Optimal. Leaf size=17 \[ \log ^2\left (\frac {x}{120}+2 e^{e^{10}} x\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {12, 2421, 2301} \begin {gather*} \log ^2\left (\frac {1}{120} \left (1+240 e^{e^{10}}\right ) x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2301
Rule 2421
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {\log \left (\frac {1}{120} \left (x+240 e^{e^{10}} x\right )\right )}{x} \, dx\\ &=2 \int \frac {\log \left (\frac {1}{120} \left (1+240 e^{e^{10}}\right ) x\right )}{x} \, dx\\ &=\log ^2\left (\frac {1}{120} \left (1+240 e^{e^{10}}\right ) x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} \log ^2\left (\left (\frac {1}{120}+2 e^{e^{10}}\right ) x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 13, normalized size = 0.76 \begin {gather*} \log \left (2 \, x e^{\left (e^{10}\right )} + \frac {1}{120} \, x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 13, normalized size = 0.76 \begin {gather*} \log \left (2 \, x e^{\left (e^{10}\right )} + \frac {1}{120} \, x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 13, normalized size = 0.76
method | result | size |
derivativedivides | \(\ln \left (\left (2 \,{\mathrm e}^{{\mathrm e}^{10}}+\frac {1}{120}\right ) x \right )^{2}\) | \(13\) |
default | \(\ln \left (\left (2 \,{\mathrm e}^{{\mathrm e}^{10}}+\frac {1}{120}\right ) x \right )^{2}\) | \(13\) |
norman | \(\ln \left (2 x \,{\mathrm e}^{{\mathrm e}^{10}}+\frac {x}{120}\right )^{2}\) | \(14\) |
risch | \(\ln \left (2 x \,{\mathrm e}^{{\mathrm e}^{10}}+\frac {x}{120}\right )^{2}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 28, normalized size = 1.65 \begin {gather*} -2 \, {\left (\log \relax (5) + \log \relax (3) + 3 \, \log \relax (2) - \log \left (240 \, e^{\left (e^{10}\right )} + 1\right )\right )} \log \relax (x) + \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.17, size = 13, normalized size = 0.76 \begin {gather*} {\ln \left (\frac {x}{120}+2\,x\,{\mathrm {e}}^{{\mathrm {e}}^{10}}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.82 \begin {gather*} \log {\left (\frac {x}{120} + 2 x e^{e^{10}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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