Optimal. Leaf size=21 \[ 3-3 \log (x)+\log \left (\log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 5.54, 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 {x^2+e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x} \left (-1+x^2\right )+\left (-3 e^{e^{\frac {1}{x}+x}} x-3 x^2\right ) \log \left (2 e^{e^{\frac {1}{x}+x}}+2 x\right )}{\left (e^{e^{\frac {1}{x}+x}} x^2+x^3\right ) \log \left (2 e^{e^{\frac {1}{x}+x}}+2 x\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2+e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x} \left (-1+x^2\right )+\left (-3 e^{e^{\frac {1}{x}+x}} x-3 x^2\right ) \log \left (2 e^{e^{\frac {1}{x}+x}}+2 x\right )}{\left (e^{e^{\frac {1}{x}+x}} x^2+x^3\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx\\ &=\int \left (\frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x} (-1+x) (1+x)}{x^2 \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}-\frac {-x+3 e^{e^{\frac {1}{x}+x}} \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )+3 x \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}{x \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}\right ) \, dx\\ &=\int \frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x} (-1+x) (1+x)}{x^2 \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx-\int \frac {-x+3 e^{e^{\frac {1}{x}+x}} \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )+3 x \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}{x \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx\\ &=-\int \left (\frac {3}{x}-\frac {1}{\left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}\right ) \, dx+\int \left (\frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x}}{\left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}-\frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x}}{x^2 \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )}\right ) \, dx\\ &=-3 \log (x)+\int \frac {1}{\left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx+\int \frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x}}{\left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx-\int \frac {e^{e^{\frac {1}{x}+x}+\frac {1}{x}+x}}{x^2 \left (e^{e^{\frac {1}{x}+x}}+x\right ) \log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.10, size = 20, normalized size = 0.95 \begin {gather*} -3 \log (x)+\log \left (\log \left (2 \left (e^{e^{\frac {1}{x}+x}}+x\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.72, size = 55, normalized size = 2.62 \begin {gather*} -3 \, \log \relax (x) + \log \left (\log \left (2 \, {\left (x e^{\left (\frac {x^{2} + 1}{x}\right )} + e^{\left (\frac {x^{2} + x e^{\left (\frac {x^{2} + 1}{x}\right )} + 1}{x}\right )}\right )} e^{\left (-\frac {x^{2} + 1}{x}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.38, size = 55, normalized size = 2.62 \begin {gather*} -3 \, \log \relax (x) + \log \left (\log \left (2 \, {\left (x e^{\left (\frac {x^{2} + 1}{x}\right )} + e^{\left (\frac {x^{2} + x e^{\left (\frac {x^{2} + 1}{x}\right )} + 1}{x}\right )}\right )} e^{\left (-\frac {x^{2} + 1}{x}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.29, size = 25, normalized size = 1.19
method | result | size |
risch | \(-3 \ln \relax (x )+\ln \left (\ln \left (2 \,{\mathrm e}^{{\mathrm e}^{\frac {x^{2}+1}{x}}}+2 x \right )\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 19, normalized size = 0.90 \begin {gather*} -3 \, \log \relax (x) + \log \left (\log \relax (2) + \log \left (x + e^{\left (e^{\left (x + \frac {1}{x}\right )}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.71, size = 21, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (2\,x+2\,{\mathrm {e}}^{{\mathrm {e}}^{1/x}\,{\mathrm {e}}^x}\right )\right )-3\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 9.15, size = 22, normalized size = 1.05 \begin {gather*} - 3 \log {\relax (x )} + \log {\left (\log {\left (2 x + 2 e^{e^{\frac {1}{x}} e^{x}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________