Optimal. Leaf size=10 \[ e^{\log ^2\left (-3 x^2\right )} \]
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Rubi [A]
time = 0.04, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {12, 2308, 2235,
2240} \begin {gather*} e^{\log ^2\left (-3 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2235
Rule 2240
Rule 2308
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {e^{\log ^2\left (-3 x^2\right )} \log \left (-3 x^2\right )}{x} \, dx\\ &=2 \text {Subst}\left (\int e^{x^2} x \, dx,x,\log \left (-3 x^2\right )\right )\\ &=e^{\log ^2\left (-3 x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} e^{\log ^2\left (-3 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 10, normalized size = 1.00
method | result | size |
derivativedivides | \({\mathrm e}^{\ln \left (-3 x^{2}\right )^{2}}\) | \(10\) |
default | \({\mathrm e}^{\ln \left (-3 x^{2}\right )^{2}}\) | \(10\) |
norman | \({\mathrm e}^{\ln \left (-3 x^{2}\right )^{2}}\) | \(10\) |
risch | \({\mathrm e}^{\ln \left (-3 x^{2}\right )^{2}}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (\log \left (-3 \, x^{2}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (\log \left (-3 \, x^{2}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 10, normalized size = 1.00 \begin {gather*} e^{\log {\left (- 3 x^{2} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (\log \left (-3 \, x^{2}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.39, size = 38, normalized size = 3.80 \begin {gather*} 3^{\pi \,2{}\mathrm {i}}\,{\mathrm {e}}^{{\ln \left (x^2\right )}^2}\,{\mathrm {e}}^{{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-\pi ^2}\,{\left (x^2\right )}^{2\,\ln \left (3\right )+\pi \,2{}\mathrm {i}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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