Optimal. Leaf size=22 \[ e^{1-e^2-x+4 \log ^2\left (\frac {x}{e^3}\right )} \]
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Rubi [A] time = 0.27, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6706} \begin {gather*} e^{-x+4 \log ^2\left (\frac {x}{e^3}\right )-e^2+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{1-e^2-x+4 \log ^2\left (\frac {x}{e^3}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 1.00 \begin {gather*} \frac {e^{37-e^2-x+4 \log ^2(x)}}{x^{24}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 19, normalized size = 0.86 \begin {gather*} e^{\left (4 \, \log \left (x e^{\left (-3\right )}\right )^{2} - x - e^{2} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 19, normalized size = 0.86 \begin {gather*} e^{\left (4 \, \log \left (x e^{\left (-3\right )}\right )^{2} - x - e^{2} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.91
method | result | size |
risch | \({\mathrm e}^{4 \ln \left (x \,{\mathrm e}^{-3}\right )^{2}-{\mathrm e}^{2}-x +1}\) | \(20\) |
norman | \({\mathrm e}^{4 \ln \left (x \,{\mathrm e}^{-3}\right )^{2}-{\mathrm e}^{2}-x +1}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 20, normalized size = 0.91 \begin {gather*} \frac {e^{\left (4 \, \log \relax (x)^{2} - x - e^{2} + 37\right )}}{x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.15, size = 22, normalized size = 1.00 \begin {gather*} \frac {{\mathrm {e}}^{4\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-{\mathrm {e}}^2}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{37}}{x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 17, normalized size = 0.77 \begin {gather*} e^{- x + 4 \log {\left (\frac {x}{e^{3}} \right )}^{2} - e^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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