Optimal. Leaf size=25 \[ e^{e^{11-x \left (x-\left (-x+\frac {\log (x)}{x}\right )^2\right )}} \]
________________________________________________________________________________________
Rubi [F] time = 11.61, 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*} \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right )-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x+3 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2-\frac {2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2}-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2}\right ) \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \left (\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2}\right ) \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x) \, dx+2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F] time = 0.53, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.64, size = 87, normalized size = 3.48 \begin {gather*} e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \relax (x) + x e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \relax (x) + \log \relax (x)^{2} + 11 \, x}{x}\right )} + \log \relax (x)^{2} + 11 \, x}{x} - \frac {x^{4} - x^{3} - 2 \, x^{2} \log \relax (x) + \log \relax (x)^{2} + 11 \, x}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (3 \, x^{4} - 2 \, x^{3} - 2 \, x^{2} - 2 \, {\left (x^{2} - 1\right )} \log \relax (x) - \log \relax (x)^{2}\right )} e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \relax (x) + \log \relax (x)^{2} + 11 \, x}{x} + e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \relax (x) + \log \relax (x)^{2} + 11 \, x}{x}\right )}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 29, normalized size = 1.16
method | result | size |
risch | \({\mathrm e}^{x^{-2 x} {\mathrm e}^{\frac {x^{4}-x^{3}+\ln \relax (x )^{2}+11 x}{x}}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.16, size = 25, normalized size = 1.00 \begin {gather*} e^{\left (e^{\left (x^{3} - x^{2} - 2 \, x \log \relax (x) + \frac {\log \relax (x)^{2}}{x} + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.15, size = 30, normalized size = 1.20 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{11}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{\frac {{\ln \relax (x)}^2}{x}}}{x^{2\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.24, size = 27, normalized size = 1.08 \begin {gather*} e^{e^{\frac {x^{4} - x^{3} - 2 x^{2} \log {\relax (x )} + 11 x + \log {\relax (x )}^{2}}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________