Optimal. Leaf size=27 \[ \frac {1}{e^2}-\frac {\log (4)}{-4+e^{\left (e^4+x\right )^2}+x-\log (\log (x))} \]
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Rubi [A]
time = 0.71, antiderivative size = 24, normalized size of antiderivative = 0.89, number of steps
used = 3, number of rules used = 3, integrand size = 150, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6820, 12,
6818} \begin {gather*} \frac {\log (4)}{-x-e^{\left (x+e^4\right )^2}+\log (\log (x))+4} \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 {\log (4) \left (-1+x \left (1+2 e^{4+e^8+2 e^4 x+x^2}+2 e^{\left (e^4+x\right )^2} x\right ) \log (x)\right )}{x \log (x) \left (4-e^{\left (e^4+x\right )^2}-x+\log (\log (x))\right )^2} \, dx\\ &=\log (4) \int \frac {-1+x \left (1+2 e^{4+e^8+2 e^4 x+x^2}+2 e^{\left (e^4+x\right )^2} x\right ) \log (x)}{x \log (x) \left (4-e^{\left (e^4+x\right )^2}-x+\log (\log (x))\right )^2} \, dx\\ &=\frac {\log (4)}{4-e^{\left (e^4+x\right )^2}-x+\log (\log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 23, normalized size = 0.85 \begin {gather*} -\frac {\log (4)}{-4+e^{\left (e^4+x\right )^2}+x-\log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 1.00
method | result | size |
risch | \(-\frac {2 \ln \left (2\right )}{x +{\mathrm e}^{{\mathrm e}^{8}+2 x \,{\mathrm e}^{4}+x^{2}}-\ln \left (\ln \left (x \right )\right )-4}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 26, normalized size = 0.96 \begin {gather*} -\frac {2 \, \log \left (2\right )}{x + e^{\left (x^{2} + 2 \, x e^{4} + e^{8}\right )} - \log \left (\log \left (x\right )\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 26, normalized size = 0.96 \begin {gather*} -\frac {2 \, \log \left (2\right )}{x + e^{\left (x^{2} + 2 \, x e^{4} + e^{8}\right )} - \log \left (\log \left (x\right )\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 29, normalized size = 1.07 \begin {gather*} - \frac {2 \log {\left (2 \right )}}{x + e^{x^{2} + 2 x e^{4} + e^{8}} - \log {\left (\log {\left (x \right )} \right )} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 26, normalized size = 0.96 \begin {gather*} -\frac {2 \, \log \left (2\right )}{x + e^{\left (x^{2} + 2 \, x e^{4} + e^{8}\right )} - \log \left (\log \left (x\right )\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.57, size = 28, normalized size = 1.04 \begin {gather*} -\frac {2\,\ln \left (2\right )}{x-\ln \left (\ln \left (x\right )\right )+{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^8}-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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