Optimal. Leaf size=22 \[ \frac {3}{4}+x+e^{e^{3-x+x \log ^2(x)}} x \]
________________________________________________________________________________________
Rubi [B] time = 0.09, antiderivative size = 46, normalized size of antiderivative = 2.09, number of steps used = 2, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2288} \begin {gather*} x+\frac {e^{e^{-x+x \log ^2(x)+3}} \left (x-x \log ^2(x)-2 x \log (x)\right )}{-\log ^2(x)-2 \log (x)+1} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{e^{3-x+x \log ^2(x)}} \left (1+e^{3-x+x \log ^2(x)} \left (-x+2 x \log (x)+x \log ^2(x)\right )\right ) \, dx\\ &=x+\frac {e^{e^{3-x+x \log ^2(x)}} \left (x-2 x \log (x)-x \log ^2(x)\right )}{1-2 \log (x)-\log ^2(x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.08, size = 19, normalized size = 0.86 \begin {gather*} x+e^{e^{3-x+x \log ^2(x)}} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 17, normalized size = 0.77 \begin {gather*} x e^{\left (e^{\left (x \log \relax (x)^{2} - x + 3\right )}\right )} + 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 {\left ({\left (x \log \relax (x)^{2} + 2 \, x \log \relax (x) - x\right )} e^{\left (x \log \relax (x)^{2} - x + 3\right )} + 1\right )} e^{\left (e^{\left (x \log \relax (x)^{2} - x + 3\right )}\right )} + 1\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 18, normalized size = 0.82
method | result | size |
risch | \(x \,{\mathrm e}^{{\mathrm e}^{x \ln \relax (x )^{2}+3-x}}+x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 17, normalized size = 0.77 \begin {gather*} x e^{\left (e^{\left (x \log \relax (x)^{2} - x + 3\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.20, size = 19, normalized size = 0.86 \begin {gather*} x\,\left ({\mathrm {e}}^{{\mathrm {e}}^{-x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{x\,{\ln \relax (x)}^2}}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 5.08, size = 15, normalized size = 0.68 \begin {gather*} x e^{e^{x \log {\relax (x )}^{2} - x + 3}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________