Optimal. Leaf size=29 \[ e^{x+x \left (4+\frac {(2+x)^2}{x}-\log (4)-\log (2-x)\right )} \]
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Rubi [A]
time = 0.26, antiderivative size = 25, normalized size of antiderivative = 0.86, number of steps
used = 1, number of rules used = 1, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6838}
\begin {gather*} 4^{-x} e^{x^2+9 x+4} (2-x)^{-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4^{-x} e^{4+9 x+x^2} (2-x)^{-x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.89, size = 20, normalized size = 0.69 \begin {gather*} e^{4+9 x+x^2} (8-4 x)^{-x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 23, normalized size = 0.79
method | result | size |
risch | \(\left (2-x \right )^{-x} \left (\frac {1}{4}\right )^{x} {\mathrm e}^{x^{2}+9 x +4}\) | \(23\) |
norman | \({\mathrm e}^{-x \ln \left (2-x \right )-2 x \ln \left (2\right )+x^{2}+9 x +4}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 23, normalized size = 0.79 \begin {gather*} e^{\left (x^{2} - 2 \, x \log \left (2\right ) - x \log \left (-x + 2\right ) + 9 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 23, normalized size = 0.79 \begin {gather*} e^{\left (x^{2} - 2 \, x \log \left (2\right ) - x \log \left (-x + 2\right ) + 9 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 22, normalized size = 0.76 \begin {gather*} e^{x^{2} - x \log {\left (2 - x \right )} - 2 x \log {\left (2 \right )} + 9 x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 0.79 \begin {gather*} e^{\left (x^{2} - 2 \, x \log \left (2\right ) - x \log \left (-x + 2\right ) + 9 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 27, normalized size = 0.93 \begin {gather*} \frac {{\mathrm {e}}^{9\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4}{2^{2\,x}\,{\left (2-x\right )}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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