Optimal. Leaf size=19 \[ -x+\log \left (4 e^5 x\right )+\log \left (4 (5+x)^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.63, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1607, 907}
\begin {gather*} -x+\log (x)+2 \log (x+5) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 907
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5-2 x-x^2}{x (5+x)} \, dx\\ &=\int \left (-1+\frac {1}{x}+\frac {2}{5+x}\right ) \, dx\\ &=-x+\log (x)+2 \log (5+x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} -x+\log (x)+2 \log (5+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.85, size = 13, normalized size = 0.68
method | result | size |
default | \(-x +\ln \left (x \right )+2 \ln \left (5+x \right )\) | \(13\) |
norman | \(-x +\ln \left (x \right )+2 \ln \left (5+x \right )\) | \(13\) |
risch | \(-x +\ln \left (x \right )+2 \ln \left (5+x \right )\) | \(13\) |
meijerg | \(2 \ln \left (1+\frac {x}{5}\right )+\ln \left (x \right )-\ln \left (5\right )-x\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 12, normalized size = 0.63 \begin {gather*} -x + 2 \, \log \left (x + 5\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 12, normalized size = 0.63 \begin {gather*} -x + 2 \, \log \left (x + 5\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 10, normalized size = 0.53 \begin {gather*} - x + \log {\left (x \right )} + 2 \log {\left (x + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 14, normalized size = 0.74 \begin {gather*} -x + 2 \, \log \left ({\left | x + 5 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.77, size = 12, normalized size = 0.63 \begin {gather*} 2\,\ln \left (x+5\right )-x+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________