Optimal. Leaf size=16 \[ -1-\log \left (\log \left (\frac {20 \left (e^x+x\right )}{x^2}\right )\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 1, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6684} \begin {gather*} -\log \left (\log \left (\frac {20 \left (x+e^x\right )}{x^2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (\log \left (\frac {20 \left (e^x+x\right )}{x^2}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 14, normalized size = 0.88 \begin {gather*} -\log \left (\log \left (\frac {20 \left (e^x+x\right )}{x^2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 13, normalized size = 0.81 \begin {gather*} -\log \left (\log \left (\frac {20 \, {\left (x + e^{x}\right )}}{x^{2}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 13, normalized size = 0.81 \begin {gather*} -\log \left (\log \left (\frac {20 \, {\left (x + e^{x}\right )}}{x^{2}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 17, normalized size = 1.06
method | result | size |
norman | \(-\ln \left (\ln \left (\frac {20 \,{\mathrm e}^{x}+20 x}{x^{2}}\right )\right )\) | \(17\) |
risch | \(-\ln \left (\ln \left ({\mathrm e}^{x}+x \right )-\frac {i \left (\pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{x}+x \right )}{x^{2}}\right )^{3}-\pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{x}+x \right )}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )-\pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{x}+x \right )}{x^{2}}\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+x \right )\right )+\pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{x}+x \right )}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+x \right )\right )-\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \ln \relax (5)+4 i \ln \relax (2)-4 i \ln \relax (x )\right )}{2}\right )\) | \(165\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 19, normalized size = 1.19 \begin {gather*} -\log \left (\log \relax (5) + 2 \, \log \relax (2) + \log \left (x + e^{x}\right ) - 2 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.81, size = 16, normalized size = 1.00 \begin {gather*} -\ln \left (\ln \left (\frac {20\,x+20\,{\mathrm {e}}^x}{x^2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 15, normalized size = 0.94 \begin {gather*} - \log {\left (\log {\left (\frac {20 x + 20 e^{x}}{x^{2}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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