Optimal. Leaf size=25 \[ \frac{x^2}{2}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0356623, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08, Rules used = {1593, 1620} \[ \frac{x^2}{2}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1593
Rule 1620
Rubi steps
\begin{align*} \int \frac{-1-x-x^3+x^4}{-x^2+x^3} \, dx &=\int \frac{-1-x-x^3+x^4}{(-1+x) x^2} \, dx\\ &=\int \left (-\frac{2}{-1+x}+\frac{1}{x^2}+\frac{2}{x}+x\right ) \, dx\\ &=-\frac{1}{x}+\frac{x^2}{2}-2 \log (1-x)+2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0061798, size = 25, normalized size = 1. \[ \frac{x^2}{2}-\frac{1}{x}-2 \log (1-x)+2 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 22, normalized size = 0.9 \begin{align*}{\frac{{x}^{2}}{2}}-2\,\ln \left ( x-1 \right ) -{x}^{-1}+2\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.02026, size = 28, normalized size = 1.12 \begin{align*} \frac{1}{2} \, x^{2} - \frac{1}{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 = 1.26056, size = 63, normalized size = 2.52 \begin{align*} \frac{x^{3} - 4 \, x \log \left (x - 1\right ) + 4 \, x \log \left (x\right ) - 2}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.094558, size = 19, normalized size = 0.76 \begin{align*} \frac{x^{2}}{2} + 2 \log{\left (x \right )} - 2 \log{\left (x - 1 \right )} - \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20626, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{2} \, x^{2} - \frac{1}{x} - 2 \, \log \left ({\left | x - 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]