Optimal. Leaf size=14 \[ -e^{x+(x-\log (x))^2} \]
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Rubi [A]
time = 0.20, antiderivative size = 18, normalized size of antiderivative = 1.29, number of steps
used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6838}
\begin {gather*} x^{-2 x} \left (-e^{x^2+x+\log ^2(x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-e^{x+x^2+\log ^2(x)} x^{-2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 18, normalized size = 1.29 \begin {gather*} -e^{x+x^2+\log ^2(x)} x^{-2 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 18, normalized size = 1.29
method | result | size |
norman | \(-{\mathrm e}^{\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+x}\) | \(18\) |
risch | \(-x^{-2 x} {\mathrm e}^{\ln \left (x \right )^{2}+x^{2}+x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 17, normalized size = 1.21 \begin {gather*} -e^{\left (x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 17, normalized size = 1.21 \begin {gather*} -e^{\left (x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 19, normalized size = 1.36 \begin {gather*} - e^{x^{2} - 2 x \log {\left (x \right )} + x + \log {\left (x \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 17, normalized size = 1.21 \begin {gather*} -e^{\left (x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.72, size = 20, normalized size = 1.43 \begin {gather*} -\frac {{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\ln \left (x\right )}^2}\,{\mathrm {e}}^x}{x^{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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