Optimal. Leaf size=23 \[ e^{-5 e^2 x+\frac {3 x}{\log (x)}} \log \left (16 x^4\right ) \]
________________________________________________________________________________________
Rubi [B] time = 0.19, antiderivative size = 93, normalized size of antiderivative = 4.04, number of steps used = 1, number of rules used = 1, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2288} \begin {gather*} -\frac {e^{\frac {3 x}{\log (x)}-5 e^2 x} \left (3 x+5 e^2 x \log ^2(x)-3 x \log (x)\right ) \log \left (16 x^4\right )}{x \log ^2(x) \left (\frac {-5 e^2 \log (x)-5 e^2+3}{\log (x)}-\frac {3 x-5 e^2 x \log (x)}{x \log ^2(x)}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{-5 e^2 x+\frac {3 x}{\log (x)}} \left (3 x-3 x \log (x)+5 e^2 x \log ^2(x)\right ) \log \left (16 x^4\right )}{x \log ^2(x) \left (\frac {3-5 e^2-5 e^2 \log (x)}{\log (x)}-\frac {3 x-5 e^2 x \log (x)}{x \log ^2(x)}\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 23, normalized size = 1.00 \begin {gather*} e^{-5 e^2 x+\frac {3 x}{\log (x)}} \log \left (16 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.56, size = 25, normalized size = 1.09 \begin {gather*} 4 \, {\left (\log \relax (2) + \log \relax (x)\right )} e^{\left (-\frac {5 \, x e^{2} \log \relax (x) - 3 \, x}{\log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.28, size = 45, normalized size = 1.96 \begin {gather*} 4 \, e^{\left (-\frac {5 \, x e^{2} \log \relax (x) - 3 \, x}{\log \relax (x)}\right )} \log \relax (2) + 4 \, e^{\left (-\frac {5 \, x e^{2} \log \relax (x) - 3 \, x}{\log \relax (x)}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.22, size = 46, normalized size = 2.00
method | result | size |
default | \(\frac {\left (\left (\ln \left (16 x^{4}\right )-4 \ln \relax (x )\right ) \ln \relax (x )+4 \ln \relax (x )^{2}\right ) {\mathrm e}^{-\frac {5 x \,{\mathrm e}^{2} \ln \relax (x )-3 x}{\ln \relax (x )}}}{\ln \relax (x )}\) | \(46\) |
risch | \(\left (4 \ln \relax (2)+4 \ln \relax (x )-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )}{2}-\frac {i \pi \mathrm {csgn}\left (i x^{3}\right )^{3}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )^{2}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right )^{2}}{2}-\frac {i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )}{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )^{2}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{4}\right )^{2}}{2}-\frac {i \pi \mathrm {csgn}\left (i x^{4}\right )^{3}}{2}\right ) {\mathrm e}^{-\frac {x \left (5 \,{\mathrm e}^{2} \ln \relax (x )-3\right )}{\ln \relax (x )}}\) | \(224\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 21, normalized size = 0.91 \begin {gather*} 4 \, {\left (\log \relax (2) + \log \relax (x)\right )} e^{\left (-5 \, x e^{2} + \frac {3 \, x}{\log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.53, size = 21, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{\frac {3\,x}{\ln \relax (x)}-5\,x\,{\mathrm {e}}^2}\,\ln \left (16\,x^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 7.48, size = 27, normalized size = 1.17 \begin {gather*} \left (4 \log {\relax (x )} + 4 \log {\relax (2 )}\right ) e^{- \frac {5 x e^{2} \log {\relax (x )} - 3 x}{\log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________