Optimal. Leaf size=27 \[ \log \left (3-e^5-x-4 x^2-4 \left (e^{4-x}+x\right )\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps
used = 1, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6816}
\begin {gather*} \log \left (-4 x^2-5 x-4 e^{4-x}-e^5+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (3-e^5-4 e^{4-x}-5 x-4 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 3.45, size = 30, normalized size = 1.11 \begin {gather*} -x+\log \left (4 e^4+e^{5+x}+e^x \left (-3+5 x+4 x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 22, normalized size = 0.81
method | result | size |
derivativedivides | \(\ln \left (4 \,{\mathrm e}^{-x +4}+{\mathrm e}^{5}+4 x^{2}+5 x -3\right )\) | \(22\) |
default | \(\ln \left (4 \,{\mathrm e}^{-x +4}+{\mathrm e}^{5}+4 x^{2}+5 x -3\right )\) | \(22\) |
norman | \(\ln \left (4 \,{\mathrm e}^{-x +4}+{\mathrm e}^{5}+4 x^{2}+5 x -3\right )\) | \(22\) |
risch | \(-4+\ln \left (x^{2}+\frac {{\mathrm e}^{5}}{4}+\frac {5 x}{4}+{\mathrm e}^{-x +4}-\frac {3}{4}\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 21, normalized size = 0.78 \begin {gather*} \log \left (4 \, x^{2} + 5 \, x + e^{5} + 4 \, e^{\left (-x + 4\right )} - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 21, normalized size = 0.78 \begin {gather*} \log \left (4 \, x^{2} + 5 \, x + e^{5} + 4 \, e^{\left (-x + 4\right )} - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 0.81 \begin {gather*} \log {\left (x^{2} + \frac {5 x}{4} + e^{4 - x} - \frac {3}{4} + \frac {e^{5}}{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 25, normalized size = 0.93 \begin {gather*} \log \left (-4 \, {\left (x - 4\right )}^{2} - 37 \, x - e^{5} - 4 \, e^{\left (-x + 4\right )} + 67\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 19, normalized size = 0.70 \begin {gather*} \ln \left (\frac {5\,x}{4}+\frac {{\mathrm {e}}^5}{4}+{\mathrm {e}}^{4-x}+x^2-\frac {3}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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