Optimal. Leaf size=19 \[ -\frac {e^{10}}{9}+\log (3)-\frac {\log ^2(x)}{e^8} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.47, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2301} \begin {gather*} -\frac {\log ^2(x)}{e^8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {2 \int \frac {\log (x)}{x} \, dx}{e^8}\\ &=-\frac {\log ^2(x)}{e^8}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 9, normalized size = 0.47 \begin {gather*} -\frac {\log ^2(x)}{e^8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 8, normalized size = 0.42 \begin {gather*} -e^{\left (-8\right )} \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.25, size = 8, normalized size = 0.42 \begin {gather*} -e^{\left (-8\right )} \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 9, normalized size = 0.47
method | result | size |
risch | \(-\ln \relax (x )^{2} {\mathrm e}^{-8}\) | \(9\) |
derivativedivides | \(-\ln \relax (x )^{2} {\mathrm e}^{-8}\) | \(11\) |
default | \(-\ln \relax (x )^{2} {\mathrm e}^{-8}\) | \(11\) |
norman | \(-\ln \relax (x )^{2} {\mathrm e}^{-8}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 8, normalized size = 0.42 \begin {gather*} -e^{\left (-8\right )} \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 8, normalized size = 0.42 \begin {gather*} -{\mathrm {e}}^{-8}\,{\ln \relax (x)}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 8, normalized size = 0.42 \begin {gather*} - \frac {\log {\relax (x )}^{2}}{e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________