Optimal. Leaf size=22 \[ e^{1+x-x \left (-2+2 x+\frac {4}{3} x \log ^2(x)\right )} \]
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Rubi [A]
time = 0.15, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps
used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 6838}
\begin {gather*} e^{\frac {1}{3} \left (-6 x^2-4 x^2 \log ^2(x)+9 x+3\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{\frac {1}{3} \left (3+9 x-6 x^2-4 x^2 \log ^2(x)\right )} \left (9-12 x-8 x \log (x)-8 x \log ^2(x)\right ) \, dx\\ &=e^{\frac {1}{3} \left (3+9 x-6 x^2-4 x^2 \log ^2(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 23, normalized size = 1.05 \begin {gather*} e^{1+3 x-2 x^2-\frac {4}{3} x^2 \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 21, normalized size = 0.95
method | result | size |
norman | \({\mathrm e}^{-\frac {4 x^{2} \ln \left (x \right )^{2}}{3}-2 x^{2}+3 x +1}\) | \(21\) |
risch | \({\mathrm e}^{-\frac {4 x^{2} \ln \left (x \right )^{2}}{3}-2 x^{2}+3 x +1}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 20, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {4}{3} \, x^{2} \log \left (x\right )^{2} - 2 \, x^{2} + 3 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 20, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {4}{3} \, x^{2} \log \left (x\right )^{2} - 2 \, x^{2} + 3 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 22, normalized size = 1.00 \begin {gather*} e^{- \frac {4 x^{2} \log {\left (x \right )}^{2}}{3} - 2 x^{2} + 3 x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {4}{3} \, x^{2} \log \left (x\right )^{2} - 2 \, x^{2} + 3 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.39, size = 23, normalized size = 1.05 \begin {gather*} {\mathrm {e}}^{3\,x}\,\mathrm {e}\,{\mathrm {e}}^{-2\,x^2}\,{\mathrm {e}}^{-\frac {4\,x^2\,{\ln \left (x\right )}^2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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