Optimal. Leaf size=22 \[ \log \left (e^{-20 x^2 \left (x+\frac {2}{\log (5)}\right )^2} x^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.27, number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 14} \begin {gather*} -20 x^4-\frac {80 x^3}{\log (5)}-\frac {80 x^2}{\log ^2(5)}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-160 x^2-240 x^3 \log (5)+\left (2-80 x^4\right ) \log ^2(5)}{x} \, dx}{\log ^2(5)}\\ &=\frac {\int \left (-160 x-240 x^2 \log (5)+\frac {2 \log ^2(5)}{x}-80 x^3 \log ^2(5)\right ) \, dx}{\log ^2(5)}\\ &=-20 x^4-\frac {80 x^2}{\log ^2(5)}-\frac {80 x^3}{\log (5)}+2 \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 28, normalized size = 1.27 \begin {gather*} -20 x^4-\frac {80 x^2}{\log ^2(5)}-\frac {80 x^3}{\log (5)}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 36, normalized size = 1.64 \begin {gather*} -\frac {2 \, {\left (10 \, x^{4} \log \relax (5)^{2} + 40 \, x^{3} \log \relax (5) - \log \relax (5)^{2} \log \relax (x) + 40 \, x^{2}\right )}}{\log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 37, normalized size = 1.68 \begin {gather*} -\frac {2 \, {\left (10 \, x^{4} \log \relax (5)^{2} + 40 \, x^{3} \log \relax (5) - \log \relax (5)^{2} \log \left ({\left | x \right |}\right ) + 40 \, x^{2}\right )}}{\log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 29, normalized size = 1.32
method | result | size |
risch | \(-20 x^{4}-\frac {80 x^{3}}{\ln \relax (5)}-\frac {80 x^{2}}{\ln \relax (5)^{2}}+2 \ln \relax (x )\) | \(29\) |
norman | \(\frac {-80 x^{3}-\frac {80 x^{2}}{\ln \relax (5)}-20 x^{4} \ln \relax (5)}{\ln \relax (5)}+2 \ln \relax (x )\) | \(33\) |
default | \(\frac {-20 x^{4} \ln \relax (5)^{2}-80 x^{3} \ln \relax (5)-80 x^{2}+2 \ln \relax (x ) \ln \relax (5)^{2}}{\ln \relax (5)^{2}}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.66, size = 36, normalized size = 1.64 \begin {gather*} -\frac {2 \, {\left (10 \, x^{4} \log \relax (5)^{2} + 40 \, x^{3} \log \relax (5) - \log \relax (5)^{2} \log \relax (x) + 40 \, x^{2}\right )}}{\log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 28, normalized size = 1.27 \begin {gather*} 2\,\ln \relax (x)-\frac {80\,x^2}{{\ln \relax (5)}^2}-\frac {80\,x^3}{\ln \relax (5)}-20\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 37, normalized size = 1.68 \begin {gather*} \frac {- 20 x^{4} \log {\relax (5 )}^{2} - 80 x^{3} \log {\relax (5 )} - 80 x^{2} + 2 \log {\relax (5 )}^{2} \log {\relax (x )}}{\log {\relax (5 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________