Optimal. Leaf size=15 \[ \frac {24 \log (3)}{4+2 x+\log (-16+x)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.08, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {12, 6820, 6818}
\begin {gather*} \frac {24 \log (3)}{2 x+\log (x-16)+4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \frac {744-48 x}{-256-240 x-48 x^2+4 x^3+\left (-128-56 x+4 x^2\right ) \log (-16+x)+(-16+x) \log ^2(-16+x)} \, dx\\ &=\log (3) \int \frac {-744+48 x}{(16-x) (4+2 x+\log (-16+x))^2} \, dx\\ &=\frac {24 \log (3)}{4+2 x+\log (-16+x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \frac {24 \log (3)}{4+2 x+\log (-16+x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.48, size = 16, normalized size = 1.07
method | result | size |
derivativedivides | \(\frac {24 \ln \left (3\right )}{\ln \left (x -16\right )+2 x +4}\) | \(16\) |
default | \(\frac {24 \ln \left (3\right )}{\ln \left (x -16\right )+2 x +4}\) | \(16\) |
norman | \(\frac {24 \ln \left (3\right )}{\ln \left (x -16\right )+2 x +4}\) | \(16\) |
risch | \(\frac {24 \ln \left (3\right )}{\ln \left (x -16\right )+2 x +4}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 15, normalized size = 1.00 \begin {gather*} \frac {24 \, \log \left (3\right )}{2 \, x + \log \left (x - 16\right ) + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 15, normalized size = 1.00 \begin {gather*} \frac {24 \, \log \left (3\right )}{2 \, x + \log \left (x - 16\right ) + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 14, normalized size = 0.93 \begin {gather*} \frac {24 \log {\left (3 \right )}}{2 x + \log {\left (x - 16 \right )} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 15, normalized size = 1.00 \begin {gather*} \frac {24 \, \log \left (3\right )}{2 \, x + \log \left (x - 16\right ) + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.12, size = 23, normalized size = 1.53 \begin {gather*} -\frac {6\,\ln \left (3\right )\,\left (2\,x+\ln \left (x-16\right )\right )}{2\,x+\ln \left (x-16\right )+4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________