Optimal. Leaf size=30 \[ e^{-2 e^3+2 \left (x-x^2+\frac {2 x}{e^x+\log (x)}\right )^2} \]
________________________________________________________________________________________
Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [B] time = 1.93, size = 110, normalized size = 3.67 \begin {gather*} e^{-\frac {2 \left (e^{3+2 x}-4 x^2+4 e^x (-1+x) x^2-e^{2 x} (-1+x)^2 x^2+\left (e^3-(-1+x)^2 x^2\right ) \log ^2(x)\right )}{\left (e^x+\log (x)\right )^2}} x^{-\frac {4 \left (e^{3+x}+2 (-1+x) x^2-e^x (-1+x)^2 x^2\right )}{\left (e^x+\log (x)\right )^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.50, size = 116, normalized size = 3.87 \begin {gather*} e^{\left (\frac {2 \, {\left ({\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} \log \relax (x)^{2} + 4 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{3} - x^{2}\right )} e^{x} - 2 \, {\left (2 \, x^{3} - 2 \, x^{2} - {\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} e^{x}\right )} \log \relax (x)\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 7.80, size = 155, normalized size = 5.17 \begin {gather*} e^{\left (\frac {2 \, {\left (2 \, x^{4} e^{x} \log \relax (x) + x^{4} \log \relax (x)^{2} + x^{4} e^{\left (2 \, x\right )} - 4 \, x^{3} e^{x} \log \relax (x) - 2 \, x^{3} \log \relax (x)^{2} - 2 \, x^{3} e^{\left (2 \, x\right )} - 4 \, x^{3} e^{x} - 4 \, x^{3} \log \relax (x) + 2 \, x^{2} e^{x} \log \relax (x) + x^{2} \log \relax (x)^{2} + x^{2} e^{\left (2 \, x\right )} + 4 \, x^{2} e^{x} + 4 \, x^{2} \log \relax (x) - e^{3} \log \relax (x)^{2} + 4 \, x^{2} - 2 \, e^{\left (x + 3\right )} \log \relax (x) - e^{\left (2 \, x + 3\right )}\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.13, size = 157, normalized size = 5.23
method | result | size |
risch | \({\mathrm e}^{-\frac {2 \left (-x^{4} \ln \relax (x )^{2}-2 x^{4} {\mathrm e}^{x} \ln \relax (x )+2 x^{3} \ln \relax (x )^{2}+4 x^{3} {\mathrm e}^{x} \ln \relax (x )-{\mathrm e}^{2 x} x^{4}-x^{2} \ln \relax (x )^{2}-2 x^{2} {\mathrm e}^{x} \ln \relax (x )+4 x^{3} \ln \relax (x )+4 \,{\mathrm e}^{x} x^{3}+2 \,{\mathrm e}^{2 x} x^{3}+{\mathrm e}^{3} \ln \relax (x )^{2}+2 \ln \relax (x ) {\mathrm e}^{3+x}-4 x^{2} \ln \relax (x )-4 \,{\mathrm e}^{x} x^{2}-{\mathrm e}^{2 x} x^{2}+{\mathrm e}^{2 x +3}-4 x^{2}\right )}{\ln \relax (x )^{2}+2 \,{\mathrm e}^{x} \ln \relax (x )+{\mathrm e}^{2 x}}}\) | \(157\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 2.17, size = 429, normalized size = 14.30 \begin {gather*} e^{\left (\frac {4 \, x^{4} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{4} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{4} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, x^{3} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, x^{3} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} e^{x}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {4 \, x^{2} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{2} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{2} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2} e^{x}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {2 \, e^{3} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, e^{\left (x + 3\right )} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {2 \, e^{\left (2 \, x + 3\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.87, size = 345, normalized size = 11.50 \begin {gather*} x^{\frac {4\,\left (x^2\,{\mathrm {e}}^x-2\,x^3\,{\mathrm {e}}^x+x^4\,{\mathrm {e}}^x-{\mathrm {e}}^3\,{\mathrm {e}}^x+2\,x^2-2\,x^3\right )}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^2\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^4\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {4\,x^3\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^2\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^4\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {4\,x^3\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^3}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^3\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^x}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {8\,x^3\,{\mathrm {e}}^x}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {8\,x^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 2.40, size = 122, normalized size = 4.07 \begin {gather*} e^{\frac {2 \left (4 x^{2} + \left (- 4 x^{3} + 4 x^{2}\right ) e^{x} + \left (- 4 x^{3} + 4 x^{2} + \left (2 x^{4} - 4 x^{3} + 2 x^{2} - 2 e^{3}\right ) e^{x}\right ) \log {\relax (x )} + \left (x^{4} - 2 x^{3} + x^{2} - e^{3}\right ) e^{2 x} + \left (x^{4} - 2 x^{3} + x^{2} - e^{3}\right ) \log {\relax (x )}^{2}\right )}{e^{2 x} + 2 e^{x} \log {\relax (x )} + \log {\relax (x )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________