Optimal. Leaf size=18 \[ \left (x+\log \left (4+x+\frac {\log (x)}{x}+\log (4 x)\right )\right )^2 \]
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Rubi [A]
time = 0.18, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 117, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6820, 12,
6818} \begin {gather*} \left (x+\log \left (x+\log (4 x)+\frac {\log (x)}{x}+4\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (1+x+5 x^2+x^3+(-1+x) \log (x)+x^2 \log (4 x)\right ) \left (x+\log \left (4+x+\frac {\log (x)}{x}+\log (4 x)\right )\right )}{x (\log (x)+x (4+x+\log (4 x)))} \, dx\\ &=2 \int \frac {\left (1+x+5 x^2+x^3+(-1+x) \log (x)+x^2 \log (4 x)\right ) \left (x+\log \left (4+x+\frac {\log (x)}{x}+\log (4 x)\right )\right )}{x (\log (x)+x (4+x+\log (4 x)))} \, dx\\ &=\left (x+\log \left (4+x+\frac {\log (x)}{x}+\log (4 x)\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 18, normalized size = 1.00 \begin {gather*} \left (x+\log \left (4+x+\frac {\log (x)}{x}+\log (4 x)\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (2 x^{2} \ln \left (4 x \right )+\left (2 x -2\right ) \ln \left (x \right )+2 x^{3}+10 x^{2}+2 x +2\right ) \ln \left (\frac {x \ln \left (4 x \right )+\ln \left (x \right )+x^{2}+4 x}{x}\right )+2 x^{3} \ln \left (4 x \right )+\left (2 x^{2}-2 x \right ) \ln \left (x \right )+2 x^{4}+10 x^{3}+2 x^{2}+2 x}{x^{2} \ln \left (4 x \right )+x \ln \left (x \right )+x^{3}+4 x^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (18) = 36\).
time = 0.38, size = 55, normalized size = 3.06 \begin {gather*} x^{2} + 2 \, x \log \left (\frac {x^{2} + 2 \, x \log \left (2\right ) + {\left (x + 1\right )} \log \left (x\right ) + 4 \, x}{x}\right ) + \log \left (\frac {x^{2} + 2 \, x \log \left (2\right ) + {\left (x + 1\right )} \log \left (x\right ) + 4 \, x}{x}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (17) = 34\).
time = 0.23, size = 51, normalized size = 2.83 \begin {gather*} x^{2} + 2 x \log {\left (\frac {x^{2} + x \left (\log {\left (x \right )} + \log {\left (4 \right )}\right ) + 4 x + \log {\left (x \right )}}{x} \right )} + \log {\left (\frac {x^{2} + x \left (\log {\left (x \right )} + \log {\left (4 \right )}\right ) + 4 x + \log {\left (x \right )}}{x} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.80, size = 24, normalized size = 1.33 \begin {gather*} {\left (x+\ln \left (\frac {4\,x+\ln \left (x\right )+x\,\ln \left (4\,x\right )+x^2}{x}\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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