Optimal. Leaf size=10 \[ e^{\log ^2\left (-3 x^2\right )} \]
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Rubi [A] time = 0.11, 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, 2276, 2204, 2209} \begin {gather*} e^{\log ^2\left (-3 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2204
Rule 2209
Rule 2276
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 \operatorname {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 = 0.04, 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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fricas [A] time = 0.94, 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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giac [A] time = 0.23, 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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maple [A] time = 0.02, 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 = 0.58, 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 \relax (3)}^2}\,{\mathrm {e}}^{-\pi ^2}\,{\left (x^2\right )}^{2\,\ln \relax (3)+\pi \,2{}\mathrm {i}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, 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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