Optimal. Leaf size=31 \[ \frac {2 e^{3+\frac {e^{2+e^x}}{5}} x}{x-\frac {1}{2} e^x \log (x)} \]
________________________________________________________________________________________
Rubi [B] time = 0.28, antiderivative size = 65, normalized size of antiderivative = 2.10, number of steps used = 1, number of rules used = 1, integrand size = 89, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2288} \begin {gather*} \frac {4 e^{-x+\frac {e^{e^x+2}}{5}+3} \left (2 e^x x^2-e^{2 x} x \log (x)\right )}{4 x^2+e^{2 x} \log ^2(x)-4 e^x x \log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{3+\frac {e^{2+e^x}}{5}-x} \left (2 e^x x^2-e^{2 x} x \log (x)\right )}{4 x^2-4 e^x x \log (x)+e^{2 x} \log ^2(x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 1.42, size = 30, normalized size = 0.97 \begin {gather*} -\frac {4 e^{3+\frac {e^{2+e^x}}{5}} x}{-2 x+e^x \log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.59, size = 26, normalized size = 0.84 \begin {gather*} -\frac {4 \, x e^{\left (e^{\left (e^{x} - \log \relax (5) + 2\right )} + 3\right )}}{e^{x} \log \relax (x) - 2 \, x} \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 {4 \, {\left ({\left (x - 1\right )} e^{x} \log \relax (x) + {\left (2 \, x^{2} e^{x} - x e^{\left (2 \, x\right )} \log \relax (x)\right )} e^{\left (e^{x} - \log \relax (5) + 2\right )} + e^{x}\right )} e^{\left (e^{\left (e^{x} - \log \relax (5) + 2\right )} + 3\right )}}{4 \, x e^{x} \log \relax (x) - e^{\left (2 \, x\right )} \log \relax (x)^{2} - 4 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 26, normalized size = 0.84
method | result | size |
risch | \(\frac {4 x \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{x}+2}}{5}+3}}{-{\mathrm e}^{x} \ln \relax (x )+2 x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 24, normalized size = 0.77 \begin {gather*} -\frac {4 \, x e^{\left (\frac {1}{5} \, e^{\left (e^{x} + 2\right )} + 3\right )}}{e^{x} \log \relax (x) - 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.42, size = 23, normalized size = 0.74 \begin {gather*} \frac {2\,x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^2}{5}+3}}{x-\frac {{\mathrm {e}}^x\,\ln \relax (x)}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.53, size = 24, normalized size = 0.77 \begin {gather*} \frac {4 x e^{\frac {e^{e^{x} + 2}}{5} + 3}}{2 x - e^{x} \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________