Optimal. Leaf size=2 \[ \tanh ^{-1}(x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1584, 206} \[ \tanh ^{-1}(x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 206
Rule 1584
Rubi steps
\begin {align*} \int \frac {x}{x-x^3} \, dx &=\int \frac {1}{1-x^2} \, dx\\ &=\tanh ^{-1}(x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.00, size = 19, normalized size = 9.50 \[ \frac {1}{2} \log (x+1)-\frac {1}{2} \log (1-x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.93, size = 13, normalized size = 6.50 \[ \frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.17, size = 15, normalized size = 7.50 \[ \frac {1}{2} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 3, normalized size = 1.50 \[ \arctanh \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.28, size = 13, normalized size = 6.50 \[ \frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 2, normalized size = 1.00 \[ \mathrm {atanh}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.12, size = 12, normalized size = 6.00 \[ - \frac {\log {\left (x - 1 \right )}}{2} + \frac {\log {\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________