Optimal. Leaf size=17 \[ e^{2 x} \log (\log (5)+e (11+x+\log (x))) \]
________________________________________________________________________________________
Rubi [A] time = 0.18, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 2, number of rules used = 2, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6688, 2288} \begin {gather*} e^{2 x} \log (e (x+11)+e \log (x)+\log (5)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2 x} \left (\frac {e (1+x)}{x (e (11+x)+\log (5)+e \log (x))}+2 \log (e (11+x)+\log (5)+e \log (x))\right ) \, dx\\ &=e^{2 x} \log (e (11+x)+\log (5)+e \log (x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 19, normalized size = 1.12 \begin {gather*} e^{2 x} \log (e (11+x)+\log (5)+e \log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.11, size = 20, normalized size = 1.18 \begin {gather*} e^{\left (2 \, x\right )} \log \left ({\left (x + 11\right )} e + e \log \relax (x) + \log \relax (5)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (2 \, x\right )} \log \left (x e + e \log \relax (x) + 11 \, e + \log \relax (5)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 21, normalized size = 1.24
method | result | size |
risch | \({\mathrm e}^{2 x} \ln \left ({\mathrm e} \ln \relax (x )+\ln \relax (5)+\left (11+x \right ) {\mathrm e}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (2 \, x\right )} \log \left (x e + e \log \relax (x) + 11 \, e + \log \relax (5)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {\ln \left (\ln \relax (5)+\mathrm {e}\,\left (x+11\right )+\mathrm {e}\,\ln \relax (x)\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (\mathrm {e}\,\left (2\,x^2+22\,x\right )+2\,x\,\ln \relax (5)\right )+2\,x\,{\mathrm {e}}^{2\,x+1}\,\ln \relax (x)\right )+{\mathrm {e}}^{2\,x+1}\,\left (x+1\right )}{x\,\ln \relax (5)+\mathrm {e}\,\left (x^2+11\,x\right )+x\,\mathrm {e}\,\ln \relax (x)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 4.59, size = 22, normalized size = 1.29 \begin {gather*} e^{2 x} \log {\left (e \left (x + 11\right ) + e \log {\relax (x )} + \log {\relax (5 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________