Optimal. Leaf size=26 \[ \frac {1}{3} \log \left (\frac {-e^{-e^{14}+e^x}-x}{x}\right ) \]
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Rubi [F]
time = 0.67, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{-e^{14}+e^x} \left (-1+e^x x\right )}{3 e^{-e^{14}+e^x} x+3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^{e^x+x}}{3 \left (e^{e^x}+e^{e^{14}} x\right )}-\frac {e^{e^x}}{3 x \left (e^{e^x}+e^{e^{14}} x\right )}\right ) \, dx\\ &=\frac {1}{3} \int \frac {e^{e^x+x}}{e^{e^x}+e^{e^{14}} x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{x \left (e^{e^x}+e^{e^{14}} x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 23, normalized size = 0.88 \begin {gather*} \frac {1}{3} \left (-\log (x)+\log \left (e^{e^x}+e^{e^{14}} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.46, size = 19, normalized size = 0.73
method | result | size |
norman | \(-\frac {\ln \left (x \right )}{3}+\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{x}-{\mathrm e}^{14}}+x \right )}{3}\) | \(19\) |
risch | \(-\frac {\ln \left (x \right )}{3}+\frac {{\mathrm e}^{14}}{3}+\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{x}-{\mathrm e}^{14}}+x \right )}{3}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 0.65 \begin {gather*} \frac {1}{3} \, \log \left (x e^{\left (e^{14}\right )} + e^{\left (e^{x}\right )}\right ) - \frac {1}{3} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 18, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, \log \left (x + e^{\left (-e^{14} + e^{x}\right )}\right ) - \frac {1}{3} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 0.65 \begin {gather*} - \frac {\log {\left (x \right )}}{3} + \frac {\log {\left (x + e^{e^{x} - e^{14}} \right )}}{3} \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 = 0.96 \begin {gather*} -\frac {1}{3} \, x + \frac {1}{3} \, \log \left (x e^{x} + e^{\left (x - e^{14} + e^{x}\right )}\right ) - \frac {1}{3} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 19, normalized size = 0.73 \begin {gather*} \frac {\ln \left (x+{\mathrm {e}}^{-{\mathrm {e}}^{14}}\,{\mathrm {e}}^{{\mathrm {e}}^x}\right )}{3}-\frac {\ln \left (x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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