Optimal. Leaf size=21 \[ e^{-2+e^{x+x^2}+(-6+x) x} (1+\log (x)) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(95\) vs. \(2(21)=42\).
time = 1.07, antiderivative size = 95, normalized size of antiderivative = 4.52, number of steps
used = 1, number of rules used = 1, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2326}
\begin {gather*} \frac {e^{x^2+e^{x^2+x}-6 x-2} \left (-2 x^2-e^{x^2+x} \left (2 x^2+x\right )+\left (-2 x^2-e^{x^2+x} \left (2 x^2+x\right )+6 x\right ) \log (x)+6 x\right )}{x \left (-e^{x^2+x} (2 x+1)-2 x+6\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-2+e^{x+x^2}-6 x+x^2} \left (6 x-2 x^2-e^{x+x^2} \left (x+2 x^2\right )+\left (6 x-2 x^2-e^{x+x^2} \left (x+2 x^2\right )\right ) \log (x)\right )}{x \left (6-2 x-e^{x+x^2} (1+2 x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.30, size = 22, normalized size = 1.05 \begin {gather*} e^{-2+e^{x+x^2}-6 x+x^2} (1+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 21, normalized size = 1.00
method | result | size |
risch | \(\left (\ln \left (x \right )+1\right ) {\mathrm e}^{{\mathrm e}^{\left (x +1\right ) x}+x^{2}-6 x -2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 20, normalized size = 0.95 \begin {gather*} {\left (\log \left (x\right ) + 1\right )} e^{\left (x^{2} - 6 \, x + e^{\left (x^{2} + x\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 = 20, normalized size = 0.95 \begin {gather*} {\left (\log \left (x\right ) + 1\right )} e^{\left (x^{2} - 6 \, x + e^{\left (x^{2} + x\right )} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 126.09, size = 20, normalized size = 0.95 \begin {gather*} \left (\log {\left (x \right )} + 1\right ) e^{x^{2} - 6 x + e^{x^{2} + x} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.03, size = 23, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x}\,\left (\ln \left (x\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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