Optimal. Leaf size=10 \[ -\frac {25}{51} x (-5+x+\log (3)) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.50, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} -\frac {25}{204} (-2 x+5-\log (3))^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {25}{204} (5-2 x-\log (3))^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 1.50 \begin {gather*} -\frac {25}{51} \left (-5 x+x^2+x \log (3)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.24, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 9, normalized size = 0.90
method | result | size |
gosper | \(-\frac {25 x \left (\ln \relax (3)-5+x \right )}{51}\) | \(9\) |
default | \(-\frac {25 x \ln \relax (3)}{51}-\frac {25 x^{2}}{51}+\frac {125 x}{51}\) | \(15\) |
norman | \(\left (-\frac {25 \ln \relax (3)}{51}+\frac {125}{51}\right ) x -\frac {25 x^{2}}{51}\) | \(15\) |
risch | \(-\frac {25 x \ln \relax (3)}{51}-\frac {25 x^{2}}{51}+\frac {125 x}{51}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} -\frac {25\,x\,\left (x+\ln \relax (3)-5\right )}{51} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 17, normalized size = 1.70 \begin {gather*} - \frac {25 x^{2}}{51} + x \left (\frac {125}{51} - \frac {25 \log {\relax (3 )}}{51}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________