Optimal. Leaf size=23 \[ \frac {3 e^{1+e^2 \left (-x+\log ^2(x)\right )}}{4 x} \]
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Rubi [B] time = 0.10, antiderivative size = 53, normalized size of antiderivative = 2.30, number of steps used = 2, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {12, 2288} \begin {gather*} \frac {3 e^{e^2 \log ^2(x)-e^2 x} \left (e^3 x-2 e^3 \log (x)\right )}{4 x^2 \left (e^2-\frac {2 e^2 \log (x)}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {e^{-e^2 x+e^2 \log ^2(x)} \left (-3 e-3 e^3 x+6 e^3 \log (x)\right )}{x^2} \, dx\\ &=\frac {3 e^{-e^2 x+e^2 \log ^2(x)} \left (e^3 x-2 e^3 \log (x)\right )}{4 x^2 \left (e^2-\frac {2 e^2 \log (x)}{x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 25, normalized size = 1.09 \begin {gather*} \frac {3 e^{1-e^2 x+e^2 \log ^2(x)}}{4 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 20, normalized size = 0.87 \begin {gather*} \frac {3 \, e^{\left (e^{2} \log \relax (x)^{2} - x e^{2} + 1\right )}}{4 \, x} \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 {3 \, {\left (x e^{3} - 2 \, e^{3} \log \relax (x) + e\right )} e^{\left (e^{2} \log \relax (x)^{2} - x e^{2}\right )}}{4 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 21, normalized size = 0.91
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{{\mathrm e}^{2} \ln \relax (x )^{2}-{\mathrm e}^{2} x +1}}{4 x}\) | \(21\) |
norman | \(\frac {3 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{2} \ln \relax (x )^{2}-{\mathrm e}^{2} x}}{4 x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 20, normalized size = 0.87 \begin {gather*} \frac {3 \, e^{\left (e^{2} \log \relax (x)^{2} - x e^{2} + 1\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.29, size = 21, normalized size = 0.91 \begin {gather*} \frac {3\,\mathrm {e}\,{\mathrm {e}}^{{\mathrm {e}}^2\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^2}}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 22, normalized size = 0.96 \begin {gather*} \frac {3 e e^{- x e^{2} + e^{2} \log {\relax (x )}^{2}}}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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