Optimal. Leaf size=13 \[ 25+\log ^2\left (5 e^4 x^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2301} \begin {gather*} \log ^2\left (5 e^4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {\log \left (5 e^4 x^2\right )}{x} \, dx\\ &=\log ^2\left (5 e^4 x^2\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 17, normalized size = 1.31 \begin {gather*} 16 \log (x)+4 \log (5) \log (x)+\log ^2\left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 10, normalized size = 0.77 \begin {gather*} \log \left (5 \, x^{2} e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 10, normalized size = 0.77 \begin {gather*} \log \left (5 \, x^{2} e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 11, normalized size = 0.85
method | result | size |
risch | \(\ln \left (5 x^{2} {\mathrm e}^{4}\right )^{2}\) | \(11\) |
derivativedivides | \(\ln \left (5 x^{2} {\mathrm e}^{4}\right )^{2}\) | \(13\) |
default | \(\ln \left (5 x^{2} {\mathrm e}^{4}\right )^{2}\) | \(13\) |
norman | \(\ln \left (5 x^{2} {\mathrm e}^{4}\right )^{2}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 10, normalized size = 0.77 \begin {gather*} \log \left (5 \, x^{2} e^{4}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.68, size = 10, normalized size = 0.77 \begin {gather*} {\left (\ln \left (5\,x^2\right )+4\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 10, normalized size = 0.77 \begin {gather*} \log {\left (5 x^{2} e^{4} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________