Optimal. Leaf size=26 \[ \frac {e^{-\frac {e^x}{\log (-9+x)}}+5 x}{(5+e) x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(99\) vs. \(2(26)=52\).
time = 0.22, antiderivative size = 99, normalized size of antiderivative = 3.81, number of steps
used = 1, number of rules used = 1, integrand size = 79, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {2326}
\begin {gather*} \frac {e^{-\frac {e^x}{\log (x-9)}} \left (e^x \left (9 x-x^2\right ) \log (x-9)+e^x x\right )}{\left (-5 x^3+45 x^2+e \left (9 x^2-x^3\right )\right ) \left (\frac {e^x}{(9-x) \log ^2(x-9)}+\frac {e^x}{\log (x-9)}\right ) \log ^2(x-9)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-\frac {e^x}{\log (-9+x)}} \left (e^x x+e^x \left (9 x-x^2\right ) \log (-9+x)\right )}{\left (45 x^2-5 x^3+e \left (9 x^2-x^3\right )\right ) \left (\frac {e^x}{(9-x) \log ^2(-9+x)}+\frac {e^x}{\log (-9+x)}\right ) \log ^2(-9+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 22, normalized size = 0.85 \begin {gather*} \frac {e^{-\frac {e^x}{\log (-9+x)}}}{(5+e) x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.73, size = 22, normalized size = 0.85
method | result | size |
risch | \(\frac {{\mathrm e}^{-\frac {{\mathrm e}^{x}}{\ln \left (x -9\right )}}}{x \left ({\mathrm e}+5\right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 22, normalized size = 0.85 \begin {gather*} \frac {e^{\left (-\frac {e^{x}}{\log \left (x - 9\right )}\right )}}{x e + 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 19, normalized size = 0.73 \begin {gather*} \frac {e^{- \frac {e^{x}}{\log {\left (x - 9 \right )}}}}{e x + 5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 34, normalized size = 1.31 \begin {gather*} \frac {e^{\left (\frac {x \log \left (x - 9\right ) - e^{x}}{\log \left (x - 9\right )}\right )}}{x e^{\left (x + 1\right )} + 5 \, x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.62, size = 21, normalized size = 0.81 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{\ln \left (x-9\right )}}}{x\,\left (\mathrm {e}+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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