Optimal. Leaf size=15 \[ -2+\frac {x}{4-x}+\log (2+x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps
used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2099}
\begin {gather*} \frac {4}{4-x}+\log (x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4}{(-4+x)^2}+\frac {1}{2+x}\right ) \, dx\\ &=\frac {4}{4-x}+\log (2+x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 12, normalized size = 0.80 \begin {gather*} -\frac {4}{-4+x}+\log (2+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 13, normalized size = 0.87
method | result | size |
default | \(\ln \left (2+x \right )-\frac {4}{x -4}\) | \(13\) |
norman | \(\ln \left (2+x \right )-\frac {4}{x -4}\) | \(13\) |
risch | \(\ln \left (2+x \right )-\frac {4}{x -4}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 12, normalized size = 0.80 \begin {gather*} -\frac {4}{x - 4} + \log \left (x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 16, normalized size = 1.07 \begin {gather*} \frac {{\left (x - 4\right )} \log \left (x + 2\right ) - 4}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} \log {\left (x + 2 \right )} - \frac {4}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 13, normalized size = 0.87 \begin {gather*} -\frac {4}{x - 4} + \log \left ({\left | x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} \ln \left (x+2\right )-\frac {4}{x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________