \frac {\left (-5 + \log {\relax (5 )}\right ) \log {\left (4 x^{2} \right )}}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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