Optimal. Leaf size=16 \[ \frac {5}{\log \left (\frac {2}{x^2}-\frac {1}{x}\right )} \]
________________________________________________________________________________________
Rubi [F] time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-20+5 x}{\left (-2 x+x^2\right ) \log ^2\left (\frac {2-x}{x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20+5 x}{(-2+x) x \log ^2\left (\frac {2-x}{x^2}\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 14, normalized size = 0.88 \begin {gather*} \frac {5}{\log \left (\frac {2-x}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.75, size = 13, normalized size = 0.81 \begin {gather*} \frac {5}{\log \left (-\frac {x - 2}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 13, normalized size = 0.81 \begin {gather*} \frac {5}{\log \left (-\frac {x - 2}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 15, normalized size = 0.94
method | result | size |
norman | \(\frac {5}{\ln \left (\frac {2-x}{x^{2}}\right )}\) | \(15\) |
risch | \(\frac {5}{\ln \left (\frac {2-x}{x^{2}}\right )}\) | \(15\) |
derivativedivides | \(\frac {5}{\ln \left (\frac {\frac {2}{x}-1}{x}\right )}\) | \(17\) |
default | \(\frac {5}{\ln \left (\frac {\frac {2}{x}-1}{x}\right )}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 17, normalized size = 1.06 \begin {gather*} -\frac {5}{2 \, \log \relax (x) - \log \left (-x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.73, size = 13, normalized size = 0.81 \begin {gather*} \frac {5}{\ln \left (-\frac {x-2}{x^2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 8, normalized size = 0.50 \begin {gather*} \frac {5}{\log {\left (\frac {2 - x}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________