Optimal. Leaf size=17 \[ \frac {8}{-e^{e^2}-x+\log (x)} \]
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Rubi [A] time = 0.30, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 3, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {8}{x-\log (x)+e^{e^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 (-1+x)}{x \left (e^{e^2}+x-\log (x)\right )^2} \, dx\\ &=8 \int \frac {-1+x}{x \left (e^{e^2}+x-\log (x)\right )^2} \, dx\\ &=-\frac {8}{e^{e^2}+x-\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 15, normalized size = 0.88 \begin {gather*} -\frac {8}{e^{e^2}+x-\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8}{x + e^{\left (e^{2}\right )} - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8}{x + e^{\left (e^{2}\right )} - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 14, normalized size = 0.82
method | result | size |
norman | \(-\frac {8}{{\mathrm e}^{{\mathrm e}^{2}}+x -\ln \relax (x )}\) | \(14\) |
risch | \(-\frac {8}{{\mathrm e}^{{\mathrm e}^{2}}+x -\ln \relax (x )}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8}{x + e^{\left (e^{2}\right )} - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.50, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8}{x+{\mathrm {e}}^{{\mathrm {e}}^2}-\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.59 \begin {gather*} \frac {8}{- x + \log {\relax (x )} - e^{e^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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