Optimal. Leaf size=23 \[ \frac {1}{2+e^{e^{2+\frac {e^2}{3}} (259-x)}} \]
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Rubi [A]
time = 0.34, antiderivative size = 34, normalized size of antiderivative = 1.48, number of steps
used = 3, number of rules used = 3, integrand size = 75, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2320, 12, 32}
\begin {gather*} \frac {1}{e^{259 e^{2+\frac {e^2}{3}}-e^{2+\frac {e^2}{3}} x}+2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (e^{-2-\frac {e^2}{3}} \text {Subst}\left (\int \frac {e^{2+\frac {e^2}{3}+259 e^{2+\frac {e^2}{3}}}}{\left (2+e^{259 e^{2+\frac {e^2}{3}}} x\right )^2} \, dx,x,e^{-e^{\frac {1}{3} \left (6+e^2\right )} x}\right )\right )\\ &=-\left (e^{259 e^{2+\frac {e^2}{3}}} \text {Subst}\left (\int \frac {1}{\left (2+e^{259 e^{2+\frac {e^2}{3}}} x\right )^2} \, dx,x,e^{-e^{\frac {1}{3} \left (6+e^2\right )} x}\right )\right )\\ &=\frac {1}{2+e^{259 e^{2+\frac {e^2}{3}}-e^{2+\frac {e^2}{3}} x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.25, size = 27, normalized size = 1.17 \begin {gather*} -\frac {1}{2 \left (1+2 e^{e^{2+\frac {e^2}{3}} (-259+x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 19, normalized size = 0.83
method | result | size |
risch | \(\frac {1}{{\mathrm e}^{-\left (x -259\right ) {\mathrm e}^{\frac {{\mathrm e}^{2}}{3}+2}}+2}\) | \(18\) |
derivativedivides | \(\frac {1}{{\mathrm e}^{\left (-x +259\right ) {\mathrm e}^{\frac {{\mathrm e}^{2}}{3}+2}}+2}\) | \(19\) |
default | \(\frac {1}{{\mathrm e}^{\left (-x +259\right ) {\mathrm e}^{\frac {{\mathrm e}^{2}}{3}+2}}+2}\) | \(19\) |
norman | \(\frac {1}{{\mathrm e}^{\left (-x +259\right ) {\mathrm e}^{\frac {{\mathrm e}^{2}}{3}+2}}+2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{e^{\left (-x e^{\left (\frac {1}{3} \, e^{2} + 2\right )} + 259 \, e^{\left (\frac {1}{3} \, e^{2} + 2\right )}\right )} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 39 vs.
\(2 (17) = 34\).
time = 0.36, size = 39, normalized size = 1.70 \begin {gather*} \frac {e^{\left (\frac {1}{3} \, e^{2} + 2\right )}}{e^{\left (-{\left (x - 259\right )} e^{\left (\frac {1}{3} \, e^{2} + 2\right )} + \frac {1}{3} \, e^{2} + 2\right )} + 2 \, e^{\left (\frac {1}{3} \, e^{2} + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.65 \begin {gather*} \frac {1}{e^{\left (259 - x\right ) e^{2 + \frac {e^{2}}{3}}} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (17) = 34\).
time = 0.41, size = 46, normalized size = 2.00 \begin {gather*} \frac {e^{\left (\frac {1}{3} \, e^{2} + 2\right )}}{e^{\left (-x e^{\left (\frac {1}{3} \, e^{2} + 2\right )} + \frac {1}{3} \, e^{2} + 259 \, e^{\left (\frac {1}{3} \, e^{2} + 2\right )} + 2\right )} + 2 \, e^{\left (\frac {1}{3} \, e^{2} + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.34, size = 20, normalized size = 0.87 \begin {gather*} -\frac {1}{2\,\left (2\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^2}{3}}\,{\mathrm {e}}^2\,\left (x-259\right )}+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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