Optimal. Leaf size=25 \[ \frac{1}{1-x}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0082479, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {44} \[ \frac{1}{1-x}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{(-1+x)^2 x^2} \, dx &=\int \left (\frac{1}{(-1+x)^2}-\frac{2}{-1+x}+\frac{1}{x^2}+\frac{2}{x}\right ) \, dx\\ &=\frac{1}{1-x}-\frac{1}{x}-2 \log (1-x)+2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0102419, size = 25, normalized size = 1. \[ -\frac{1}{x-1}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 24, normalized size = 1. \begin{align*} -{x}^{-1}+2\,\ln \left ( x \right ) - \left ( -1+x \right ) ^{-1}-2\,\ln \left ( -1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.923035, size = 36, normalized size = 1.44 \begin{align*} -\frac{2 \, x - 1}{x^{2} - x} - 2 \, \log \left (x - 1\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.74229, size = 92, normalized size = 3.68 \begin{align*} -\frac{2 \,{\left (x^{2} - x\right )} \log \left (x - 1\right ) - 2 \,{\left (x^{2} - x\right )} \log \left (x\right ) + 2 \, x - 1}{x^{2} - x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.100422, size = 20, normalized size = 0.8 \begin{align*} - \frac{2 x - 1}{x^{2} - x} + 2 \log{\left (x \right )} - 2 \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05045, size = 41, normalized size = 1.64 \begin{align*} -\frac{1}{x - 1} + \frac{1}{\frac{1}{x - 1} + 1} + 2 \, \log \left ({\left | -\frac{1}{x - 1} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]