Optimal. Leaf size=31 \[ \frac {4 e^{-9+\frac {2}{x}-x-\frac {x+\log (x)}{x}}-x}{x} \]
________________________________________________________________________________________
Rubi [B] time = 0.10, antiderivative size = 69, normalized size of antiderivative = 2.23, number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2288} \begin {gather*} \frac {4 e^{\frac {-x^2-10 x+2}{x}} x^{-\frac {1}{x}-3} \left (x^2-\log (x)+3\right )}{\frac {-x^2-10 x-\log (x)+2}{x^2}+\frac {2 x+\frac {1}{x}+10}{x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{\frac {2-10 x-x^2}{x}} x^{-3-\frac {1}{x}} \left (3+x^2-\log (x)\right )}{\frac {10+\frac {1}{x}+2 x}{x}+\frac {2-10 x-x^2-\log (x)}{x^2}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.29, size = 23, normalized size = 0.74 \begin {gather*} 4 e^{-10+\frac {2}{x}-x} x^{-1-\frac {1}{x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 21, normalized size = 0.68 \begin {gather*} \frac {4 \, e^{\left (-\frac {x^{2} + 10 \, x + \log \relax (x) - 2}{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 21, normalized size = 0.68 \begin {gather*} \frac {4 \, e^{\left (-\frac {x^{2} + 10 \, x + \log \relax (x) - 2}{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 22, normalized size = 0.71
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{-\frac {x^{2}+\ln \relax (x )+10 x -2}{x}}}{x}\) | \(22\) |
norman | \(\frac {4 \,{\mathrm e}^{\frac {-\ln \relax (x )-x^{2}-10 x +2}{x}}}{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 23, normalized size = 0.74 \begin {gather*} \frac {4 \, e^{\left (-x - \frac {\log \relax (x)}{x} + \frac {2}{x} - 10\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.54, size = 23, normalized size = 0.74 \begin {gather*} \frac {4\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{2/x}}{x^{\frac {1}{x}+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.25, size = 17, normalized size = 0.55 \begin {gather*} \frac {4 e^{\frac {- x^{2} - 10 x - \log {\relax (x )} + 2}{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________