Optimal. Leaf size=12 \[ -\frac {1}{2} \log \left (1-x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {1584, 260} \[ -\frac {1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 260
Rule 1584
Rubi steps
\begin {align*} \int \frac {x^2}{x-x^3} \, dx &=\int \frac {x}{1-x^2} \, dx\\ &=-\frac {1}{2} \log \left (1-x^2\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ -\frac {1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.98, size = 8, normalized size = 0.67 \[ -\frac {1}{2} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 15, normalized size = 1.25 \[ -\frac {1}{2} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 14, normalized size = 1.17 \[ -\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.29, size = 13, normalized size = 1.08 \[ -\frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 8, normalized size = 0.67 \[ -\frac {\ln \left (x^2-1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 8, normalized size = 0.67 \[ - \frac {\log {\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________