Optimal. Leaf size=17 \[ \frac {e^{x/4}}{1-\frac {5}{e^2}} \]
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Rubi [A]
time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps
used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2225}
\begin {gather*} -\frac {e^{\frac {x}{4}+2}}{5-e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{\frac {1}{4} \left (x-4 \log \left (\frac {-5+e^2}{e^2}\right )\right )} \, dx\\ &=-\frac {e^{2+\frac {x}{4}}}{5-e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {e^{2+\frac {x}{4}}}{-5+e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 20, normalized size = 1.18
method | result | size |
risch | \(\frac {{\mathrm e}^{2+\frac {x}{4}}}{{\mathrm e}^{2}-5}\) | \(14\) |
meijerg | \(-\frac {{\mathrm e}^{2} \left (1-{\mathrm e}^{\frac {x}{4}}\right )}{{\mathrm e}^{2}-5}\) | \(19\) |
gosper | \({\mathrm e}^{-\ln \left (\left ({\mathrm e}^{2}-5\right ) {\mathrm e}^{-2}\right )+\frac {x}{4}}\) | \(20\) |
derivativedivides | \({\mathrm e}^{-\ln \left (\left ({\mathrm e}^{2}-5\right ) {\mathrm e}^{-2}\right )+\frac {x}{4}}\) | \(20\) |
default | \({\mathrm e}^{-\ln \left (\left ({\mathrm e}^{2}-5\right ) {\mathrm e}^{-2}\right )+\frac {x}{4}}\) | \(20\) |
norman | \({\mathrm e}^{-\ln \left (\left ({\mathrm e}^{2}-5\right ) {\mathrm e}^{-2}\right )+\frac {x}{4}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.76 \begin {gather*} \frac {e^{\left (\frac {1}{4} \, x + 2\right )}}{e^{2} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (\frac {1}{4} \, x - \log \left ({\left (e^{2} - 5\right )} e^{\left (-2\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \frac {e^{2} e^{\frac {x}{4}}}{-5 + e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (\frac {1}{4} \, x - \log \left ({\left (e^{2} - 5\right )} e^{\left (-2\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} -\frac {{\mathrm {e}}^{x/4}}{5\,{\mathrm {e}}^{-2}-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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