Optimal. Leaf size=20 \[ \frac {2 e^{-3 e^2}}{e^2+x+16 \log (x)} \]
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Rubi [A] time = 0.17, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6688, 12, 6686} \begin {gather*} \frac {2 e^{-3 e^2}}{x+16 \log (x)+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 {2 e^{-3 e^2} (-16-x)}{x \left (e^2+x+16 \log (x)\right )^2} \, dx\\ &=\left (2 e^{-3 e^2}\right ) \int \frac {-16-x}{x \left (e^2+x+16 \log (x)\right )^2} \, dx\\ &=\frac {2 e^{-3 e^2}}{e^2+x+16 \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 e^{-3 e^2}}{e^2+x+16 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 2.32, size = 24, normalized size = 1.20 \begin {gather*} \frac {2}{{\left (x + e^{2}\right )} e^{\left (3 \, e^{2}\right )} + 16 \, e^{\left (3 \, 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 = 0.22, size = 28, normalized size = 1.40 \begin {gather*} \frac {2}{x e^{\left (3 \, e^{2}\right )} + 16 \, e^{\left (3 \, e^{2}\right )} \log \relax (x) + e^{\left (3 \, e^{2} + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 18, normalized size = 0.90
method | result | size |
norman | \(\frac {2 \,{\mathrm e}^{-3 \,{\mathrm e}^{2}}}{16 \ln \relax (x )+x +{\mathrm e}^{2}}\) | \(18\) |
risch | \(\frac {2 \,{\mathrm e}^{-3 \,{\mathrm e}^{2}}}{16 \ln \relax (x )+x +{\mathrm e}^{2}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 28, normalized size = 1.40 \begin {gather*} \frac {2}{x e^{\left (3 \, e^{2}\right )} + 16 \, e^{\left (3 \, e^{2}\right )} \log \relax (x) + e^{\left (3 \, e^{2} + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.78, size = 40, normalized size = 2.00 \begin {gather*} \frac {2\,x^2}{x^3\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}+16\,x^2\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}\,\ln \relax (x)+x^2\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}\,{\mathrm {e}}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 1.55 \begin {gather*} \frac {2}{x e^{3 e^{2}} + 16 e^{3 e^{2}} \log {\relax (x )} + e^{2} e^{3 e^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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