Optimal. Leaf size=26 \[ \log ^2\left (\frac {1+\log \left (\frac {x}{\left (x+2 e^{2/x} x\right )^5}\right )}{x}\right ) \]
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Rubi [A] time = 2.07, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 3, integrand size = 126, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6741, 6742, 6686} \begin {gather*} \log ^2\left (\frac {\log \left (\frac {x}{\left (2 e^{2/x} x+x\right )^5}\right )+1}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2\left (\frac {1+\log \left (\frac {x}{\left (x+2 e^{2/x} x\right )^5}\right )}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 26, normalized size = 1.00 \begin {gather*} \log ^2\left (\frac {1+\log \left (\frac {x}{\left (x+2 e^{2/x} x\right )^5}\right )}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 71, normalized size = 2.73 \begin {gather*} \log \left (\frac {\log \left (\frac {1}{32 \, x^{4} e^{\frac {10}{x}} + 80 \, x^{4} e^{\frac {8}{x}} + 80 \, x^{4} e^{\frac {6}{x}} + 40 \, x^{4} e^{\frac {4}{x}} + 10 \, x^{4} e^{\frac {2}{x}} + x^{4}}\right ) + 1}{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*} \int -\frac {2 \, {\left (10 \, {\left (x - 2\right )} e^{\frac {2}{x}} + {\left (2 \, x e^{\frac {2}{x}} + x\right )} \log \left (\frac {x}{{\left (2 \, x e^{\frac {2}{x}} + x\right )}^{5}}\right ) + 5 \, x\right )} \log \left (\frac {\log \left (\frac {x}{{\left (2 \, x e^{\frac {2}{x}} + x\right )}^{5}}\right ) + 1}{x}\right )}{2 \, x^{2} e^{\frac {2}{x}} + x^{2} + {\left (2 \, x^{2} e^{\frac {2}{x}} + x^{2}\right )} \log \left (\frac {x}{{\left (2 \, x e^{\frac {2}{x}} + x\right )}^{5}}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 3.47, size = 28486, normalized size = 1095.62
method | result | size |
risch | \(\text {Expression too large to display}\) | \(28486\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.70, size = 112, normalized size = 4.31 \begin {gather*} -2 \, \log \relax (5) \log \relax (x) - \log \relax (x)^{2} - 2 \, {\left (\log \relax (x) - \log \left (\frac {4}{5} \, \log \relax (x) + \log \left (2 \, e^{\frac {2}{x}} + 1\right ) - \frac {1}{5}\right )\right )} \log \left (\frac {\log \left (\frac {x}{{\left (2 \, x e^{\frac {2}{x}} + x\right )}^{5}}\right ) + 1}{x}\right ) + 2 \, {\left (\log \relax (5) + \log \relax (x)\right )} \log \left (4 \, \log \relax (x) + 5 \, \log \left (2 \, e^{\frac {2}{x}} + 1\right ) - 1\right ) - \log \left (4 \, \log \relax (x) + 5 \, \log \left (2 \, e^{\frac {2}{x}} + 1\right ) - 1\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.69, size = 25, normalized size = 0.96 \begin {gather*} {\ln \left (\frac {\ln \left (\frac {x}{{\left (x+2\,x\,{\mathrm {e}}^{2/x}\right )}^5}\right )+1}{x}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.24, size = 20, normalized size = 0.77 \begin {gather*} \log {\left (\frac {\log {\left (\frac {x}{\left (2 x e^{\frac {2}{x}} + x\right )^{5}} \right )} + 1}{x} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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