Optimal. Leaf size=22 \[ e^{2 x^2-8 \left (4-3 e^2 x^2 \log (x)\right )} \]
________________________________________________________________________________________
Rubi [A] time = 0.20, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {6, 2561, 6706} \begin {gather*} e^{2 x^2-32} x^{24 e^2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 2561
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-32+2 x^2+24 e^2 x^2 \log (x)} \left (\left (4+24 e^2\right ) x+48 e^2 x \log (x)\right ) \, dx\\ &=\int e^{-32+2 x^2+24 e^2 x^2 \log (x)} x \left (4+24 e^2+48 e^2 \log (x)\right ) \, dx\\ &=e^{-32+2 x^2} x^{24 e^2 x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 0.91 \begin {gather*} e^{-32+2 x^2} x^{24 e^2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 17, normalized size = 0.77 \begin {gather*} e^{\left (24 \, x^{2} e^{2} \log \relax (x) + 2 \, x^{2} - 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.62, size = 17, normalized size = 0.77 \begin {gather*} e^{\left (24 \, x^{2} e^{2} \log \relax (x) + 2 \, x^{2} - 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 18, normalized size = 0.82
method | result | size |
norman | \({\mathrm e}^{24 x^{2} {\mathrm e}^{2} \ln \relax (x )+2 x^{2}-32}\) | \(18\) |
risch | \(x^{24 x^{2} {\mathrm e}^{2}} {\mathrm e}^{2 \left (x -4\right ) \left (4+x \right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 17, normalized size = 0.77 \begin {gather*} e^{\left (24 \, x^{2} e^{2} \log \relax (x) + 2 \, x^{2} - 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.57, size = 18, normalized size = 0.82 \begin {gather*} x^{24\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-32}\,{\mathrm {e}}^{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.31, size = 19, normalized size = 0.86 \begin {gather*} e^{24 x^{2} e^{2} \log {\relax (x )} + 2 x^{2} - 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________